Multivariate Stats
Psych 716
Spring 2014
Homework #2
For the following questions, please provide information about specific results relevant to your interpretations. That is, be clear about which tables, plots, specific values, etc are the basis of your interpretations. You may provide values in the text of your answer, copy and paste specific pieces of output form SPSS, or print the key results (I don’t need everything) and clearly refer to facets of the output. In fact, it wouldn’t hurt to even mark on the output, so that I know exactly what you might be referring to. Your goal should be to convince me that you have a firm grasp on the issues in factor analysis, that you know what the results mean and how to interpret them. For any answers that require you to conduct analysis by hand, please show your work.
1. Interpreting Multilevel modeling results. (6 pts)
A researcher is interested in happiness, social interaction, and personality. He hypothesizes that, when people are around other people, they tend to be happier than when they are alone. He also hypothesizes that the link between “being around people” and “happiness” is stronger for people who have relatively high levels of extraversion, as compared to people who have relatively low levels of extraversion.
To evaluate these hypotheses (and others) he conducts a repeated-measures study. Each participant (oh, let’s say there are 6 participants) carries an ipod around for 5 days. Each day, participants’ ipods are set to “go off” once – they signal the participant, and the participant responds to two questions with regard to the situation that they are in at that moment: a) in whatever situation you’re in right now, how many people are you with?, and b) how happy are you in this situation (on a 1-700 scale). Each participant also completes a measure of the Big Five, from which the researcher gets an extraversion score for each participant.
The researcher collects the data, analyzes it via MLM and gets the following results. Note that she centered all relevant predictors. Also note – you probably want to consult the class handout/example to address the questions below.
a) What is the level 1 “unit of observation” and what are the level 1 variables? 1 pt
b) What is the level 2 unit of observation, and what is the level 2 variable? 1 pt
c) Interpret each of the parameter estimates in the results – what does each value represent, and are the researchers’ two hypotheses confirmed or disconfirmed? 4 pts
2. Purposes (7 pts)
o Experience in conducting and interpreting a MANOVA
o Experience in writing the relevant results
A researcher examined the effects of homeless status (chronic, acute, and currently not homeless) on people’s perceived life satisfaction as measured by quality of life and general health status. Using SPSS to analyze the “homelessness.sav” data set from the class web site, please answer the following questions….
a. Is there sufficient correlation among the dependent variables to justify the use of MANOVA?
b. Was the assumption of Equality of Covariance Matrices violated? Explain.
c. How large is the multivariate effect of homeless status (in terms of an effect size)?
d. Is there a statistically significant multivariate effect of homeless status on the dependent variate?
e. Which of the dependent variables achieved statistically significant differences among the groups? What is the size of this effect?
f. Conduct and interpret any remaining step(s) in the analyses, assuming you’re using the conventional analytic strategy
g. Write a Results section for this study.
3. Logistic Regression (4 pts)
An evolutionary psychologist is interested in mating behavior – specifically, in cheating on one’s spouse or significant other. The researcher hypothesizes that males will show a greater tendency to cheat (yeah right!). Furthermore, he hypothesizes that this gender difference arises because males have a higher level of sociosexuality (degree of interest in casual sex). He surveys 50 participants, measuring: a) whether they’ve ever cheated on a romantic partner, b) their own gender, and c) sociosexuality. (see the Based on the “Logistic.sav” data set online). Please answer the following questions (.5 each)….
Basic associations (you can just look at correlations here):
a. To what degree do males and females differ in cheating behavior?
To what degree is sociosexuality associated with cheating behavior?
To what degree does the average male have a greater/lesser degree of sociosexuality than the average female?
Simple odds ratios and probabilities
b. Compute (by hand using a 2x2 table, like we did at the beginning of the class on logistic regression) and interpret the odds ratio expressing the association between gender and cheating. Also based on this, what is the probability that a male will have cheated in this sample?
Basic Logistic regression
c. Using the output of a single-predictor logistic regression, what are the log odds, odds, and probability that a male will have cheated?
d. Does the odds ratio from the SPSS output match the odds ratio you computed above?
e. According to logistic regression, is there a significant association between gender and cheating?
Multiple Logistic regression
f. Roughly, what are the combined effects of the two predictors on cheating behavior?
g. Which predictor has the stronger unique association with cheating behavior? Note and interpret the relevant results.
h. Using multiple logistic regression (and any other relevant analyses that you’ve conducted), discuss the evidence that gender differences in sociosexuality account for the apparent gender differences in cheating behavior.
4. Regression with a Categorical Variable (AKA Oneway ANOVA through Regression) (6 pts)
This question is intended to give you practice conducting and interpreting regression when you have a categorical variable with more than two levels.
A researcher is interested in the efficacy of different types of therapy on psychological well-being. A sample of clinical clients are recruited and each participant is randomly assigned to one of three conditions: a) Cognitive Therapy, B) Behavioral Therapy, C) Freudian Therapy. Participants go through their therapy for 3 months and then complete a measure of psychological well-being. The researcher hires you to evaluate specific hypotheses about the effect of therapy on Overall well-being.
Download the “Categorical Predcitor.sav” data set from the class web site. See the “Values” information in the “Variable View” tab, to see which group is which). Note that the well-being scale had 8 items, and the researcher has computed the sum of these items to use as the “Overall Well-being” DV. Use regression to examine differences among “types of therapy”, in terms of their effects on Overall Well-being. For your own interpretational benefit, I suggest you compute the group means on the DV. Along with the grand mean (e.g. using the Descriptives procedure).
1. Please report the overall amount of variance explained (by differences among types of therapy) in well-being and report whether this is significant (providing the relevant values for both pieces of information). See Question 2 to determine how you might want to approach Question 1.
2. Use regression to test ONE of the following pairs of hypotheses:
Pair 1:
1a. Cognitive therapy is more effective than Freudian Therapy
1b. Behavioral Therapy is more effective than Freudian Therapy
Pair 2:
2a. “Modern Therapies” (i.e., Cognitive and Behavioral Therapy) are generally more effective than Freudian Therapy
2b. Cognitive Therapy is more effective than Behavioral Therapy.
Whichever pair of hypotheses you choose to test, please be sure to:
· interpret the intercept and slopes from your analysis (here’s where you might want to consider the means ,
· interpret the statistical significance of those values,
· comment on the support (or lack thereof) for the hypotheses you choose to test.