**Subject Mathematics Advanced Statistics**

## Question

1 What is a covariate?

2 What is the purpose of adding a covariate to an analysis of variance?

3 Should the covariate be related to the IV?

4 Should the covariate be related to the DV?

5 What types of covariates (level of measurement) can you use?

6 Give an example of a research question or hypothesis that can be tested with ANCOVA. List the question or scenario, then specify the IV(s), DV(s), and COV(s), and their levels of measurement.

PROFILE ANALYSIS

7 What is the general purpose of profile analysis?

8 What is a “profile”?

9 If the test of parallelism is significant, what does that mean?

10 If the test of flatness is significant, what does that mean?

11 If the test of overall group differences is significant, what does that mean?

12 How many independent variables can you use in a profile analysis, and what should their level of measurement be?

13 How many dependent variables can you use in a profile analysis, and what should their level of measurement be?

14 Give an example of a research question or hypothesis that can be tested with profile analysis. List the question or scenario, then specify the IV(s) and DV(s) and their levels of measurement.

MULTIPLE LINEAR REGRESSION

15 What is the general purpose of multiple linear regression?

16 What are the basic similarities and differences between ANOVA and regression?

17 How many independent variables can you use in a linear regression analysis, and what should their level of measurement be?

18 How many dependent variables can you use in a linear regression analysis, and what should their level of measurement be?

19 What is the meaning of the R-squared value in linear regression?

20 If the value of a regression coefficient is B = .35, what does this mean?

21 What is the difference between hierarchical, stepwise, and standard linear regression?

22 Give an example of a research question or hypothesis that can be tested with multiple regression. List the question or scenario, then specify the IV(s) and DV(s) and their levels of measurement. Does years of work experience and income predict number of children? The independent variables are years of work experience and income. Both of these two predictors are ratio measurements. The dependent variable is number of children, which is also a ratio measurement.

LOGISTIC REGRESSION

23 What is the general purpose of logistic regression?

24 What is the difference between logistic regression and linear regression?

25 How many independent variables can you use in a logistic regression analysis, and what should their level of measurement be?

26 How many dependent variables can you use in a logistic regression analysis, and what should their level of measurement be?

27 What does the likelihood ratio represent?

28 What does the odds ratio represent?

29 Give an example of a research question or hypothesis that can be tested with logistic regression. List the question or scenario, then specify the IV(s) and DV(s) and their levels of measurement.

MANOVA

30 What is the general purpose of multivariate analysis of variance (MANOVA)?

31 What is the difference between ANOVA and MANOVA?

32 How many independent variables can you use in a MANOVA, and what should their level of measurement be?

33 How many dependent variables can you use in a MANOVA, and what should their level of measurement be?

34 If two DVs are correlated at r = .87, p < .05, can/should they be included in the same analysis? Explain.

35 If two DVs are correlated at r = .19, p > .05, can/should they be included in the same analysis? Why or why not?

36 If the multivariate test is significant, which follow-up tests can you choose, and when is each one appropriate?

37 Give an example of a research question or hypothesis that can be tested with logistic regression. List the question or scenario, and then specify the IV(s) and DV(s) and their levels of measurement.

DISCRIMINANT FUNCTION ANALYSIS

38 What is the general purpose of discriminant function analysis?

39 What is the difference between discriminant function analysis and MANOVA?

40 What is the difference between discriminant function analysis and logistic regression?

41 How many independent variables can you use in a discriminant function analysis, and what should their level of measurement be?

42 How many dependent variables can you use for a discriminant function analysis, and what should their level of measurement be?

43 What is a discriminant function?

44 Give an example of a research question or hypothesis that can be tested with discriminant function analysis. List the question or scenario, and then specify the IV(s) and DV(s) and their levels of measurement.

PRINCIPAL COMPONENTS ANALYSIS

45 What is the general purpose of principal components analysis?

46 What is the difference between exploratory and confirmatory factor analysis?

47 What types of variables or items can you include in a principal components analysis (level of measurement)?

48 What is the difference between an orthogonal and an oblique rotation?

49 What are eigenvalues?

50 Give an example of a research question or hypothesis that can be tested with a principal components analysis. Specify how the variables or items are measured.

## Solution Preview

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A covariate is a variable that is known to have an effect on the Dependent variable, but not on the Independent Variable. In study of ANCOVA they are also known as Intervening or Confounding variables.

What is the purpose of adding a covariate to an analysis of variance?

The purpose of adding a covariate in to analysis of variance is that, the group means in ANOVA are adjusted based on the magnitude of effect which the covariate may be adding, in other words the formula looks at the relationship between the covariate and outcome, and comes out with an actual numeric value and remove that value from the group mean. Which controls the probability of type 2 error.

Should the covariate be related to the IV?

No, covariate should not be related to the Independent Variable, since this is the one of the critical assumption of ANCOVA. But if so happens then one should remove the covariate from the analysis

Should the covariate be related to the DV?

Yes, the covariate should be related to DV, this is also a critical assumption for ANCOVA, however this assumption needs to be checked group wise as well, i.e. if the relationship of covariate and DV differs group wise then the overall regression model is said to be inaccurate this assumption is known as homogeneity of regression slopes.

What types of covariates (level of measurement) can you use?

We can you use any covariate i.e. both categorical(properly-dummy) and continuous, however aligning with the assumption that they must be related to DV...

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