1) Be able to identify what kind of analysis is appropriate for the experimental design that is described.

Check the decision tree.

Currently our "bag of tricks" includes z-scores, 1-sample t-tests, repeated-measures t-tests, 2-independent samples t-tests, 1-way between groups ANOVA, 1-way repeated measurse ANOVA, Factorial ANOVA (between, within, and mixed).

• What test?
• What's the null hypothesis(ses)?
• How does the appropriate ANOVA analysis partition the variance (I'm not asking for the formulas here, just the parts [e.g., between treatments, between subjects, within treatments, error, factor A, etc.])

a) A researcher studies the effects of need for achievement and task difficulty on problem solving. The researcher uses two levels of achievement motivation (high versus low) and four levels of task difficulty. The number of errors each subject made was recorded. Different subjects were used for each of the conditions.

Solutions

b) Several years ago, a survey in a school district revealed that the average age at which students first tried an alcoholic drink was 14 years old. To determine if anything has changed, a random sample of students was asked questions about alcohol use. They were asked to report the age at which their drinking behavior first began.

Solutions

c) A human factores psychologist studied three computer keyboard designs. Three samples of individuals were given material to type on a particular keyboard, and the number of errors committeed by each subject was recorded.

Solutions

d) A psychologist studies the effect of practice on maze learning for rats. Rats are tested in the maze in one daily session for four days. The psychologist records the number of errors made in each daily session.

Solutions

e) A psychologist studying human memory would like to examine the process of forgetting. One group of subjects is required to memorize a list of words in the eventing just before going to bed. Their recall is tested 10 hours later in the morning. Subjects in the second group memorize the same list of words in the morning, and then their memories are tested 10 hours later after being awake all day. The psychologist hypothesizes that there will be less forgetting during sleep than during a busy day.

Solutions

f) A manufacturer of business machines would like to compare the four most popular brands of electric typewriters. A sample of eight typists is selected, and each typist spends 15 minutes testing each of the four typewirters and then rates its performance. The manufacturer would like to know if there are any significant differences among the four brands.

Solutions

2) Complete the following ANOVA tables.

(hint: write out all the information that you know from the table and given in the question. Then start with degrees of freedom. This should get you on your way. Remember: F = a ratio of Mean Squares (MS), MS = SS/df, SStotal = SS_{between treatments} + SS_{within treatments})

a) A common science-fair project involves testing the effects of music on the growth of plants. For one of these projects, a sample of 24 newly sprouted bean plants is obtained. These plants are randoml assigned to four treatments, with n = 6 in each group. The four conditions are rock, heavy metal, country, and classical music. The dependent variable is the height of each plant after 2 weeks. The data from this experiment werer examined using an ANOVA, and the results are summarized in the following table. Fill in all the missing values.

Source	SS	df	MS	F
Between treatments	90	_____	_____	_____
Within treatments	_____	_____	5
Total	______	_____

Solutions

b) A researcher studies the effects of need for achievement and task difficulty on problem solving. A two-factor design is used in which there are two levels of amount of achievment motivation and four levels of task difficulty. Each cell consists of n = 6 subjects. The number of errors each subject made was recorded, and the data were analyzed. The following table summarizes the results of the ANOVA, but it is not complete. Fill in the missing values.

Source	SS	df	MS	F
Between treatments	280	_____
Main effect of achievement	_____	_____	_____	_____
Main effect of task	_____	_____	48	_____
Interaction	120	_____	_____	_____
Within treatments	_____	_____	_____
Total	600	_____

Solutions

c) A manufacturer of business machines would like to compare the four most popular brands of electric typewriters. A sample of eight typists is selected, and each typist spends 15 minutes testing each of the four typewirters and then rates its performance. The manufacturer would like to know if there are any significant differences among the four brands. The data from this study were examined using an analysis of variance. The results are shown in the following summary table. Fill in the missing values.

Source	SS	df	MS	F
Between treatments	270	_____	_____	9
Within treatments	_____	_____
Between Subjects	_____	_____
Error	_____	_____	_____
Total	680	_____

Solutions

3) Know how to do the 1-way between groups ANOVA and 1-way repeated measures ANOVA by hand. I will provide a formula sheet and (parts) of the F-table.

a) An educational psychologist is studying student motivation in elementary school. A sample of n = 5 students is followed over three years from fourth grade to sixth grade. Each year the students complete a questionnaire measuring their motivation and enthusiasm for school. The psychologist would like to know whether there are significant changes in motivation across the three grade levels. The data from this study are as follows:

student fourth grade fifth grade sixth grade A 4 3 1 B 8 6 4 C 5 3 3 D 7 4 2 E 6 4 0

What kind of design is this? What kind of statistical analysis should be performed? Do the data indicate any (statistically) significant differences (at an alpha level of 0.05)? State the null hypothesis(ses) that you test. Present your results in an ANOVA table State your conclusions.

Solutions

b) First-born children tend to develop language skills faster than their younger siblings. One possible explanation for the phenomenon is that first-borns have undivided attention from their parents. If this explanation is correct, then it is also reasonable that twins should show slower language development than single children and that triplets should be even slower. Davis (1937) found exactly this result. The following hypothetical data demonstrate the relationship. The dependent variable is a measure of language skill at age three for each child.

single child twin triplet 8 4 4 7 6 4 10 7 7 6 4 2 9 9 3

What kind of design is this? What kind of statistical analysis should be performed? Do the data indicate any (statistically) significant differences (at an alpha level of 0.05)? State the null hypothesis(ses) that you test. Present your results in an ANOVA table State your conclusions.

Solutions

c) The following data are from a study examining the influence of a specific hormone on eating behavior. Three different drug does were used, including a control condition (no drug), and the study measured eating behavior for males and females. The dependent variable was the amount of food consumed over a 48-hour period.

No drug Small dose large dose Males 1 6 1 1 1 7 7 11 4 6 3 1 1 6 4 Females 0 3 7 5 5 0 0 0 5 0 5 2 0 0 3

What kind of design is this? What kind of statistical analysis should be performed? Do the data indicate any (statistically) significant differences (at an alpha level of 0.05)? (I won't ask you to do this kind by hand on the exam.) State the null hypothesis(ses) that you test. Present your results in an ANOVA table State your conclusions.

Solutions

4) Be able to identify the critical information from the SPSS output so that you can make decisions about your null hypotheses (including post hoc and planned comparison output for a 1-way between groups ANOVA).

a) A human factors psychologist studied three computer keyboard designs. Keyboard A is a standard keyboard, keyboards B and C are new designs. Three samples of individuals were given material to type on a particular keyboard, and the number of errors committed by each subject was recorded. The results of the statistical analysis are presented below. Based on these results are there differences between the different keyboards? How do the new keyboard designs compare with the standard keyboard?

Solutions

b) Individuals who are identified as having an antisocial personality disorder also tend to have reduced physiological responses to painful or anxiety-producing stimuli. In everyday terms, these individuals show a limited physical response to fear, guilt, or anxiety. One way of measuring the response is with the galvanic skin response (GSR). Normally, when a person is aroused, there is an increase in perspiration, which causes a measurable reduction in the electrical resistance on the skin. The results of the statistical analysis are presented below. In words, explain the findings of this study.

Solutions

c) When a stimulus is presented continuously and it does not vary in intensity, the individual will eventually perceive the stimulus as less intense or not perceive it at all. This phenomenon is known as sensory adaptation. Years ago, Zigler (1932) studied adaptation for skin sensation by placing a small weight on part of the body and measuring how much time lapsed until subjects reportd they felt nothing at all. Suppose that a researcher does a similar study, comparing adaptation for four regions of the body for a sample of n = 7 subjects. A 500-milligram weight is gently placed on the region, and the latency (in seconds) for a report that it is is no longer felt is recordd for each subject. The results of the statistical analysis are presented below. In words, explain the findings of this study.

Solutions

5) Conceptual questions.

a) Explain why you should never get a negative F-ratio

b) Why should we use planned contrasts or post-hoc tests instead of several t-tests to rule out alternative hypotheses?

c) What advantages does a repeated-measures design have over an independent-measures design?

d) How does the denominator of the F-ratio differ for a repeated-measures analysis of variance compared to an independent-measures (between groups) ANOVA?

e) What advantages does a factorial design have over 1-factor designs?