Statistical - Write up of Results

For each problem, submit a document that describes:

1. (1)  the research question(s) of interest

2. (2)  the method of analysis and why it is appropriate

3. (3)  the assumptions that underlie the method

4. (4)  the statistical tests to be conducted

5. (5)  a discussion of results that will answer the research question

Assume you are writing the "methods" section of a research paper to be submitted to a professional journal.

Problem Set 2 answer

1- The research questions

Is to determine whether the means of the outcome variables described above differ depending on performance level.

2- The method of analysis used in this case is MANOVA and why it is appropriate Multivariate analysis of variance (MANOVA) is simply an ANOVA with several dependent variables. That is to say, ANOVA tests for the difference in means between two or more groups, while MANOVA tests for the difference in two or more vectors of means this is why we have to used here.

3- Assumptions

· Equality regarding covariance matrices

· Each sample group is taken from a normally distributed population

· The observations are sampled independently and randomly of each other

4- the statistical tests to be conducted

It's better to conduct Bonferroni is more flexible and easier to compute, it has limitations. Bonferroni assumes that tests are independent while calculating familywise error

-5-discussion of results that will answer the research question

- Discussion of results - MANOVA

Test Criteria and Exact F Statistics. for the Hypothesis of No Overall PERLEVEL Effect

H = Anova SSCP Matrix for PERLEVEL E = Error SSCP Matrix

S=1 M=1.5 N=36

Statistic Value F Value Num DF Den DF Pr > F

Wilks' Lambda 0.67500180 7.13 5 74 <.0001

Pillai's Trace 0.32499820 7.13 5 74 <.0001

Hotelling-Lawley Trace 0.48147752 7.13 5 74 <.0001

Roy's Greatest Root 0.48147752 7.13 5 74 <.0001

(p-values for MANOVA test of Ho: no mean vector differences between the 2 PERLEEVEL groups)

Levene's Test for Homogeneity of EFFORT Variance

Sum of Mean

Source DF Squares Square F Value Pr > F

PERLEVEL 1 1.0414 1.0414 0.30 0.5832

p-value for testing equality of variances in DV for 2 PERLEVEL groups

(Fail to reject Ho implies equality of variances)

- Discussion of results - ANOVA

1st Dependent Variable analyzed EFFORT

Corrected Total 79 136.1875000

R-Square Coeff Var Root MSE EFFORT Mean

0.167933 28.78363 1.205315 4.187500

Source DF Anova SS Mean Square F Value Pr > F

PERLEVEL 1 22.87039385 22.87039385 15.74 0.0002

· There is a significant difference in the mean

2en Dependent Variable analyzed UND

Source DF Squares Mean Square F Value Pr > F

Model 1 9.3002113 9.3002113 3.92 0.0513

Error 78 185.1872887 2.3741960

Corrected Total 79 194.4875000

R-Square Coeff Var Root MSE UND Mean

0.047819 36.36207 1.540843 4.237500

Source DF Anova SS Mean Square F Value Pr > F

PERLEVEL 1 9.30021129 9.30021129 3.92 0.0513

· There is NO significant difference in the mean

3rd Dependent Variable analyzed QUALIT

Source DF Squares Mean Square F Value Pr > F

Model 1 7.6597701 7.6597701 5.45 0.0221

Error 78 109.5402299 1.4043619

Corrected Total 79 117.2000000

R-Square Coeff Var Root MSE QUALITY Mean

0.065356 28.90385 1.185058 4.100000

Source DF Anova SS Mean Square F Value Pr > F

PERLEVEL 1 7.65977011 7.65977011 5.45 0.0221

• There is NO significant difference in the mean

4rd Dependent Variable analyzed LUCK

Source DF Squares Mean Square F Value Pr > F

Model 1 10.5261663 10.5261663 3.64 0.0599

Error 78 225.2738337 2.8881261

Corrected Total 79 235.8000000

R-Square Coeff Var Root MSE LUCK Mean

0.044640 37.35052 1.699449 4.550000

Source DF Anova SS Mean Square F Value Pr > F

PERLEVEL 1 10.52616633 10.52616633 3.64 0.0599

• There is NO significant difference in the mean

5rd Dependent Variable analyzed DIFF

Source DF Squares Mean Square F Value Pr > F

Model 1 4.3206981 4.3206981 2.50 0.1180

Error 78 134.8668019 1.7290616

Corrected Total 79 139.1875000

R-Square Coeff Var Root MSE DIFF Mean

0.031042 39.69624 1.314938 3.312500

Source DF Anova SS Mean Square F Value Pr > F

PERLEVEL 1 4.32069811 4.32069811 2.50 0.1180

• There is NO significant difference in the mea