# Analysis of variance

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The dependent variables are Cognitive (COG), Affective (AFFECT) and Behavioral (BEHAVE). 2 Why is a one-way between-subject NOVA appropriate to use for this research design? HINT: Consider the number of Avis and the number of DVD 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 NOVA 3 Did you find any errors that the researcher made when setting up the SPAS 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, universal outliers, multivariate outliers, normality? . What should you consider when you find these kinds of outcomes? HINTS: For missing values, see Case Processing Summary Universal 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 Classed as the DVD and Country as the IV in order to compute the Inhalations 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 AMAH 1).

Then, Explore AMAH 1 scores, remembering to check the “Outliers” box that is found with Plots. This will give you information about multivariate outliers. Normality: Examine the keenness and kurtosis values for each dependent variable: Examining the histograms Examine the Shapiro-Wills’ results SPAS 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 Inhalations 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 keenness value is -0. 656 which is smaller than O. 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 Plasticity because the arability for extreme values is less than for a normal distribution, and the values are wider spread around the mean. The p-value for Shapiro-Will 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 keenness value is -1 . 134 which is smaller than O.

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. 50 which is less than 3. It means that distribution is Plasticity 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-Will 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. With standard deviation as 2. 28. The keenness value is -0. 919 which is smaller than 0. It means on the left of the mean, with extreme values to the right. The kurtosis value is 0. 24 which is less than 3. It means that distribution is Plasticity 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 Sponsorship 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. Perform one- way between-subjects NOVA on the data. Before interpreting the results of the NOVA, check outcomes that test other assumptions for this statistic: equality of covariance matrices (see Box’s Test) and sufficient correlation among he DVD (see Barrette’s Test of Specificity). Also check the results of the Eleven’s Test of Equality of Error Variances to evaluate that assumption for the universal Novas 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 NOVA and follow up Novas?

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 SSP matrix within Options to get the results of the Barrette’s Test of Specificity). 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. SPAS 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. Barrette’s Test of Specificity 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. Eleven’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 lining’s Trace is commonly used for two dependent roofs and Wills’ 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 DVD 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 Wills’ lambda or Pillar’s trace to interpret outcomes, or does it make a difference? Report either the Pillar’s Trace or Wilkins Lambda for your results, as well as the associated value and its statistical significance. Use the following format for notation: Pillar’s Trace OR Wills’ lambda = F(UDF, UDF) 02- . What does this information tell you about the difference between the two countries on the linear combination (the variant) of the dependent variables?

HINT: Here, and ONLY for a one-way NOVA with only two groups for the IV, ate squared and partial ate squared are the same value; you can use the value given for partial ate squared in the SPAS results of the Multivariate Tests to be ate squared, 02, and save the step of hand calculating 02 . ) Since there are three dependent groups so Wills’ Lambda will be used to interpret the outcome of ultimate 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 universal NOVA effects for factor and interaction (and in MANIOCS each covariate). The significance of F and ate-squared have the same interpretation as in the multivariate analysis above. For instance, all universal 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 A = 0. 917, partial n2 = . 083. 7 Given the results of the ultivariate tests, is it 0K now to move on to interpret the results of the Tests of Between-Subjects Tests? 