CRIM 483

Chapter 9: Testing differences between the means of different

groups

Putting It Into Perspective

• Two essential components in using statistics appropriate include:– Having a clear understanding of what you are

testing– Having a clear understanding of which

statistical test is appropriate• T-test statistic is method that expands the

types of questions you can examine

The T-Test Statistic• The t-test can be used to examine the following:

– The mean difference between two groups– The mean difference within related groups (pre/post-test)

• This class only focuses on the first type of test– See formula on p. 163

• Deciding to use the t-test:– Must be examining the difference between groups on one factor– The same participants are not being tested more than once– There are only two groups (Note: A t-test cannot be used to test

the mean differences between more than two groups)

When to Use--Examples• A t-test of this type is appropriate to use in the

following examples:– To determine whether perceptions of equality differ

across males and females– To determine age differs between property offenders

and violent offenders• In each of the examples above, only one point in

time is considered (i.e., data were not collected at multiple points in time)

• Do not use a t-test for nominal variables

Book Example

1. State the null and research hypothesisNull: The teaching methods for Alzheimer patients will

not result in different levels of memory recall.Research: Alzheimer patients who received visual aid

teaching methods will differ in their ability to remember the order of daily tasks from the patients who received intense verbal rehearsal.

Example, Continued

2. Set the level of risk: .05—There is only a 5% chance that the relationship is due to chance alone.

3. Select the appropriate statistic—Since the hypotheses are testing whether the level of memory recall differed across two different teaching styles, a t-test would be appropriate.

Example, Continued4. Compute the value—Using the data on p. 164, the

resulting t-value is -.145. Identify the critical value—The point at which the

probability is .05 or less• Determine the degrees of freedom ((n1+n2)-

2))=df; 30+30-2=58• Using the t-test table, determine that the critical t-

value is 2.0016. Compare obtained value to critical value

• -.14 is less than 2.0017. Make a decision…does memory recall differ by

teaching method?

Effect Size• Significance v. meaningfulness• An effect may be significant but not meaningful—to

assess meaningfulness, you can calculate effect size: – ES=(X1-X2)/SD (NOTE: Assumes the standard deviations

between two groups is equal• Evaluating effect size

– 0=very similar and overlap entirely– Small effect=0-.20– Medium effect=.20-.50– Large effect=.50 and above – 1.00=overlap between variables=45%

• In the current example, the effect size is .37 ((7.46-6.90)/1.53) or medium

Book example using SPSS: Chapter 9 Data Set 1

Homework

• Page 176: 1-3

• Chapter 9 Data Sets 2 & 3 are posted on the class website