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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