MODULE 06

t-tests

A t-test asks whether means differ.

Research question
Variables
Variable roles
Measurement levels
Method choice (trained here)
Statistical logic (trained here)
SPSS workflow (trained here)
Output interpretation (trained here)
Defensible conclusion

Understand

Choose the comparison

The three t-tests share the same logic (difference ÷ standard error). What differs is what is being compared.

What are you comparing?

One-sample t-testOne variable, one group, one fixed reference number.

Independent-samples t-testEach respondent belongs to exactly one group. Needs a grouping variable.

Paired-samples t-testThe test works with each person's difference, so stable individual differences cancel out.

The paired trap

If the two numbers come from the same respondents (two questions, two waves, before and after), the observations are not independent. Use the paired-samples t-test, even if it ‘looks like’ two groups.

Try

Practice: from research question to hypotheses

For each example: identify the dependent variable and grouping variable, choose the test, and formulate H₀ and H₁.

“Is average interview completion time equal to 60 minutes?”

Step 1 of 5

What is the dependent variable (the one whose mean we compare)?

SPSS

SPSS workflows

Before you open SPSS

1What is the research question?Is the average interview completion time equal to 60 minutes?
2What is Y?Yinterview length (minutes)
3Measurement level?Scale, so a mean makes sense.
4What are we comparing?One sample mean with a fixed value (60).
5Which method?One-sample t-test, H₀: μ = 60.

Analyze›Compare Means›One-Sample T Test

One-Sample T Test

respid

interviewer

mode

region

1Test Variable(s):

intlength

2Test Value:

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1
Test Variable(s):
The scale variable whose mean you test.
2
Test Value:
The value stated in H₀. SPSS's default is 0, which is almost never what you want.

One-Sample Test (Test Value = 60)
	t	df	Sig. (2-tailed)	Mean Difference	95% CI Lower	95% CI Upper
intlength	3.12	199	.002	2.84	1.04	4.64

1t = mean difference / standard error.
2p < .05: reject H₀: μ = 60.
3Interviews last on average 2.84 minutes longer than 60. Is that substantively important?

SPSS

Independent t-test: which row do I read?

Keep it short: Levene first, then the t-test row it points to.

asks whether the group variances can be treated as equal. It does not test your hypothesis; it only tells you which row to read.

p ≥ .05 → read “Equal variances assumed”

Independent Samples Test (happiness by political interest)
	Levene's Test		t-test for Equality of Means
	F	Sig.	t	df	Sig. (2-tailed)	Mean Diff.
Equal variances assumed	0.67	.412	2.14	1198	.033	.31
Equal variances not assumed			2.08	961.4	.038	.31

1Levene's test lives in the first row only. Its Sig. decides which row of the t-test to use.

Understand

Significant does not mean large Next step / advanced

An effect size expresses the difference relative to the spread of the data, so it does not grow with sample size the way significance does.

Cohen's d0.50

Distance between the group means in standard-deviation units.

d = 0.50

moderate

The distributions overlap by about 80%.

Rules of thumb: ~0.2 small, ~0.5 moderate, ~0.8 large. Benchmarks, not laws: judge size in context.

Cohen's d

d = M₁ − M₂sₚ

M₁, M₂: the two group means
sₚ: pooled standard deviation

Hedges' g

The same idea with a small-sample correction. d slightly overestimates the population effect in small samples; g shrinks it a little. With a few hundred respondents the two are practically identical.

Test yourself

Mastery check

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Choose t-test

Is the average interview completion time equal to 60 minutes?

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