ANOVA Statistics in Psychology - Essay Example

While a two-sample t-test attempts to verify if the difference seen in the means of two groups is significant, the ANOVA attempts to understand if the variance estimates of the two groups are significantly different. Thus, the ANOVA helps in understanding if two groups with similar mean scores also share estimates of variance or whether the groups are genuinely different in the way the scores vary within the group.

The ANOVA can be used to verify the differences among groups’ performance in different settings. For example, it could be used to verify which of the different mnemonic devices are useful for a particular subject. In order to do so, it is possible to choose two or three mnemonic devices and ask different groups of students to use one device each while studying for a mock test. A control group could be asked to study without using any mnemonic devices to serve as a control group. After the test, the scores for each group may be collected, and by using the ANOVA it would be possible to see if the groups’ variance is similar or different from that of the others. For this study, the type of mnemonic device used would be the independent variable and the scores (performance) on the mock test would be the dependent variable.

Part 2

A researcher compares men's and women's attitudes toward "road rage." Specifically, college students are asked to read a brief scenario describing a road rage incident in which a driver of a car attempts to scare a bicycle rider who accidentally cut across his path. The driver aims his car at the bicyclist and the bicycle rider, in an attempt to get out of the way, falls and gets hurt. Men and women rate how much they are disturbed by the driver's reaction using a 10-point scale (1 = not disturbed at all, 10 = very disturbed). The mean for men was 7.4 and the mean rating for women was 8.6. A t-test for independent groups indicated the following result: t (28) = 2.76, p = .01. Answer the following questions about the results of this hypothetical experiment.

1. Were the results statistically significant?

Yes, the results of the t-test conducted were statistically significant; showing that women's ratings of how disturbed they were by the driver’s reaction were significantly higher than that of men.

2. How many men and women were there in this study (assuming equal numbers in each condition)?

The sample for this study consisted of 30 individuals (d.f. +2 = n). thus, assuming equal numbers, the sample has 15 men and 15 women.

3. What does the p-value tell you in addition to the fact that the results may be considered statistically significant?

The p-value shows that the chances of the observed difference between the ratings of men and women’s scores occurring by chance and thus, of it being not representative of the population are 1 in 100. This means that the chance of the observed difference being a genuine reflection of the population condition is 99 out of 100.

4. Is a Type II error possible in this study?

No, Type II error is not possible in this study. A Type II error is when the null hypothesis is accepted even though is actually false. In this study, the null hypothesis has been rejected as the difference between the two groups was found to be significant.

5. What should the researcher report along with the results of the t-test?

The researcher should report the confidence intervals for the results and the effect size of the t-statistic. This will help in understanding the strength of the observed difference.