# Hypothesis Testing In Trading – Step by Step Guide

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In this blog post, we will understand what hypothesis formation is and how to perform hypothesis testing in trading.

There is a need for a disciplined approach to building a quantitative trading strategy. Any quantitative trading system consists of four major components:

1. Hypothesis formation – Finding a strategy
2. Backtesting and optimizing the hypothesis – Obtaining data, coding the strategy, analyzing the performance
3. Automating the strategy – Linking to brokerage
4. Risk management – Optimal capital allocation, bid-ask size etc.

Hypothesis formation is about what you think the market is. If you think the market is trending bullish, you may buy the asset or if you believe the market is trending bearish, you may short the asset. But to validate the hypothesis, you need to perform the hypothesis testing.

### Hypothesis Testing

Hypothesis testing is a systematic way to test a hypothesis or idea about the population. In hypothesis testing, we measure the behaviour in samples to learn more about the population, as samples are somewhat related to populations. For example, if the return of all the stocks in Nifty 50 index is 3% and if we randomly select 10 stocks from the index, then on average the value of the sample mean will be equal to the population mean.

Suppose you are an analyst and you believe that the average return on all the stocks in Nifty 50 index was greater than 3%. You assume that the returns are normally distributed.

### Hypothesis Testing Method

The method of hypothesis testing can be summarized in four steps:

#### Step 1:State the hypothesis

Stating the hypothesis is the initial step in a defined process for hypothesis testing. It involves stating the null and alternative hypothesis.

##### Null Hypothesis:

In hypothesis testing, the null hypothesis is usually the hypothesis that we want to reject. It is usually denoted by Ho and always includes some form of equal sign.

Here in our example, the null hypothesis is:

###### Ho: μ < = 3.

μ is the population mean.

##### Alternative Hypothesis:

The alternative hypothesis is a statement that will be accepted when the null hypothesis is rejected. It is usually denoted by Ha.

Here in our example, the alternative hypothesis is:

#### Step 2: Set the decision criterion

The decision has to be based on certain parameters of datasets and this is where the concept of normal distribution, significance level, one-tailed, two-tailed tests come into the picture.

##### Normal Distribution

A normal distribution is a probability distribution in which most of the values lie around mean and others lie symmetrically above or below the mean.

For a normal distribution, 68% of the values fall within one standard deviation of the mean. 95% of the values fall within two standard deviations of the mean and 99.7% of the values lie within three standard deviations of the mean.

#### Significance level

Significance level or level of significance is used to set the criterion upon which a decision is made regarding the null hypothesis. It is defined as the probability that a test statistic will reject the null hypothesis by chance when it is actually true. It is denoted by alpha or α. If we choose a significance level of 0.05, it means there is a 5% chance that we are rejecting the null hypothesis when it is true. A significance level of 0.01 means that there is a 1% chance of rejecting the null hypothesis when it is true.

As a rule, the significance level is specified prior to calculating the test statistic, as a result of the test statistic may impact the choice of significance level.

#### One-Tailed test

The one-tailed test implies to the hypothesis test, where the region of rejection appears on one side of the sampling distribution. If the population parameter is “less than” or “greater than”, then we use the one-tailed test. For example, if the return on all stocks of Nifty 50 is greater than 3%, then the hypothesis test carried out is the one-tailed test.

#### Two-Tailed Test

Two-tailed test signifies to the hypothesis test, where the region of rejection is on both sides of the sampling distributions. If the population parameter is characterized by the words “equal to” or “not equal to”, then we use the two-tailed test. For example, if the return on all stocks of Nifty 50 is equal to 3%, then it is a two-tailed test and we can reject the null hypothesis based on observations in either tail.

The alternative hypothesis determines whether to place the level of significance in one or both tails of the sampling distribution. If μ is the actual value of a population parameter (e.g. mean or standard deviation), and μ0 is the value of the population parameter according to our hypothesis, then:

 Alternative Hypothesis Type of test H1: μ ≠ μ0 Two-Tailed test H1: μ > μ0 One-Tailed (Right) H1: μ < μ0 One-Tailed (Left)

#### Step 3: Calculate the test statistics

In hypothesis testing, a test statistic is defined as a quantity taken from a sample that is used for deciding whether to reject or accept the null hypothesis.

The general formula for calculating a test statistic is

Test statistic = [Sample statistic – Value of parameter according to null] / Standard error (SE) of the sample statistic

Standard Error = Standard deviation / √ (number of samples)

#### Step 4: Make a Decision

1. Test statistics
2. Critical value: Critical value is a point on the test distribution that is compared to the test statistics to determine whether to reject the null hypothesis.  It is the function of significance level ), probability distribution and whether the test is one-tailed or two-tailed.

The critical value for one and two-tailed tests ( Normal Distribution) at three commonly used levels of significance.

 Level of Significance (α) One-Tailed Test Two-Tailed Test 0.05 (5%) +1.625 or -1.625 1.96 0.01 (1%) +2.33 or  -2.33 2.58 0.001 (0.1%) +3.09 or -3.09 3.30

For the two-tailed test, the level of significance ) is split in half and placed in each tail of normal distribution as shown in the above two-tailed diagram.

If the value of the test statistic is less than or equal to the critical value, we reject the null hypothesis, and state that the result is statistically significant. If the test statistic is greater than the critical value, then we fail to reject the null hypothesis and we state that the result is not statistically significant.

where,

Zα = critical value at a significance level

### Types of Error

There are two types of error in hypothesis testing: Type I and Type II.

#### Type I Error:

Type I error is defined as rejecting the null hypothesis when it is true. The probability of making a type I error is α. An α of 0.05 indicates that you are willing to accept a 5% chance that you are wrong when you reject the null hypothesis. Type I error can be reduced by choosing the lower value of α.

#### Type II Error:

When the null hypothesis is false and we fail to reject it, we make a type II error. The probability of making a type II error is β. We can decrease the risk of committing a type II error by increasing the sample size.

### Conclusion

To create a profitable trading strategy, you need to have a hypothesis and to validate a hypothesis you need to perform a hypothesis test. The steps involved in hypothesis testing are:

1. State the hypothesis
2. Set the decision criterion
3. Calculate the test statistics
4. Make a decision

Hypothesis testing is usually the first step before we start formulating a trading strategy. You can go through the different strategies by checking out the algorithmic trading strategies bundle.

Disclaimer: All investments and trading in the stock market involve risk. Any decisions to place trades in the financial markets, including trading in stock or options or other financial instruments is a personal decision that should only be made after thorough research, including a personal risk and financial assessment and the engagement of professional assistance to the extent you believe necessary. The trading strategies or related information mentioned in this article is for informational purposes only.

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# How to Make More Money in 2019

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None of us has enough money.

On Two Cents we often focus on maximizing your money: Leveling up investments or employing new savings hacks. But what do you do when just need to make more?

Lifehacker talked with five people, including a familiar face (hi, Kristin!), to get a sense of how people across the country are planning to increase their income. We’re retiring the cliché, vague advice you’d normally find in personal finance articles—get a side hustle, launch an Etsy store, etc.—that’s only relevant to a handful of people, and learning how real people are making more for themselves in 2019.

Here’s how real people are planning to level up their income this year.

These interviews have been condensed and lightly edited for clarity.

Name: Teresa B.

Age: 31

Location: Portland, Oregon

Job &amp; Income: I work in the non-profit sector and I’m a data specialist. My salary is just below \$43,000 (including a 403(b) match).

How much of your monthly income do bills take up? Rent and bills take up around 50-60 percent of my take-home pay each month, including student loans. I have about \$60,000 in private and federal loans.

Do you have a specific money goal right now?

My goal right now is to pay off my loans as soon as possible. I want to build up my savings a little bit more before I really tackle that, but that is the main goal. It’s about \$60,000.

What’s your plan to make more more money this year?

I have been looking for work since September, so ideally the goal is to increase my salary. But I haven’t been super successful in the past few months, so I got an additional part-time job, I’m going to be working a few nights a week in a reception job. I am going to put all the income from that job toward my student loans, and I’m still looking for another job.

It’s not the first time that I’ve done this, I think I’m just used to being really busy, whether it was school, or having an extra part-time job, or dog sitting for my friends—I’ve always had something else going on.

Those nights that I would normally be going out, I’ll be working so I’ll be saving money that way, but I kind of told my friends what my situation was straight up, like, ‘I won’t be hanging out with you as much.’ My approach is to just be transparent with my friends about it.

Why do you want to earn more?

I don’t know if it’s just because of being done with school, so it feels more final, but I want to take my finances more seriously. I haven’t been living month-to-month, but I haven’t really been super strict with myself … Once I saw the total student loans, it was just kind of a sobering experience, but in general I think I’ve been putting off getting my finances in order.

I probably didn’t really have savings until about two years ago, I was just working paycheck-to-paycheck. Now I have a little nest egg, so I am working on trying to increase that. I have a new budget [Teresa is following the 50/20/30 budget] for 2019 that I set up and I’m trying to save more.

Is there a piece of general money advice that you find helpful?

I’ve had a lot of financial stress before and it’s not very healthy, it doesn’t feel great, so when I’m buying something I try to think, ‘Will this be worth it? Will it be worth that stress, that uneasy feeling in your stomach?’ I have that question in the back in my mind.”

Name: Phil M*

Age: 26

Location: Los Angeles, California

Job &amp; Income: I’m an Administrative Assistant at Sony Pictures making \$50,000 a year (plus a six percent 401(k) match).

How much of your monthly income do bills take up?

I would say maybe 80 percent, including rent, which is \$945 split with my girlfriend, and I just bought a used car, which is around \$350 per month with the payment and insurance. We don’t have cable, we have internet which is around \$60 per month. I’m fortunate enough not to have any student loan debt, and just the car loan. I contribute to a 401(k) through my company.

Do you have a specific money goal right now?

I want to save around \$10,000 in liquid cash, which would be a comfortable enough cushion if something terrible happened. And right now it’s nowhere near that. I just bought the car, and I’m sure I can get some money reserves back, but I’m focused on savings.

What’s your plan to make more more money this year?

I was considering driving for Uber or Lyft or taking on odd jobs, but I thought it might be more cost effective to learn some more admin skills. I am lucky enough that Sony offers classes on site, where they teach more advanced stuff like Excel, so I want to learn low-level programming stuff. I’ve learned some of it already and it’s helpful. The goal would be a raise or a promotion at Sony.

And, basically, for the last six months I’ve also had two other bosses. I manage their schedules … so with that increased workload, I’ve learned minor, cool programming tricks to save me some time. Those kinds of things already, I’ve showed my coworkers and my boss is impressed. So I’m hoping to say, come review time, that I’m taking on more responsibilities, I’m making things more efficient, I think I deserve this and this because of that.

Is there a specific pathway you’re interested in?

I want to get more involved in animation … I don’t want to necessarily be an illustrator, I want to be in production. I like the job I’m in right now, it’s not a creative role, but I think the skills I’m learning here will help me in a creative role. I like the team here and I like the relative security.

When I graduated from college, I worked at a digital media startup. It had some funding and the hours were long, but it grew really fast and collapsed really fast, so then I was jumping from job to job until I ended up here. Here, I love my hours, my bosses, my coworkers—it’s a better work-life balance in addition to making more money than I had in previous roles.

They offer bonuses basically once a year. I got like a \$3,000 bonus last year and most of that went into my 401(k). I don’t expect, even if I hit all my goals, I don’t expect a raise this year to go over their pre-approved amount for what Admins can get.

Why do you want to earn more?

I’d sleep better at night knowing that I don’t have to start selling things or call my parents … I’m blessed to have parents who are very willing to help out, but maybe it’s a pride thing. I really don’t want to be in a situation where they would scold me for not being responsible.

I am also thinking long-term, like a marriage, kids, a house, a picket fence. I think it’ll look a little different in southern California, I don’t think we’ll own a home that you could in the Midwest, but having a cash reserve, that’s on my mind when I look over my finances.

In my schedule, being an assistant, I definitely organize my schedule a lot. On paper, it’s like every two weeks, which is when I get a paycheck, I look at my budget and make adjustments. After buying a car, and after the holidays especially, I’m looking every day and wondering what I can adjust, what I can scrimp on, like a phone bill or something.

Why do you have this desire to get it in order now?

I’m getting older, and a lot of our friends over the holidays got engaged, and it was one of those things. And definitely getting a car, it’s like you’re going to pay this off in 2024, and I’m like, oh my god am I even going to be alive in 2024? So it was looking at it longterm like that.

Is there a piece of general money advice that you find helpful?

Obviously I read Lifehacker and Two Cents, but my stepdad is a day trader and I think he’s been lucky enough to make a living doing something that’s relatively risky, and he also plays poker, and I think those two strategies play into each other and he likes to think about money as logically as possible. I can’t do that all of the time, but when discussing money, try to think about it like a game rather than as part of your identity. If it’s like Tetris or something, I’ve never seen anyone start crying because they lost a game of Tetris. Looking at finances, it’s scary. Most people, myself included, there’s so much of “who am I” or “where am I going” wrapped up in how much we make. Whenever I’m looking over stuff, I try to remember it’s not the end of the world.

I do feel very blessed to have supportive parents, and I realize it’s not available to everyone. So as much as people tell me I’m on top of it, I can only do it because of friends and family.

*Name has been changed.

Name: Jackie Lam

Age: 36

Location: Los Angeles, California

Job &amp; Income: I’m a freelance writer, I invoiced over \$100,000 in 2018 and am on track to earn the same or more in 2019.

Last year was an interesting year because it was the most I’ve earned but I worked the least. I took six weeks off, I consciously took June off and then took two weeks off in December. That was cool.

How much of your monthly income do bills take up?

Basic living expenses take up 20 to 25 percent, because I live pretty frugally. My savings is probably, I save pretty aggressively, so I think most of my extra money goes toward savings, savings plus basic living expenses is around 50 percent.

I have some savings for my own short term goals, a splurge fund, and in terms of retirement I have an (individual) HSA which I try to max out, and then I have a traditional IRA, which I contribute to regularly, \$500 per month. I also have an individual 401(k) and I try to put as much in as possible, focusing on employer contributions, and employee if I can.

Do you have a specific money goal right now?

The only thing that’s kind of ambiguous because I haven’t committed to it fully is maybe buying a house. I took out a small car loan last year because the APR was pretty low so I want to pay it off. Other than that, I think I’m just fine surviving as a freelancer.

I’m also working toward an AFCPE [a type of financial education certificate]. I hope to finish that in the next year or two to help freelancers and creatives with their money. I like writing about money but I want to help people with their money.

What’s your plan to make more money this year?

Last year, I got some gigs that were more ongoing, I got contracts that were more retainer-y. This was my fourth year freelancing and before that I was getting ongoing clients, but more erratic. But now I’m getting more consistent assignments, like, “Hey we’d like one article a week, or two a week” and I’m getting a higher rate.

And building community, and referring each other is really helpful. I think some of my work came from referrals, from editors but also just from my friends who work in the space. That was a big part of [earning more].

This year my strategy is really to focus on retainer, so having more clients who pay X and guarantee X, which helps with my sanity.

Building out community is great, because it’s lower risk. You have to find clients who will meet your rates, and you need to diversify your income stream. Every day if you just refer a friend or share a post or support your colleagues, build out your tribe, I call it, it can come back to help you. And it really does. In freelancing it’s helpful in a lot of ways.

By definition, if you’re self-employed, a “solo-preneur,” you think of lone wolves working out of their living rooms. We run our own businesses but having friends to talk to about everything, like, “Have you worked for this client? What is it like, how much should I charge?” That’s helpful.

It is the wild, wild west in a lot of ways, you can’t go online and look up the standard pay … it’s like, ok, how much do you earn as a writer? It can vary depending on a lot of factors: Your knowledge, your ability to negotiate, your client. Your client can pay different rates for the same thing. So having a friend to talk to about that is helpful. But also basic tips on negotiating, basic tips on managing cash flow, all of those things are interesting.

Why do you want to make more?

It’s always nice to have more money because you might need it as a financial cushion, and it also is interesting because it has to do with potential. I’m not bound to earning money as a marker of success, but when you’re freelancing it’s a risk, you’re taking on a lot of responsibility, so I wanted to see how well I could do. I don’t put pressure on myself to make a certain amount of money because you’ll go crazy doing that.

[Earning more] was a byproduct of working hard and trying to strategize a bit. I think it just happened, I know it sounds weird but I didn’t intend for it to happen. But it is good to have as a cushion, and it’s good to have more options.

The one thing I think about a lot…is just to approach money as a resource, a tool. You want it to be like water, running in the background. You want it to be operating on autopilot, you don’t stress about it, you don’t treat it like a status symbol. It’s a resource that’s running in the background but isn’t the end goal or a representation of the totality of your success. It’s a single metric.

And when you freelance, get clients you like working for and that have value outside of the money. Do you learn things, do you like working them? I feel better about the work I do now, and that’s a sign you’re going in the right direction. You know the saying, not all money is good money. Just feeling happy about the clients I have and the work that I have is powerful and a good metric.

Name: Courtney Freeland

Age: 31

Location: Shelby Township, Michigan

Job &amp; Income: I work as a senior applications engineer for an engineering firm. My salary there is \$84,000 (including a 401(k) match).

How much of your monthly income do bills take up?

Me and my fiancée put \$500 a month into a savings account and that’s our joint account. We’re using that to pay for the wedding, we’re getting married in May. I put 15 percent in my 401(k), and watch the bills. I pay my fiancée for half of the mortgage on her house, but other than that I don’t really do anything else.

Do you have a specific money goal right now?

For me, I’m not really looking to make any more income, because I just got a big salary increase.

What’s your plan to make more more money this year?

When I was at my last job I was really underpaid. Last year I was making \$73,000, and in the \$80s was more normal for someone eight years out of college in my field. I trusted the manager and didn’t negotiate, I thought he wasn’t going to screw me over, but he did. Then I found out I was underpaid and I left.

How did you figure out you were underpaid?

I think I was watching “Adam Ruins Everything,” and they talked about how you should talk to your friends about how much you make [Alicia’s note: It’s this episode]. Then I searched on the internet, too, and I talked to friends and got to that number.

I talked to my boss and asked for a raise. I didn’t say “Hey, I’m being underpaid,” but I said, and I was the only woman on my team, “Hey, based on the salaries of, comparatively to the guys, I know I’m being underpaid.” And my boss was like, “Yeah, I know you’re being underpaid too.”

I was like, “Ok, well, I’d like to get paid equally,” and he said he would work on it. My other boss [the hiring manager] hadn’t been as straight-forward with me, so that was nice. I reminded him a few months later because I hadn’t heard anything, and I kept looking for another job, because they usually say you’re not going to get that much of an increase at your current job … you have to move to a new job to make more money.

I got an offer at my [current] job for \$84,000, and then the next day my boss at my old job, coincidentally, said, “We’ll give you \$80,000,” and I was like no. This other place is giving me \$4,000 more.

I had that angry feeling of when you know you’ve been underpaid for so long. I was almost five years in. At the new job, they didn’t ask me what my salary was at my last job, they gave me the actual salary I should have been paid.

Why do you want to earn more?

I’m not looking to do a side hustle, I don’t need to do a whole lot more or anything. I’m also doing graduate school, so being able to get this money increase made that all possible.

Is there a piece of general money advice that you find helpful?

I try to read one kind of financial book a year. I just like learning about this stuff, I just felt like I was ignorant about this stuff for a long time. Right out of school I didn’t even have a savings account, I probably had \$200 or less in a checking and I was like, ok, I need to get my shit together. Find out what works for you, but I really like Ramit Sethi and I Will Teach You to Be Rich, and I follow his advice.

But also, talk to your friends about salary even though you think it’s taboo.

Name: Kristin Wong

Age: 35

Job &amp; Income: Freelance writer and author. I make about \$75k-\$100k a year, but about 20 percent of that goes toward business expenses.

I’ve probably earned an average of about \$75k from freelance writing over the past five years, that doesn’t include book advances or speaking gigs or anything like that, just writing clients. Last year I earned about \$60k freelance writing because I had to take some time off to write a book. This might sound like a lot, but the costs of freelancing—health insurance, business expenses—offsets a lot of that income.

How much of your monthly income do bills take up?

Including housing, bills take up about 25 percent of my income.

Do you have a specific money goal right now?

Aside from saving for my own retirement, I’d like to help my parents save for theirs.

What’s your plan to make more money this year?

I want to get more comfortable with negotiating. It’s something I encourage other people to do in my writing, but it’s not something I’ve been great at lately.

I’m really trying to get over the fear of saying, “My standard rate is X amount.” I’ve been afraid of setting a standard because I don’t want to lose work, but I also know it’s important if you want to level up your income.

Why do you want to earn more?

I want to earn more so I can help my parents. They are financially struggling right now, and while they’re able to pay the bills and save a bit for retirement, it would be nice to be able to support them so they can enjoy life a little bit more and not have to worry about money so much.

Is there a piece of general money advice that you find helpful?

Have a specific, meaningful goal for your finances. This is the overarching theme of my book, Get Money. When you have a solid reason to be better with money, you’ll be much more motivated to make smarter financial moves, whether it’s cutting back on restaurants, negotiating, or sticking to a budget or debt payoff plan.

Now it’s your turn: How are you making more money this year?

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# Relationship Experts Reveal 6 Secrets for Valentine’s Day Gifts that Don’t Suck

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With all the corny gift guide clichés and tacky holiday-themed products available this time of year, picking the perfect Valentine’s Day gift for your partner can be tricky. That’s why it pays to put a bit of thought into figuring out what constitutes a good gift ahead of time.

To help, we called on two of our favorite New York City-based relationship experts: psychotherapist Lisa Brateman, and Dr. Jane Greer, author of “What About Me? Stop Selfishness From Ruining Your Relationship,” for advice on securing a solid Valentine’s gift. Here’s what they had to say…

### 1. Scour your partner’s schedule for opportunities

“Go through their calendar and see what activities they have scheduled—the gym, lunch with a friend—and get them a gift certificate to that restaurant, or renew their membership,” says Greer. “If they don’t have a membership already, you can get them one.”

### 2. Write something down

“Writing an old fashioned letter that actually arrives in the mail on Valentine’s Day is a novel idea in this day and age,” says Brateman. “Write down a handful of your favorite couple sayings or send a handwritten note listing five different things you love about your partner and mail it to them the old-fashioned way.”

### 3. Put yourself in their shoes

“Browse a few stores with some of their favorite things (colors, hobbies, etc.) in mind and see if any items jump out at you,” suggests Greer. “Think about comforting items they might buy for themselves, like bathrobes or slippers, and have them monogrammed.”

### 4. Express yourself

“Sometimes being vulnerable with your partner about how you feel and why you feel it can be the most romantic gesture to make on Valentine’s Day,” says Brateman. “Whether it’s in a card or over dinner, use the holiday as a chance to articulate to your partner how deeply you love and care for them.”

### 5. Make a memory together

“Create a lasting memory for your partner on Valentine’s Day by taking them to a concert they’d really like to see or to an art museum,” says Greer. “Use the day as an opportunity to experience something new and exciting with your partner to make a lasting impression. ”

“Whatever you decide to do or buy for Valentine’s Day, make sure it conveys the time and energy you put into it,” says Brateman. “A last-minute gesture or repeated gift can make a person feel unimportant.”

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# How to Handle Romantic Rejection

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The mystery of love is dwarfed by the far greater mystery of how to get the hell over being dumped. Here’s how to begin.

Most functional adults have experienced rejection in some aspects of their lives, from apartment applications to jobs to being chosen last for dodge ball. Hearing “no” is far more common than hearing “yes,” so we mostly get used to it. Being rejected romantically, however, is a whole other can of worms. Whether you’re in love or just in like, someone not being into you can feel far more painful than missing out on a promotion.

### Let yourself grieve

The loss of a relationship is like a small death—the death of a future you, whom you pictured alongside a specific person. It’s normal to feel sad about it the way you would about any loss. Take some time to feel your feelings; there’s no rush to get back out there. It will gradually get better, though there will be good days and bad days. Days when you stay in bed and eat ice cream; days when you cry at an insurance commercial. Try to balance them out with days spent outside and days doing the stuff that makes life fun. Which could also include staying in bed eating ice cream.

### It’s not as personal as it feels

When you ask someone out and get turned down, or worse, someone dumps you, it feels like a wholesale rejection of your soul. And also your body. And your style?! So much is encompassed in someone not liking you back, which is why it’s so upsetting.

Try to remember that everyone is exactly as complicated as you are. There’s no way to parse the reasons they’re not into you. Some of those reasons are entirely outside your control. Maybe you remind them of someone who hurt them in the past; maybe they’re not really ready for a relationship (it’s true sometimes!); maybe they’re not even attracted to your gender. A rejection has as much to do with the person doing the rejecting. As personal as it may feel, there are a lot of factors you will never know.

### Hide their number

This is a clever trick someone recommended to me when I was falling prey to the temptation to text someone who ghosted me: delete their number. I couldn’t bring myself to do that, so instead I labeled their name as Don’t Text. It’s not a fail-safe, but it does make you pause before you hit Send. During your better moments, you know you shouldn’t text or call them. Leave a clue for when you’re in a worse moment.

### Try something new

It’s hard to get over someone when everything about your routine reminds you of the hole they left. Disrupt your pattern by trying something different: a new hobby, a new class, a new restaurant, a new park. Anything to shake things up. Not only will it give you something else to think about, you’ll be more likely to hang out with other people with the same interests. There’s nothing like a new prospect to help clear the clouds away.

True friends are there for you through thick and thin. You’re also allowed to have as many of them as you want—unlike romantic relationships, which usually have far less wiggle room. Invest in your friendships, be social, talk through your feelings.

The caveat here is that you have to invest in your friendships when you’re in a relationship, too. If you’re the type to neglect friends whenever you’re dating someone, you’ll be in for a rough time. Luckily, building up those friendships again is a great project, and one that will sustain you in future.

### Get out there again

After the grieving has subsided, after you’ve built up your self-esteem, you’ll need to get back out there. I know, dating is often horrible, but the longer you avoid it, the harder it will be to start—sort of like going to the gym. Even if you’re not ready to commit to someone new, getting a coffee with somebody cute is a good exercise. Romantic rejection sucks, but don’t be fooled into thinking that one rejection is a life sentence.

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# How to Dump a Friend

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A few years ago, one of my best friends from college broke up with me. “I think it might be healthier if we took a step back from constantly talking to each other,” she wrote in an email. “Maybe one day we’ll see eye to eye, but for now this feels unhealthy.”

The breakup wasn’t out of the blue. We lived in different cities and mostly spoke via Gchat, and in the last few months we had started bickering a lot. There were a number of reasons for the uptick in arguments, but the main one, really, was that at the time, I was depressed, she was coming out of a period of depression, and our differing emotional states made me toxic to her. I didn’t grasp that the unrelenting negativity manifesting from my depression was hurting her, and I sent her a defensive email in response. But looking back on it now, I get why she needed to take space and I respect her for asking for it, even if I still miss her sometimes.

It’s tough to dump an old friend. “There is a reluctance to end longer term friendships, especially those formed in childhood,” says Jennifer Verdolin, an animal behavior expert and adjunct professor at Duke University. “Social animals, which we are, need and depend on social needs that extend beyond the immediate family. When you forge them, and they’re strong and they’re long, there’s a difficulty in letting them go.”

Some of that is because it takes a long time to build that kind of friendship, and since it’s harder to make friends as you get older, you might not be able replace your ex-buddy. And some of it is because when you say goodbye to someone, you say goodbye to a part of yourself, and it’s difficult to bury the version of you who used to love this person, even if you know you need the space.

Still, friendships change as we age, and sometimes you find yourself in one that’s no longer serving either one or both of you. When that happens, you need to evaluate whether or not it’s time to cut the cord. Here’s how to do it. But first:

## Pinpoint why you want to end the friendship

There are a number of reasons a friendship might go sour. An obvious one is when you find one friend is pulling far more of the relationship’s weight than the other. “Some warning signs would be persistent imbalances in terms of who is always having needs and who is always meeting those needs,” says Peg O’Connor, a Professor of Philosophy at Gustavus Adolphus College who blogs for Psychology Today. Though friendships aren’t always 50/50, particularly during short periods when one friend needs more support than the other, “when there’s a persistent balance, when it’s always pretty much ‘70 percent my friend’s needs, 30 percent mine,’ then that’s a problem,” she said. Basically, if you find yourself being used in a friendship, it’s time to get out.

Sometimes, the soured relationship is due to more insidious behavior, like lying or backstabbing. And sometimes, the friendship just doesn’t make you the kind of person you want to be—politically, behaviorally, or otherwise. “What happens when you are putting to the side your needs or your wants, or you’re compromising your values or you’re going against your own beliefs?” O’Connor says. “That is fundamentally going to harm your moral character and at the end of the day, what you have is your moral character and you are responsible for it.”

So, if your friend is turning you into a mean gossip, or bringing you down, or stealing your boyfriends, or is just generally taking more out of you than you can handle, it might be worth cutting the cord. If so:

## Don’t ghost

It’s fine to let new or distant friendships naturally fade out, but if you’re dumping a good friend, you owe them some warning and an explanation. “We’re uncomfortable with cutting out people from our lives, and sometimes that leads to not communicating at all, and completely ghosting,” Verdolin says. “Then, we have this weird inconsistency that creates a lot of stress and tension for both parties.”

Instead of disappearing, ask them to meet you for coffee, or call them on the phone, or, if you must, send them an email. The latter is least preferable, since it doesn’t give the dump-ee the opportunity to hear your cadence or to respond, but if it makes it easier for you to say what you need to, feel free to do your thing. Do note that if you are planning to do the break up in writing, don’t send anything angry or rash, and maybe give yourself an extra day to read it over with fresh eyes.

“See if they are feeling something similar to what you’re feeling and if it seems like this is completely out of the blue to them, well, that’s good indication that you haven’t been on the same page,” O’Connor says. “Then you might have to say, ‘You know what? I need some space.’”

Be clear about why you need space, cite specific examples if you must, and be sure not to place a lot of blame on them, even if you believe strongly that you are the wronged party. Telling someone “I don’t want to be friends with you because you are bad and needy,” will only put them on the defensive; instead, make it clear that the relationship is broken, and not specifically them. Something like, “I feel that I am not being heard enough in this friendship, and that makes it hard for me to feel comfortable sharing with you” might work better.

“You’ve got to be clear,” O’Connor says. “You’ve got to be clean. You’ve got to be honest in it. You can’t be a wiener dog.”

## Treat it like a breakup

When you end any relationship, you need to set boundaries. That goes for a friendship as much as a romantic relationship. “Sometimes the mistake we make is this gray space, where we are either not certain what we’re going to do, or we feel feelings like guilt or something that prevents us from clean breaks,” Verdolin says. That doesn’t mean you need to commit to killing the friendship forever; instead, considering severing it completely in the short term to give yourself and your friend space and time to self-reflect. “Say, ‘Let’s take six months, in those six months we won’t talk, and then we’ll regroup and decide what we want to do,’” Verdolin says.

In that time—or, in the long term, if you plan on cutting off the friendship without an X-month caveat—do not communicate with them. Do not text them, call them, post things on social media that are designed to elicit a response, smoke signal them, or stand outside their window blasting a Peter Gabriel song, and if they do any of that to you, remind them gently but firmly that you asked for your space. If you have mutual friends and run into them at group events, be respectful when you see them, but make it clear you’re not reopening the friendship door, lest you both start falling back into toxic patterns.

“We create so much more stress for ourselves by having a lack of clarity,” Verdolin says. “If I am not going to be your friend, I don’t want to be involved in your life at all, not even peripherally.”

If you think there’s a possibility your now ex-friend won’t respect your need for space, it might be a good idea to block their number so they can’t text or call you. You can also block them over e-mail or G-chat, or make yourself “invisible” to them on online chat programs.

## Mute them on social media

Speaking of peripheral friendship, a great way to extend the amount of time it takes to get over a friend breakup is to regularly watch their Instagram stories. As Verdolin puts it, “Social media makes it really difficult to get good endings of relationships of all kinds.” Like with a romantic breakup, when you end a friendship, you don’t want to know who your friend is hanging out with or what they’re doing all the time or be fed more of the terrible political ramblings that prompted you to end the relationship in the first place.

Unfollow or mute them on Twitter, mute them or unfriend them on Facebook, and mute them or unfollow them on Instagram. It may feel extreme to remove them from your life so completely, but it gives you way more room to move on.

## Allow yourself to grieve

It is a real loss to end a friendship. No matter how draining the relationship may have been at its worst, when you let a friend go, you lose a whole part of you. And so, though it will certainly feel empowering to drop something that started to feel toxic, it will also make you sad. That is fine and normal, and you should let yourself feel the sadness, instead of writing it off. It’s unfortunate that society gives a lot of attention and weight to the end of romantic relationships and not nearly enough to the ends of friendships, but the latter can be equally painful.

“Ending relationships is very hard,” Verdolin says. “Depending on the previous strength of that friendship, we go through a grief process.”

Some ways to move through that grief process include journaling, immersing yourself in activities and hobbies you love or used to love, and finding new social groups that fit you better than whatever relationship you had with your now ex-friend. “We all have friends for a reason or for a season and then when the season or the reason changes you can move on and drift apart and there’s really no harm, no foul,” O’Connor says. And if your ended friendship was strong enough to start with—and the breakup mutually respectful and clean—it is always possible you can reconcile when both parties are ready.

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# European colonizers killed so many indigenous Americans that the planet cooled down, a new study reveals

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• Following Christopher Columbus’ arrival in North America in 1492, violence and disease killed 90% of the indigenous population — nearly 55 million people — according to a new study.
• Diseases like smallpox, measles, and influenza, which colonizers brought to the Americas, were responsible for many millions of deaths.
• The new research also reveals that following this rapid population decline and the subsequent reduction in land use, there was a global cooling trend.

Prior to Columbus’s arrival in the Americas in 1492, the area boasted thriving indigenous populations totaling to more than 60 million people.

A little over a century later, that number had dropped close to 6 million.

European contact brought with it not only war and famine, but also diseases like smallpox that decimated local populations. Now, a new study published in the journal Quarternary Science Reviews shows that those deaths occurred on such a large scale that they led to a "Little Ice Age": an era of global cooling between the 16th and mid-19th century.

Researchers from University College London found that, after the rapid population decline, large swaths of vegetation and farmland were abandoned. The trees and flora that repopulated that unmanaged farmland started absorbing more carbon dioxide and keeping it locked in the soil, removing so much greenhouse gas from the atmosphere that the planet’s average temperature dropped by 0.15 degrees Celsius.

Typically, experts look to the Industrial Revolution as the genesis of human-driven climate impacts. But this study shows that effects may have began some 250 years earlier.

"Humans altered the climate already before the burning of fossil fuels had started," the study’s lead author, Alexander Koch, told Business Insider. "Fossil fuel burning then turned up the dial."

## More than 50 million indigenous people perished by 1600

Experts have long struggled to quantify the extent of the slaughter of indigenous American peoples in North, Central, and South America. That’s mostly because no census data or records of population size exist to help pinpoint how many people were living in these areas prior to 1492.

To approximate population numbers, researchers often rely on a combination of European eyewitness accounts and records of "encomienda" tribute payments set up during colonial rule. But neither metric is accurate — the former tends to overestimate population sizes, since early colonizers wanted to advertise riches of newly discovered lands to European financial backers. The latter reflects a payment system that was put in place after many disease epidemics had already run their course, the authors of the new study noted.

So the new study offers a different method: the researchers divided up North and South America into 119 regions and combed through all published estimates of pre-Columbian populations in each one. In doing so, authors calculated that about 60.5 million people lived in the Americas prior to European contact.

Once Koch and his colleagues collated the before-and-after numbers, the conclusion was stark. Between 1492 and 1600, 90% of the indigenous populations in the Americas had died. That means about 55 million people perished because of violence and never-before-seen pathogens like smallpox, measles, and influenza.

According to these new calculations, the death toll represented about 10% of the entire Earth’s population at the time. It’s more people than the modern-day populations of New York City, London, Paris, Tokyo, and Beijing combined.

## The disappearance of so many people meant less farming

Using these population numbers and estimates about how much land people used per capita, the study authors calculated that indigenous populations farmed roughly 62 million hectares (239,000 square miles) of land prior to European contact.

That number, too, dropped by roughly 90%, to only 6 million hectares (23,000 square miles) by 1600. Over time, trees and vegetation took over that previously farmed land and started absorbing more carbon dioxide from the atmosphere.

Carbon dioxide traps heat in the planet’s atmosphere (it’s what human activity now emits on an unprecedented scale), but plants and trees absorb that gas as part of photosynthesis. So when the previously farmed land in North and South America — equal to an area almost the size of France — was reforested by trees and flora, atmospheric carbon-dioxide levels dropped.

Antarctic ice cores dating back to the late 1500s and 1600s confirm that decrease in carbon dioxide.

That CO2 drop was enough to lower global temperatures by 0.15 degrees Celsius and contribute to the enigmatic global cooling trend called the "Little Ice Age," during which glaciers expanded.

## Lingering doubts

Not all scientists are convinced by Koch’s explanation.

"The researchers are likely overstating their case," Joerg Schaefer from the Lamont-Doherty Earth Observatory of Columbia University, told Live Science. "I am absolutely sure this paper does not explain the cause of the carbon dioxide change and the temperature change during that time."

Koch said that some of the drop in carbon dioxide could have been caused by other, natural factors like volcanic eruptions or changes in solar activity. But he and his colleagues concluded that the death of 55 million indigenous Americans explained about 50% of the overall reduction in atmospheric carbon dioxide.

"So you need both natural and human forces to explain the drop," he said.

Koch said the findings revise our understanding of how long human activity has been influencing Earth’s climate.

"Human actions at that time caused a drop in atmospheric CO₂ that cooled the planet long before human civilization was concerned with the idea of climate change," he and his co-authors wrote.

But they warned that if a similar reforestation event were to happen today, it wouldn’t do much to mitigate the Earth’s current rate of warming. The drop in atmospheric carbon dioxide that happened in the 1600s only represents about three years’ worth of fossil fuel emissions today, Koch said.

"There’s no way around reducing fossil fuel emissions," he said, adding that reforestation and forest restoration remain crucial, too.

SEE ALSO: The dangerous measles outbreak near Portland, Oregon, is what happens when people refuse to vaccinate their kids

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# Andromeda galaxy will deliver a ‘glancing blow’ to our Milky Way later than expected

Astronomers have long suspected that the colossal Andromeda galaxy would, in billions years, collide with our humble Milky Way.

The collision was forecast to happen in some 3.9 billion years. But after astronomers analyzed new data captured by the European Space Agency’s star-surveying satellite Gaia, they now put the imminent date at 4.5 billion years — so 600 million years later than initially expected.

The event, detailed in The Astrophysical Journal, is characterized as a “swipe” rather than a direct collision. The end result would be a merger of the galaxies into one, monstrous galaxy.

“This finding is crucial to our understanding of how galaxies evolve and interact,”  Timo Prusti, ESA Gaia Project Scientist who had no role in the study, said in a statement

While of immense importance to our corner of the universe, this event will be of little importance to Earth: By then, our aging sun will have grown brighter and likely have boiled the oceans while burning away our protective atmosphere.

To arrive at their conclusions about the future galactic meeting, scientists observed how stars moved within two “nearby”  galaxies that are moving around each other —  the Andromeda and Triangulum galaxies  — to forecast how Andromeda will ultimately travel through intergalactic space.

”We combed through the Gaia data to identify thousands of individual stars in both galaxies, and studied how these stars moved within their galactic homes,” said study coauthor Mark Fardal in a statement. “While Gaia primarily aims to study the Milky Way, it’s powerful enough to spot especially massive and bright stars within nearby star-forming regions – even in galaxies beyond our own.”

When Andromeda does eventually meet, or “swipe,” the Milky Way, it doesn’t mean chaos and destruction will ensue.

“That event will be less dramatic than it sounds, however,” noted The New Times cosmos reporter Dennis Overbye. “Because galaxies are mostly empty space, they will pass through each other like ghosts.”

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# I’m 25, and I talked to 3 single women in their 50s about what it’s like to use dating apps like Tinder and Bumble. Their experiences surprised me

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• Single women over the age of 50 are finding themselves discouraged with dating apps that tend to cater to younger generations and embrace hook-up culture.
• Tinder can be too aggressive for someone fresh out of a 20-year marriage, while Bumble can give an older woman control over her preferences and allow her not be bombarded by messages, women say.
• Some find apps catered to their age group, like eHarmony and Match, "too old" and others like Happn too "trendy."
• Despite frustration, many are leaning into the apps, using them as means to meet people and explore their new single lives.

A few weeks ago, my mom came to me with a question: She was becoming increasingly frustrated with dating apps. Were other single women her age feeling that way, too?

What she was searching for was innocent enough: someone who she can have fun with, travel with, and ultimately be in a long-term relationship with. Marriage? No, thank you. Kids? Been there, done that. A one night stand? TMI.

She’s over 55, has been married, had kids, owns a home, and has been providing for herself for years. She was no longer looking for someone to take care of her — she was doing a fine job already — but someone to love and be loved by.

She moved to Abu Dhabi in 2015 and was teaching at a university there, when a female colleague two decades younger introduced her to Tinder. It was exciting and unlike any other dating experience she had before.

"What was exciting was I was meeting people I would never meet," she told me over the phone recently. "It is different when you are in a foreign country, you have people from all over the world, and unless you are going out to clubs and bars, it is difficult to meet people."

So, she swiped right. And she swiped right a lot. One man she met she described as a multimillionaire who picked her up in a Jaguar limo and took her to the Dubai opera. Another asked her to be his fourth wife after only a couple of dates. There were lots of late nights out dancing, followed by cozy nights in chatting online, getting to know someone.

At this point, my mom estimates she’s been on nearly 50 dates — some with men 20 years younger. And though she didn’t join Tinder with specific expectations, something wasn’t clicking. After a year of using the app, she deleted it.

"No one I met on the app, none of them, wanted a committed, long-term relationship," she said. "A lot of them are looking for threesomes or just want to have a conversation, but what about me? What am I getting out of that other than having a date once in a while?"

As an older woman, my mom was confronted with a simple fact: she was now living in a society where the most popular way to date catered to younger generations and fully embraced hook-up culture.

## So, what’s an older lady to do?

This is also a truth Carolina Gonzalez, a writer in London, came face-to-face with after her 28-year marriage ended.

At 57, she downloaded Bumble — Tinder seemed too aggressive, she told me. She’s also tried Happn and OkCupid, but quickly trashed them because she didn’t find a big enough pool of users in her age range, or found the app to be too trendy. Sites like eHarmony and Match, she said, seemed "a little too old" and hard to "get a full sense of who is available.”

She enjoyed the control Bumble gave her, and the ability to not be bombarded by messages but to make the first move instead. It seemed noncommittal, she said; clean, in fact. The variety, though, "can be scary."

"When you just get out of a long marriage or a long relationship, it is weird to go out with anybody," Gonzalez told me. "Though there is still a hope you will meet someone and fall in love, but I am probably never going to meet someone and have what I had before."

But that, she said, was also liberating. She was free to have 15-minute coffee dates, be vulnerable, and feel sexy. At her age, Gonzalez said, she feels much more confident in who she is — a trait, she said, that younger men find appealing.

My mom said this, too. She frequently matched with men 10 to 15 years younger than her because, she said, she was able to "hold a conversation."

For Gonzalez, dating apps only proved to her that her life wasn’t missing anything, except maybe the cherry on top. Bumble lets her go out to the movies and dinner with people and form relationships, even friendships, with men she would have never met before. She’s in a place where she is not doing anything she doesn’t want to do, and experimenting with dating apps as a way to have fun as a 50-something divorcée. Her life is not shutting down with age, she said, but opening up.

She did, however, see that the options available to her younger girlfriends were much more plentiful. Peaking over their shoulders, she saw her younger friends swiping with much more fervor and not running up against the spinning wheel — an indication the app is searching for more people with your age range and location.

"This is a big business and they are missing out," said Gonzalez, referring to popular dating app companies who don’t cater to older people.

Tinder declined to comment when asked to provide its app’s age demographics and whether or not it thought its platform catered to older users. Match, eharmony, Happn, and OkCupid did not respond to Business Insider’s request for comment.

Jess Carbino, a sociologist for Bumble, told Business Insider in a statement that out of its female users over 40, 60% believe the app will "most likely to lead to the type of relationship they desire."

But how many swipes must a single lady swipe to get there? My mom compared it to panning for gold. (I swear she is not that old.) "You really have to dig in the dirt for that speck of gold, you have to go through hundreds of different profiles," she said.

Though, she questioned, this may not be entirely the fault of dating apps, but how people use them.

"Dating apps work for men, and older men, but don’t work for older women," my mom said. "Most women who are older are not looking for hookups, where most men are looking for whatever experiences they can get. How do you find those few men who are out there who are looking for a relationship?"

That is a question Crystal, 57, has been asking for the 15 years she’s been single. (Crystal declined to have her last name published.) She’s a single mom living in Pittsburgh, and she’s tried it all: eharmony, Match, OkCupid, Plenty of Fish. Just before the holidays, she canceled Bumble, finding it all to be too stressful.

She’s hopped from app to app like most people do — hoping to find a new pool of available people. But what she found was just recycled profiles.

"Whenever I go out, I see all these license plates from states all over and think, ‘There has to be some available people here!’" said Crystal. "I am self-sufficient, I just prefer not to be alone. I guess the idea of the long-term relationship scares people away."

Crystal wants to try Silver Singles after Valentine’s Day and plans to change her profile to say "just looking to date."

Her best advice to other ladies her age on the apps: don’t list yourself as looking for an activities partner.

"That is when all the weirdos come out of the woodwork," she said.

## The takeaway

I have to admit: as a 25-year-old, the kind of dating the 50-plus ladies I spoke with described is the only dating I have ever known. However, I grew up in the digital era, where you can be flaky in real life, flirty over text, have low expectations, and shallow notions.

This is a new frontier for older women like my mom. She’s living in a world where society tells older men that they’re silver foxes, and older women to take up knitting. It’s not the best message to take into the next chapter of her life — one where she is newly single and searching for something not so vapid, all the while playing the dating game with rules made up by a younger generation and tools that condone it.

In light of that, she’s gotten a lot more specific. She realized she didn’t have to feel frustrated so often if she just leaned into it.

These days, she refuses to date Cancers — or any water sign, for that matter. And that is why she recently re-downloaded Bumble: she gets to see right away if a potential match has an unappetizing astrological sign.

I asked her why she decided to do it all over again.

"If I didn’t have the apps, I would have no options," she said, laughing. "The benefit is it gives you options. You get frustrated and get off it and then get lonely and get back on. It’s a cycle. It’s like anything else, you run the gauntlet. That’s life."

Are you over 50 and using dating apps? Want to share your story? Contact this reporter at mgebel@businessinsider.com, (646) 768-1658, or by Twitter DM @MeiraGebel

SEE ALSO: Startup founder Melissa Hanna says more Silicon Valley investors need to be courageous and invest in people ‘who are not like them’