MANOVA ANALYSISAD 601RESEARCH METHODS II

Elif Aydınlıyurt, Işıl Candemir

AGENDA

Introduction Stage 1: Objectives of MANOVA Stage 2: Research Design Stage 3: Testing the Assumptions Stage 4: Estimation of the MANOVA

Model and Assessing Overall Fit Stage 5: Interpretation of the Results Stage 6: Validation of the Results

INTRODUCTION

MANOVA is a dependence technique that uses the set of metric variables as dependent variables and its objective is to find groups that exhibit differences on the set of dependent variables.

It uses independent nonmetric variables to form groups then looks for significant differences in the dependent variable variate that is associated with specific nonmetric variables.

Manova combines the dependent variables to form a “new” dependent variable in such a way as to maximize the differences between the groups of the independent variable. In this new composite variable the objective is to test for statistically significant differences between the groups.

STAGE 1: OBJECTIVES OF MANOVA Research Question:What differences are there in terms of e-

commerce success and product quality between the two different industry types?

The task is to identify whether any differences exist between these two industry types and assess the extent to which these differences are significantly different, both individually and collectively.

VARIABLES

In order to run a one-way MANOVA, one independent variable that is categorical with two or more levels and two or more dependent variables that are continuous are required.

E-commerce + Product Quality = Industry Type

STAGE 2: RESEARCH DESIGN Sample Size The sample in each group must be greater than the number

of dependent variables and the recommended minimum group size is 20 observations.

Another requirement is that researchers should try to maintain equal or approximately equal sample sizes per group.

In our sample, we have two groups and each group has 100 observations. Our sample size per group (100) is greater than the number of our dependent variables and it also exceeds the minimum level of 20. Also the sample size in each group are equal.

SAMPLE SIZE

To achieve the suggested power level of 0.80 in MANOVA we also checked the Sample Size Requirements table and we concluded that our sample size is even greater than the required sample size when the group size is 3, the number of dependent variables is 2 and the effect size is small (100 > 98), so our sample size is adequate.

MISSING DATA & OUTLIERS

Missing Data There is no missing data.

Outliers To detect outliers first we converted the metric

dependent variables to their standard scores to see if there are very large positive or negative standard scores.

Converting them to standard scores gave us a standard deviation unit of measurement so that the distance from the mean for any variable was expressed.

OUTLIERS

Since our sample is bigger than 80, our threshold value is 4 and looking at the results, we didn’t detect any outliers.

OUTLIERS

To inspect outliers further, we also looked at boxplots.

OUTLIERS

There are a few outliers, but since no observation was an extreme value on all two dependent measures and no observation had a value so extreme, the boxplots do not suggest exclusion of the outliers.

OUTLIERS

Our last check for detecting outliers was to calculate the Mahalanobis D² which measured the distance from the center for a set of scores. We used the conservative level of significance; 0.005 for statistical significance.

STAGE 3: TESTING THE ASSUMPTIONS

1- Independence of Observations2- Multivariate Normality

3- No multicollinearity4- Correlation5- Linearity

6- Homoscedasticity

STAGE 3: TESTING THE ASSUMPTIONS1- Independence of Observations

- No relationship between the observations

- Ensured as much as possible by random sampling

- HBAT data used, assumed no relationship between respondents and they chosen randomly

2- Multivariate normality

- Sampling distribution normally distributed, central limit theorem

- Multivariate normality , each metric variable assessed

-3 techniques used: (1) Graphical analysis, (2) z-scores, (3) Kolmogorov-Smirnov Test and Shapiro-Wilk Test

STAGE 3: TESTING THE ASSUMPTIONS2- Multivariate normality

(1) Graphical analysis

STAGE 3: TESTING THE ASSUMPTIONS2- Multivariate normality

(2) Z-scores

Product quality

z-skewness: 1.6570

z-kurtosis: 3.1062

E-commerce

z-skewness: 2.8291

z-kurtosis: 0.2136

p=0.01 threshold z: +/- 2.68

p=0.001 thresold z: +/- 3.29

STAGE 3: TESTING THE ASSUMPTIONS2- Multivariate normality

(3) Kolmogorov-Smirnov Test and Shapiro-Wilk Test

Conclusion:

- Tests are sensitive for larger sample

- Central limit theorem, sample size is 200. Our data is nonnormal, but nonnormality is negligible. We keep the data.

STAGE 3: TESTING THE ASSUMPTIONS3- No multicollinearity

- No strong correlation between variables

4- Correlation

- Dependent variables are significantly correlated

STAGE 3: TESTING THE ASSUMPTIONS5- Linearity

- A linear relationship btw dependent variable for each group of independent variable. In the reverse case, power loss

- No linear relationship, we accept the loss of power

STAGE 3: TESTING THE ASSUMPTIONS6- Homoscedasticity (Homogeneity of variance-

covariance matrices)

- The dependent variable exhibits similar amounts of variance across the range of values for an independent variable

- 2 techniques used: (1) Graphical analysis, (2) Box’s Test and Levene’s Test

(1) Graphical analysis

STAGE 3: TESTING THE ASSUMPTIONS6- Homoscedasticity (Homogeneity of variance-

covariance matrices)

(2) Box’s Test and Levene’s Test

STAGE 4: ESTIMATION OF THE MANOVA MODEL AND ASSESSING OVERALL FIT Our next step in our analysis was to see whether if the two

groups exhibited statistically significant differences for the different dependent variables; product quality and e-commerce.

We first specified the maximum allowable Type 1 error rate. We accepted that 5 times out of 100, we might conclude that the type of industry has an impact on the product quality and e-commerce success when in fact it did not.

  Then we used the multivariate tests to test the set of

dependent variables for differences between the two groups and then performed univariate tests on each dependent variable.

OUTPUTS

The descriptive statistics table contains the overall and group means and standard deviations for each dependent variable.

OUTPUTS

In the multivariate test results, looking at the group effects we see that they are all (0.102) bigger than 0.05 therefore not significant. Therefore we accept the null hypothesis that there are no between-group differences.

OUTPUTS

Looking at the univariate tests we saw that there was an insignificant difference between industry types in terms of product quality (0.488>0.05) but a significant difference between industry types in terms of e-commerce (0.041<0.05).

STATISTICAL POWER

Power is the probability of detecting an effect, given that the effect is really there.

STAGE 5: INTERPRETATIONS OF THE RESULTS- The effect of the industry type on e-commerce and product quality

success

- Data is not normally distributed, but because our sample size is 200, effects of nonnormality may be negligible and we keep the data

- No univariate and multivariate outliers, as assessed by boxplot and Mahalanobis distance (p>0.001)

- No multicollienarity (r=-.034, p=.630)

- There is homogeneity of variance-covariance matrices, as assessed by Box’s M test (p=0.019)

- HBAT success in magazine industry and newspaper industry with respect to product quality (7.962 +/- 1.3342, 7.826 +/- 1.4336, respectively) is higher than with respect to e-commerce (3.654 +/- 0.7301, 3.876 +/- 0.7941, respectively)

- The differences between industry types on the combined dependent variables are not statistically significant ( F(2,197)=2.310b, p>0.05, Wilks’ Ʌ= 0.977, partial η2 =0.023)

STAGE 6: VALIDATION OF THE RESULTSIn order to validate the results, we choose first 50

measures for each group and generate a sample of size 100

Thank You