# Steps of hypothesis testing

Steps of hypothesis testing

Select the appropriate test

So far we’ve learned a couple variation on z- and t-tests

See next slide for how to select

State your research hypothesis and your null hypothesis

State them in English

Then in math

Describe the NULL distribution

Starting here is where you be a skeptic and assume the null is true!

For one-sample tests, you will need to determine μ

(For two-tailed tests, you don’t need to worry about μ)

Compute the relevant standard error

Determine your critical value(s)

Keep in mind whether it is a directional or non-directional test

Compute the test statistic

Compare the test stat to the critical value(s) and make your decision

When to use each test

All of these tests require that the sampling distribution is normal

Either because population is normal or, thanks to central limit theorem, sample size is very large

All of these tests require that the measures be quantitative variables, that is interval/ratio

(Not all quantitative variables are normal, BUT all normal variables are quantitative. So if someone tells you a variable is normal, you know it is also quantitative.)

When to use each test, cont’d

1 Sample z-test

Comparing one sample mean to a population mean

And you do know σ (population SD)

2 sample z-test

Comparing two sample means to each other

And you do know σM1-M2 (standard error of difference of means)

1 sample t-test

Comparing one sample mean to a population mean

You only know s (sample SD)

2 sample t-test

Comparing two sample means to each other

You only know s1 and s2 (sample SDs)

Dependent sample t-test

You have two scores coming from each person, such as if you measured them before and after an experimental manipulation.

Compute the differences between the two scores, then treat like a 1 sample t

What is α?

Put on your skeptic’s hat: you believe the null hypothesis is true

But you’re willing to be convinced you’re wrong

If the test statistic is sufficiently improbable, you will change your mind and decide the null hypothesis is false

What is “sufficiently” improbable?

When your test statistic is more extreme than your critical values

Critical values are selected so that only a small fraction of the entire distribution is more extreme than the critical values

This “small fraction” is called α

Conventionally, α is usually set to .05, that is 5%

Directionality of a test

Is a test simply about whether there a difference, regardless of direction?

If so, it is a non-directed, or undirected, or two-tailed test

Your α must be evenly split between the two tails

For the conventional α = .05, that means each tail should have .025 or 2.5% of the total distribution

Is the test predicting one mean will be bigger than another? Or is it predicting one mean will be less than another?

If so, it a directional, or directed, or one-tailed test

Put all your α in a single tail

Special note on one-tailed tests

Step 3 of our procedure is a little awkward when we have one-tailed tests

How do you describe the null hypothesis when it has an inequality, like μ1 ≤ μ2?

For the purposes of Step 3, pretend that the null hypothesis is simply μ1 = μ2

One-sample Z-test

For a two-tailed test and α = .05, the critical values are always both -1.96 and +1.96

For a one-tailed test and α = .05, the critical values are always both -1.96 and +1.96

two-sample Z-test

For a two-tailed test and α = .05, the critical values are always both -1.96 and +1.96

For a one-tailed test and α = .05, the critical values are always both -1.96 and +1.96 If it is one-tailed test make sure that the mean that is predicted to be bigger is M1

The standard error of the difference between means will simply be given to you; you will not need to compute it.

One-sample t-test

Critical values change depending on your df.

Make sure to keep track whether it is a one-tailed or two-tailed test.

two-sample t-test

If it is one-tailed test make sure that the mean that is predicted to be bigger is M1

Critical values change depending on your df.

Make sure to keep track whether it is a one-tailed or two-tailed test.

Dependent samples t-test

Sometimes called paired or matched samples

Compute the difference between each pair of scores

Make sure that if there is a directional prediction, then the scores predicted to be smaller are subtracted from the scores predicted to be bigger

Now just treat the difference scores as raw scores and conduct a one-sample t-test

Set μ = 0

Summary of Cohen’s d

What if my df isn’t in the table?

Use the next smaller df.

By choosing the smaller df, you make it harder to reject the null.

Scientists prefer to err on the side of caution and being skeptical, so they are inclined to retain the null

For each homework problem

You must clearly show me:

The equation for the correct test-statistic

The equation for the correct standard error

The equation for the correct df (if df is required)

The equation for the correct Cohen’s d

Your computations for all four of these

Your critical values

Make sure you show the correct sign(s)!

Depends on one- vs. two-tailed and direction if one-tailed

A comparison between the test stat and the critical value

For example: t = 2.5 > critical value = 2.131

For example: z = .73 < critical value = 1.96

A statement in English about your conclusion

See next slide

Stating your conclusion

Here are examples to cover both possible conclusions you might make.

Change the underlined part for your problem and data

“This hypothesis test shows that we should reject the null hypothesis and instead conclude that receiving the medicine does improve health outcomes. This conclusion is statistically significant with p < .05. The size of the effect was large, Cohen’s d = .83.”

“This hypothesis test shows that we should retain the null hypothesis and conclude that men and women do not differ in arithmetical ability. The test was not statistically significant with p > .05. The size of the effect was small, Cohen’s d = .07.”

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