# Mathematic Expert

Hello,

**Anxiety and Country**

This study examined differences in anxiety level between an industrial country and a nonindustrial country. Anxiety is assessed three waysâ€”cognitive, affective, and behavioralâ€”with higher scores indicating higher levels of the anxiety dimensions.

**Directions:**

Using the SPSS data file for Module 5 (located in Topic Materials), answer the following questions. NOTE: Helpful hints are provided here for you to use while answering these questions.

1. What is the ONE independent variable in this study? What are the dependent variables?

2. Why is a one-way between-subjects MANOVA appropriate to use for this research design?

HINT:

Consider the number of IVs and the number of DVs for your answer.

3. Did you find any errors that the researcher made when setting up the SPSS data file (donâ€™t forget to check the variable view)? If so, what did you find? How did you correct it?

HINT:

YES! The Measures (for scale of measurement) is wrong for each of the 4 variables! You need to indicate what was wrong and what should be the correct measures.

4. Perform Initial Data Screening. What did you find regarding missing values, univariate outliers, multivariate outliers, normality? Although you are not asked to make adjustments, what should you consider when you find these kinds of outcomes?

HINTS:

Â· For missing values, see Case Processing Summary

Â· Univariate outliers: inspect boxplots

Â· Multivariate outliers: Donâ€™t forget to create the Case ID variable to do this analysis. Then, perform a regression analysis with CaseID as the DV and Country as the IV in order to compute the Mahalanobis distance measures. Be sure to click Save when you are setting up the regression so the regression scores will be saved to a new variable (automatically named MAH_1). Then, Explore MAH_1 scores, remembering to check the â€œOutliersâ€ box that is found with Plots. This will give you information about multivariate outliers.

Â· Normality:

Â§ Examine the skewness and kurtosis values for each dependent variable:

Â§ Examining the histograms

Â§ Examine the Shapiro-Wilksâ€™ results

5. Perform a one-way between-subjects MANOVA on the data. Before interpreting the results of the MANOVA, check outcomes that test other assumptions for this statistic: equality of covariance matrices (see Boxâ€™s Test) and sufficient correlation among the DVs (see Bartlettâ€™s Test of Sphericity). Also check the results of the Leveneâ€™s Test of Equality of Error Variances to evaluate that assumption for the univariate ANOVAs that are run and show in the Tests of Between-Subjects Effects output. What have you found about whether the data meet these additional assumptions for the MANOVA and followup ANOVAs?

HINTS:

Â· Be sure to read the instructions very carefully in the textbook for what to check to get these results for these tests of assumptions (e.g., you have to check Residual SSCP matrix within Options to get the results of the Bartlettâ€™s Test of Sphericity).

Â· Be sure to review what a statistically significant outcome means for each test: in some cases, it means a violation, but in others it means an assumption is met.

6. What is the outcome of the multivariate tests (which looks at the effects of the IV on all three DVs at the same time)? Given results of your tests for homogeneity of variance-covariance matrices for the dependent variables, is it more appropriate to use Wilksâ€™ lambda or Pillaiâ€™s trace to interpret outcomes, or does it make a difference? Report either the Pillaiâ€™s Trace or Wilksâ€™s Lambda for your results, as well as the associated F value and its statistical significance. Use the following format for notation: Pillaiâ€™s Trace OR Wilksâ€™ lambda = ____; F(df, df) = ____, p = ____, h^{2}= _____. What does this information tell you about the difference between the two countries on the linear combination (the variate) of the dependent variables?

HINT:

Here, and ONLY for a one-way MANOVA with only two groups for the IV, eta squared and partial eta squared are the same value; you can use the value given for partial eta squared in the SPSS results of the Multivariate Tests to be eta squared, h^{2}, and save the step of hand calculating h^{2} .)

7. Given the results of the multivariate tests, is it OK now to move on to interpret the results of the Tests of Between-Subjects Tests? Why? Explain. If yes, what are the results and what do they mean? (Report each of the results using the format of *F*(df, df) = _____, *p* = _____ , h^{2 }= _____ for each DV. )

8. Citing the results of your statistical analyses, what is the conclusion you can draw (and support) regarding research question that was posed in this research (see problem statement)?

HINT: Use the sample results write-up in the textbook to see what you should report and how to say it. Just substitute the correct language and values for the analyses you have done for this problem.