Many research studies require comparing two or more samples at one time.

Designs that can be used to obtain two (or more) sets of data to be compared:

1. Two sets of data coming from completely different groups of participants. (ex. comparing the performance of two different groups on a task)

2. Two sets of data could come from the same group of participants (ex. taking a score from a sample before and after they perform a task)

The first research strategy represents this research strategy. It uses separate group of participants for each treatment condition (or for each population. i.e. men and women). It allows the researcher to use the data from 2 separate samples to evaluate the mean difference between the populations or treatment conditions

Null/Alternative hypotheses for hypothesis tests using this research design:

H_{0}: μ_{1} - μ_{2}= 0

H_{1}: μ_{1 - }μ_{2}≠ 0

Measuring effect size in these research designs:

1) Estimated Cohen's d is the estimated mean difference divided by the pooled (estimated) standard deviation. The formula for this would look like:

d = (M_{1} - M_{2})/√s_{p}²

2) The percentage of variance accounted for, r², is derived the same way for independent-measures test as it was for single sample tests where the variability accounted for by the treatment effect is divided by the total variability of the samples. The formula for this looks like:

r² -= t² / (t² + df)

3) Confidence intervals can be used for two-sample hypothesis tests to describe the size of a treatment effect. Using the df, determine the t statistic that will be used to define the interval, that has a particular proportion of the scores, is multiplied by the estimated standard error between M_{1} - M_{2}. This value is then added and subtracted from the sample mean difference in order to define the interval that the proportion of the distribution is within.

μ_{1} - μ_{2} = M_{1} - M_{2} +/- (t x s_{(M1 - M2)})

If the range of values does not include the H_{0} = 0_{ } it is possible to conclude, according to the proportion defined by the interval, that the value of zero is rejected. This is analogous to rejecting the H_{0} with an α of one minus the proportion defined by the confidence interval.