Statistical Methods

Until now, we’ve used inferential statistics that used a single sample as the basis for drawing conclusions about a population.

Although these single-sample techniques are used occasionally in real research, most studies require the comparison of two or more sets of data.

There are two general strategies that can be used to obtain the two sets of data being compared:

1. Completely separate samples—random assignment, teaching method a and b; by variables, male and female

2. The two sets could both come from the same sample—before and after test

Using completely separate samples is referred to as independent measures or between subjects designs

When two sets of data are obtained from the same sample, it is called a repeated measures design or a within subjects design.

Because an independent measures study involves two separate samples, we will need some special notation to help specify which data go with which sample.

This notation involves the use of subscripts—usually a 1 and a 2 to correspond to group 1 and group 2.

H₀: μ₁ – μ₂ = 0

H₁: μ₁ – μ₂ ≠ 0

For the independent measures t formula, the standard error measures the amount of error that is expected when you use a sample mean difference to represent a population mean difference

State the hypotheses and the alpha level

df = (n₁ – 1) + (n₁ – 1)

Look up corresponding value of t in t table.

Find the Pooled Variance for the two Samples

Use the Pooled Variance to compute the estimated standard error:

Compute t

Make a decision—the criteria is the same as for z and t that we’ve done before

If the computed value is greater than the critical value, reject H₀