Between-subjects/independent t-tests

When are between-subjects t-tests used? (1)

• Comparing two samples who have received different levels of an IV, to see if IV affects DV (H1) or it doesn’t (H0)

Prediction of null hypothesis (formula)

• No significant difference between population means: any observed difference is due to chance

Prediction of alternative hypothesis

• Significant difference between population means

Required info (3)

For each group:

• Sample mean

• Individual values

^^To calculate sum of squares (SS), don’t need if provided with SS

• Sample size

Step 1 (1)

• Estimate population variance

Step 1a (1→2)

• Estimate population variance from each sample

  • s²₁ = ∑(X₁ - X̅₁)² / n₁ - 1

  • s²₂ = ∑(X₂ - X̅₂)² / n₂ - 1

Step 1b (1)

• Calculate pooled variance

  • Using estimated population variances from each sample, and sample sizes of each sample

Step 2 (1)

• Estimate standard error of the distribution of sample mean differences

  • Using pooled variance and sample sizes of each sample

Step 3 (1)

• Calculate difference between sample means, i.e. mean difference

  • X̅₁ - X̅₂

Step 4 (1)

• Calculate t-obtained

  • Using mean difference and standard error

Step 5 (1, 1→2, 1)

• Compare t-obtained to t-crit.

  • Find t-crit. using

    • df = (n₁ - 1) + (n₂ - 1)

    • Alpha level (usually .05)

• Is t-obtained > t-crit.? If so, then p <.05 → reject null hypothesis (likely statistically significant, i.e. observed effect in DV is due to IV, not chance)

How do you calculate effect size for between-subjects t-tests? (1)

• d_s (Cohen’s d for between measures) = absolute value of difference between means / square root of pooled variance

Important note on one vs two-tailed t-test tables (2)

• Typically use two-tailed

• BUT if using one-tailed → double alpha level (e.g. to find a one-tailed α=.05, look under the α=.10 column)

Assumptions (4)

• Interval or ratio scale

• Normality

• Independence of observations

• Homogeneity of variance

Homogeneity of variance def (1)

• Assumes that population standard deviation is the same in both groups, i.e. population standard deviation of one sample is no more than 3-4 times larger than other sample (usually 4 probs)