ANOVA
Research Question
RQ: Is there a difference between the eating habits of mice who are subjected to
country music, rock music or classical music?
Null Hypothesis
H0: There is no significant difference between the eating habits of mice who are
subjected to country music, rock music, or classical music.
Sub-Null Hypotheses (Post Hoc)
H01sub: There is no significant difference between the eating habits of mice who are
subjected to country music and rock music.
H02sub: There is no significant difference between the eating habits of mice who are
subjected to country music and classical music.
H03sub: There is no significant difference between the eating habits of mice who are
subjected to classical music and rock music.
Data screening
Screening: Sort data and look for unusual scores and inconsistencies.
Outliers: Use a Box and Whisker plot for each group and/or variable. Look for extreme
outliers.
Assumptions
Assumption of Normality: Use Shapiro-Wilks or Kolmogorov-Smirnov.
Assumption of Equal Variance: Use Levene's Test of Equality of Error Variance
Report Results
F- statistic: Use F- statistic for the main null. If the null is not significant then stop. If null
is significant then proceed with Post Hoc analysis.
Post Hoc: Use Tukey method for testing sub-nulls.
MANOVA
Research Question
RQ: Is there a difference between the eating habits and sleep habits of mice who are
subjected to country music, rock music or classical music?
Null Hypothesis
H0: There is no significant difference between the eating habits and sleep habits of mice
who are subjected to country music, rock music or classical music.
Sub-Null Hypotheses (Post Hoc)
H01sub: There is no significant difference between the eating habits of mice who are
subjected to country music and rock music.
H02sub: There is no significant difference between the eating habits of mice who are
subjected to country music and classical music.
H03sub: There is no significant difference between the eating habits of mice who are
subjected to classical music and rock music.
H04sub: There is no significant difference between the sleep habits of mice who are
subjected to country music and rock music.
H05sub: There is no significant difference between the sleep habits of mice who are
subjected to country music and classical music.
H06sub: There is no significant difference between the sleep habits of mice who are
subjected to classical music and rock music.
Data screening
Screening: Sort data and look for unusual scores and inconsistencies.
Outliers: Use a Box and Whisker plot for each group and/or variable. Look for extreme
outliers.
Assumptions
Assumption of Normality: Use Shapiro-Wilks or Kolmogorov-Smirnov.
Assumption of Multivariate Normal Distribution: Look for a linear relationship between
each pair of dependent variables. If the variables are not linearly related, the power of
the test is reduced. You can test for this assumption by plotting a scatterplot matrix for
each group of the independent variable. Look for the classic “cigar shape.”
Assumption of Homogeneity of Variance-Covariance matrices: You can test this
assumption in SPSS using Box's M test of equality of covariance. If your data fails this
assumption (p < .05), you may also need to use SPSS to carry out Levene's test of
homogeneity of variance to determine where the problem may lies.
Absence of multicollinearity: The dependent variables should all be moderately related,
but any correlation over r = .80 presents a concern for multicollinearity. Use a Pearson
Product Moment test.
Report Results
Wilks’ Lambda: Use Wilks’ Lambda for the main null. If the null is not significant then
stop. If null is significant then proceed with Post Hoc analysis.
Post Hoc: Use Bonferroni method for testing sub-nulls.
Multiple Regression
Research Question
RQ: How accurately can GPA be predicted from a linear combination of Lifestyle Index
factors for college students?
Null Hypothesis
H0: There will be no significant predictive relationship between the criterion variable
(GPA) and the linear combination of predictor variables (sleep, diet, exercise, and social
activities) for college students.
Sub-Null Hypotheses (Post Hoc)
H01sub: There will be no significant predictive relationship between GPA and sleep for
college students.
H02sub: There will be no significant predictive relationship between GPA and diet for
college students.
H03sub: There will be no significant predictive relationship between GPA and exercise for
college students.
H04sub: There will be no significant predictive relationship between GPA and social
activities for college students.
Data screening
Screening: Sort data and look for unusual scores and inconsistencies.
Outliers: Use a Box and Whisker plot for each variable. Look for extreme outliers.
Assumptions
Assumption of Bivariate Outliers: Use scatter plots between all pairs of independent
variables (x, x) and also the predictor variables (x) and criterion variable (y). Look for
extreme bivariate outliers.
Assumption of Multivariate Normal Distribution: Look for a linear relationship between
each pair of variables. If the variables are not linearly related, the power of the test is
reduced. You can test for this assumption by plotting a scatter plot for each pair of
predictor variables (x, x) and between the predictor variables (x) and the criterion
variable (y). Look for the classic “cigar shape.”
Assumption of non-Multicollinearity among the Predictor Variables: If a predictor
variable (x) is highly correlated with another predictor variable (x), they essentially
provide the same information about the criterion variable. If the Variance Inflation Factor
(VIF) is too high (greater than 10), you have multicollinearity and have violated this
assumption. Acceptable values are between 1 and 5.
Report Results
F- statistic: Use F- statistic for the main null. If the null is not significant then stop. If null
is significant then proceed with Post Hoc analysis.
Post Hoc: Use Coefficients (t- statistics and r- statistics) for testing sub-nulls.
Remember the t-stat is measuring the regression line off a zero line slope. The r-stat is
measuring the strength and direction of the regression line.