INDEPENDENT SAMPLES T Purpose: Test whether two means are significantly different Design: between subjects scores are unpaired between groups

Sampling Distribution of the Difference Between Means We are collecting two sample means and finding out how big the difference is between them. The mean of this sampling distribution is the Ho difference between population means, which is zero.

 1 -  2 x 1 -x 2 sampling distribution of the difference between means

1. Independent observations 2. Normal population (or large N) 3. Interval or ratio level data 4. Homogeneity of variance Assumptions

Computation of Independent Samples t standard error of the difference between means

Because (  1-  2) = 0, we can simplify:

Example Patients are assigned to an experimental treatment or a placebo treatment and measured on severity of symptoms. The placebo group (n = 15) has a mean of 20 (SD = 2). The experimental group (n = 15) has a mean of 15 (SD = 3). Is there a significant difference between groups?

STEP 1: Compute the standard error of the difference.

STEP 2: Compute t.

STEP 3: Look up t-critical in the table. df = n1 + n2 - 2 df = = 28 two-tailed  =.05 t-crit = 2.048

STEP 4: Compare t to t-critical. t = 5.38, t-crit = 2.048

APA Format Sentence An independent samples t-test showed that there was a significant difference between groups, t (28) = 5.38, p <.05.

Effect Size The t-test tells you only whether the result is significant or not, not the size of the difference A significant effect may be a large or small one

Effect Size with r 2 Compute the correlation between the independent and dependent variables This will be a point-biserial correlation Square the r to get the proportion of variance explained

Computing r 2 from t

Effect Size with Cohen’s d Difference between means in units of pooled standard deviation Cannot be interpreted in terms of percentage of variance explained Guidelines Small effect =.20 Medium effect =.50 Large effect =.80