T-test

What is the main goal of the independent samples t-test?

To compare the means of two independent groups to see if the difference is significant.

What is a between-subjects design?

• A study design where different people are assigned to each group or condition.

State the null hypothesis for an independent samples t-test.

The means of the two groups are equal (μ₁ - μ₂ = 0).

Give an example of when you would use an independent samples t-test.

Comparing the effectiveness of two teaching methods with different student groups.

What does a significant result in an independent samples t-test mean?

There is enough evidence to conclude a difference exists between the group means.

What does SE stand for in the t-test formula?

Standard Error of the difference between sample means.

Why do we add variances when calculating SE?

Because there are two independent sources of variability, one from each sample.

What adjustment is made if sample sizes are unequal?

Use pooled variance in the SE formula.

If the t-statistic is greater than the critical value, what do you conclude?

Reject the null hypothesis — there is a significant difference between the groups.

What does a negative t-value mean?

It shows the direction of the difference (e.g., Sample 1 mean is lower than Sample 2).

What does the numerator in the t-test formula represent?

The difference between the means of Sample 1 and Sample 2.

What does the denominator (SE) represent?

The standard error of the difference between the sample means.

What is pooled variance?

A combined estimate of variance that accounts for unequal sample sizes by weighting larger samples more.

What is the formula for degrees of freedom in an independent samples t-test?

df= n1​ + n2​ − 2

Why do we add the degrees of freedom from both groups?

Because there are two sources of variability, one from each sample.

What is the typical significance level (α) used in hypothesis testing?

0.05

How do you find the critical value for your test?

Use the t-distribution table, based on degrees of freedom and significance level.

What does it mean if your obtained t is greater than the critical t?

Reject the null hypothesis — the difference is statistically significant.

What is a two-tailed test?

A test that looks for a difference in either direction (higher or lower).

Why is a two-tailed test safer?

It captures unexpected effects in both directions.

If you fail to reject the null hypothesis, does it mean your treatment has no effect?

No — it means you lack sufficient evidence to conclude an effect.

After finding a significant result, what question should you ask next?

What is the size of the effect?

What is the key difference between the t-test formula and the effect size formula?

• T-test divides by standard error (SE)

• Effect size divides by standard deviation (SD)

What three things should you report when reporting t-test results?

1. T-statistic and degrees of freedom (df)

2. P-value

3. Confidence interval (CI)

How does high sample variance affect the t-test?

It increases the standard error, making it harder to detect an effect.

What causes high variance in your samples?

Messy science, like inconsistent procedures, poor measurement tools, or experimental errors.

Why is careful control in experiments important?

It reduces variance, improving your chances of detecting real effects.

How does larger sample size affect the standard error?

It decreases the standard error, making it easier to detect effects.

What is the first assumption of the independent samples t-test?

Independence of observations — participants in each group are different people.

What is the second assumption of the independent samples t-test?

Normality — the populations sampled are normally distributed.

What is the third assumption of the independent samples t-test?

Homogeneity of variance — both groups should have similar variance.

What happens if you violate the assumptions of the t-test?

You risk inflating your Type I error rate (false positive).

What test checks for homogeneity of variance?

Levene’s Test

How is the ratio for testing variance calculated?

Larger variance divided by smaller variance.

What distribution does the variance ratio follow?

The F-distribution

If your F ratio equals 1, what does that mean?

Variances are equal — assumption is met.

If your F ratio is very high (e.g., F = 10), what does that suggest?

Variances are very different — likely a violation of assumptions.

What is a Type I error?

Falsely rejecting the null hypothesis when it is actually true.

How does violating t-test assumptions affect Type I error?

It increases the risk of making a Type I error (false positive).

If your data violates the assumption of homogeneity of variance, what is the risk?

Your p-value might be inaccurate, increasing your chance of false significance.

What is the assumed Type I error rate when using a significance level of 0.05?

5%

If assumptions are violated, what might your actual Type I error rate become?

Higher than expected — e.g., 0.10 (10%) or more.

What is a p-value?

The probability of observing your data, or something more extreme, assuming the null hypothesis is true.

If your p-value is below 0.05, what does that typically mean?

There is strong evidence to reject the null hypothesis.

Does a p-value tell you the probability that the null hypothesis is true?

No — it tells you the probability of the observed data if the null hypothesis is true.

If your p-value is larger than 0.05, what does this mean?

Fail to reject the null hypothesis — there is not enough evidence to support an effect.

Can a low p-value prove that the alternative hypothesis is true?

No — it provides evidence against the null, but does not "prove" the alternative hypothesis.

What does "significance level" (alpha) mean in relation to the p-value?

It's the threshold for deciding if the p-value indicates statistical significance (commonly set at 0.05).