Answer:

This study examined differences in anxiety level between an industrial country and a nonindustrial country. Anxiety is assessed three ways—cognitive, affective, and behavioral—with higher scores indicating higher levels of the anxiety dimensions. Directions:

Using the SPSS data file 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? The independent variable is COUNTRY (Industrial and Non-Industrial). The dependent variables are Cognitive (COG), Affective (AFFECT) and Behavioral (BEHAVE). 2 Why is a one-way between-subject MANOVA appropriate to use for this research design? HINT:

Consider the number of IVs and the number of DVs for your answer. Here the number of independent variable is 1 but the numbers of dependent variables are more than 1 so when the number of dependent is more than 1, the appropriate technique is one-way between-subjects MANOVA

3 Did you find any errors that the researcher made when setting up the SPSS data file (don’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. All the four variables are shown as Nominal variable but in actual the COUNTRY should be a nominal variable and Cognitive (COG), Affective (AFFECT) and Behavioral (BEHAVE) should be scale variables. The scale of these variables is changed before the analysis. 4 Perform Initial Data Screening. What did you find regarding missing values, univariate outliers, multivariate outliers, normality? a. What should you consider when you find these kinds of outcomes? HINTS:

For missing values, see Case Processing Summary

Univariate outliers: inspect box plots

Multivariate outliers: Don’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 “Outliers” box that is found with Plots. This will give you information about multivariate outliers.

Normality:

Examine the skewness and kurtosis values for each dependent variable:

Examining the histograms

Examine the Shapiro-Wilks’ results

SPSS Output is given below for above question:

There is no missing value in the dataset. All 105 records are completed. The same can be seen from Case Processing Summary. From the box plots we can see that there are some outliers in the data for these three dependent variables. Most of the outliers are presented in the Industrial country as compare to Non-industrial country. The Mahalanobis Distance showed the outliers in the extreme value tables. It means that there are outliers presented in the data. The data is normally distributed as shown by the histogram. The From the above descriptive statistics of Cognitive variable, we can see that the mean is 7.98 with standard deviation as 1.623. The skewness value is -0.656 which is smaller than 0. It means that the distribution is right skewed because most values are concentrated on the left of the mean, with extreme values to the right. The kurtosis value is -0.253 which is less than 3.

It means that distribution is Platykurtic because the probability for extreme values is less than for a normal distribution, and the values are wider spread around the mean. The p-value for Shapiro-Wilk is 0.000 which is less than 0.05; it means that data is not normally distributed. The same result can be obtained from the plot of Histogram. For Affective variable, we can see that the mean is 7.98 with standard deviation as 2.308. The skewness value is -1.134 which is smaller than 0. It means that the distribution is right skewed because most values are concentrated on the left of the mean, with extreme values to the right. The kurtosis value is 0.750 which is less than 3. It means that distribution is Platykurtic because the probability for extreme values is less than for a normal distribution, and the values are wider spread around the mean. The p-value for Shapiro-Wilk is 0.000 which is less than 0.05; it means that data is not normally distributed.

The same result can be obtained from the plot of Histogram. For Behavioral variable, we can see that the mean is 7.8 with standard deviation as 2.28. The skewness value is -0.919 which is smaller than 0. It means that the distribution is right skewed because most values are concentrated on the left of the mean, with extreme values to the right. The kurtosis value is 0.024 which is less than 3. It means that distribution is Platykurtic because the probability for extreme values is less than for a normal distribution, and the values are wider spread around the mean. The p-value for Shapiro-Wilk is 0.000 which is less than 0.05; it means that data is not normally distributed. The same result can be obtained from the plot of Histogram.

5 Perform 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 Box’s Test) and sufficient correlation among the DVs (see Bartlett’s Test of Sphericity). Also check the results of the Levene’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 follow up ANOVAs? HINTS:

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 Bartlett’s Test of Sphericity). 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. SPSS Output for above question is given below:

Box’s test of Equality of Covariance Matrices P-value=0.388 is not significant. There is no violation of assumptions. The observed covariance matrices of the dependent variables are equal across groups. Bartlett’s Test of Sphericity p-value = 0.000 is significant. It means that the residual covariance matrix is not proportional to an identity matrix. There is a violation of the assumption. Levene’s Test of equality of variances are not significant for Cognitive and Affective but it is significant for Behavioral variable because p-value is smaller than 0.05 for this group. We can conclude that the error variance of the dependent variable is not equal across groups for Behavioral group. The “multivariate tests” section simultaneously tests each factor effect on the dependent groups. This is the most important table in this output.

Each factor and each covariate has a main effect, as does the intercept. Here these things are tested by four tests. Hotel ling’s Trace is commonly used for two dependent groups and Wilks’ Lambda if there are more than two groups. The significance of the F tests show if that effect is significant as the P-value is less than .05 in this case. 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 Wilks’ lambda or Pillai’s trace to interpret outcomes, or does it make a difference? Report either the Pillai’s Trace or Wilks’s Lambda for your results, as well as the associated F value and its statistical significance. Use the following format for notation: Pillai’s Trace OR Wilks’ lambda = ____; F(df, df) = ____, p = ____, 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, 2, and save the step of hand calculating 2 .) Since there are three dependent groups so Wilks’ Lambda will be used to interpret the outcome of multivariate analysis of variance. The significance of the F tests show if that effect is significant as the P-value is less than .05 in this case. Test of between subject effect output gives the univariate ANOVA effects for factor and interaction (and in MANCOVA each covariate). The significance of F and eta-squared have the same interpretation as in the multivariate analysis above. For instance, all univariate effects for all variables are significant here.

If the F test establishes that there is an effect on the dependent variable, the researcher then proceeds to determine just which group means differ significantly from others. This helps specify the exact nature of the overall effect determined by the F test. Pair wise multiple comparison tests test each pair of groups to identify similarities and differences. So from the above analysis all the tests have the p-value is less than 0.05 for multivariate tests as well as for tests of within subjects so we can say that there is a statistically significant difference between all the countries. There was a statistically significant difference in anxiety based on country, F (3, 101) = 3.067,p < .05; Wild’s Λ = 0.917, partial η2 = .083.

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 = _____ , 2 = _____ for each DV. ) Most of the important assumptions of the analysis are met and also the p-value for Wilks’ Lambda is significant so it is OK now to move on to interpret the results of the Tests of Between-Subjects Tests. We can see from this table that country has a statistically significant effect on Cognitive Anxiety (F (1, 103) = 4.046; p < .05; partial η2 = .038), Affective Anxiety (F (1, 103) = 4.196; p < .05; partial η2 = .039) and Behavioral Anxiety (F (1, 103) = 8.936; p < .05; partial η2 = .08). In other words we can conclude that

There was a statistically significant difference in Cognitive anxiety between an industrial country and a nonindustrial country, F (1, 103) = 4.046; p < .05; partial η2 = .038. There was a statistically significant difference in Affective anxiety between an industrial country and a nonindustrial country, F (1, 103) = 4.196; p < .05; partial η2 = .039. There was a statistically significant difference in Behavioral anxiety between an industrial country and a nonindustrial country, F (1, 103) = 8.936; p < .05; partial η2 = .08). 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 This study examined differences in anxiety level between an industrial country and a nonindustrial country. Anxiety is assessed three ways—cognitive, affective, and behavioral—with higher scores indicating higher levels of the anxiety dimensions. We can conclude that there is a significant difference in the anxiety level between an industrial country and a nonindustrial country. In simple words we can conclude that 1. There is a significant difference in the cognitive between an industrial country and a nonindustrial country. 2. There is a significant difference in the affective between an industrial country and a nonindustrial country. 3. There is a significant difference in the behavioral between an industrial country and a nonindustrial country.