Statistics VIII - Exam Questions II

Question 1

What’s the linear regression model?
What assumptions are made about the errors or residuals?
What are the consequences if those assumptions are not true and what can one do about it?

Answer 1

A model about the linear effect of x on y.
Errors independent and normally distributed.
No normal distribution in a histogram.

Question 2

What’s the difference btw multiple and multivariate regression?

Answer 2

Multiple regression takes several independent variables and only one dependent variable.
Multivariate regression takes one independent variable and several dependent variables.

Question 3

How is the coefficient of determination calculated and how can it be interpreted?

Answer 3

The coefficient of determination is the squared correlation: R² = r² (squared correlation coefficient).
R² indicates how much of the variance of y can be explained by the linear relation to x.

Question 4

What’s a partial coefficient of regression?

Answer 4

y=β0 +z1 β1 +z2 β2 +z3 β3+ε
βi … partial coefficient of regression
Interpretation: β₂ is the coefficient of y and z₂, if z₁ and z₃ are held constant.
The partial coefficient of regression is NOT equal to the bivariate coefficient of regression.

Question 5

What are the differences btw a factor analysis and a PCA (in their calculation and interpretation)?

Answer 5

When an investigator has a set of hypotheses that form the conceptual basis for her/his factor analysis, the investigator performs a confirmatory, or hypothesis testing, factor analysis. In contrast, when there are no guiding hypotheses, when the question is simply what are the underlying factors the investigator conducts an exploratory factor analysis. The factors in factor analysis are conceptualized as “real world” entities such as depression, anxiety, and disturbed thought. This is in contrast to principal components analysis (PCA), where the components are simply geometrical abstractions that may not map easily onto real world phenomena.

Question 6

You designed a questionaire for a study. After a testrun you notice that questions 1 and 3 are answered in exactely the same way by all participants. Why should you consider to rethink your questions?

Answer 6

There will be no variance on these questions.

Question 7

You use three variables to measure fish in two ponds and you are interested in the differences of the two populaitons. The uncorrected p-values for the group differences (e.g. t-test) are:
body weight: 0.04
body length: 0.01
length of tail fin: 0.005
If you want to except a collective alpha-error of 5% after a Bonferroni-correction, for which of the three variables do you assume a significant group difference?

Answer 7

0.05 (5%) / 3 (number of tests) = 0.0167
->
Body length and length of tail fin is still ok

Question 8

Plants and fertilizer: height of plant (in cm) = Y and amount of fertilizer (in g) = X.
Interpret the following result (describe equation in words): Y = 10.3 + 1.7 X
What should you control for in this experiment?

Answer 8

Positive influence of x on y.
Started at 10.3 cm.
Plants are 1.7 cm higher per g fertilizer.

Question 9

What does R² usually stand for?

Answer 9

Coefficient of Determinatioin

Question 10

What does MANCOVA mean?

Answer 10

Multivariate Analysis of Covariance

Question 11

What is a partial correlation coefficient?

Answer 11

The correlation coefficient between the residuals of a regression is called partial correlation coefficient.

Question 12

What’s the difference btw 1-way and 2-way ANOVA?

Answer 12

The 2-way is an extension of the 1-way ANOVA to include different categorical independent variables on one dependent variable. (1-way ANOVA uses just one independent variable)

Question 13

You recorded 5 physiological measurments in one group of subjects before and after the treatment with a certain drug. How will you proceed statistically to investigate the effect of the drug?

Answer 13

Test covariance in paired comparison -> smaller variances can be detected that would be masked by interpersonal variance in cross-sectional studies.

Question 14

You are interested in whether students, who do have plants in their classroom, get better grades. You record grades in the subjects Maths, German and Biology and conduct your study at 5 different schools.
How many factors are there in your study and which are fixed and which are random?

Answer 14

Fixed Factors:
plants or no plants
5 different schools

Random Factors:
ethnicity?
exact age of students
grades in Maths
grades in German
grades in Biology

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Question 15

You are interested in whether students, who do have plants in their classroom, get better grades. You record grades in the subjects Maths, German and Biology and conduct your study at 5 different schools.
Which statistical analysis would you use?

Answer 15

MANOVA

Question 16

You are interested in whether students, who do have plants in their classroom, get better grades. You record grades in the subjects Maths, German and Biology and conduct your study at 5 different schools.
How can you correct for the different ages of the subjects?

Answer 16

Using MANCOVA and age as covariate.

Question 17

You are interested in whether students, who do have plants in their classroom, get better grades. You record grades in the subjects Maths, German and Biology and conduct your study at 5 different schools.
The p-value for your whole model is 0.19. What does it mean?

Answer 17

No significant difference between plants and no-plants.

Question 18

You are interested in whether students, who do have plants in their classroom, get better grades. You record grades in the subjects Maths, German and Biology and conduct your study at 5 different schools.
The p-value for your whole model is 0.01. How can you proceed?

Answer 18

Try to determine what fields are influenced how.

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Question 19

A study investigates 10 variables in 2 groups á 50 cases. For each of these variables a t-test was used to search for differences of the means. The authors of the study claim that for two variables they found significant differences between the means (p = 0.05). Would you trust their results? Why?

Answer 19

No. They apperantly haven’t conducted a Bonferroni-correction, after which the critical p-value would be 0.005.

Question 20

A study investigates 10 variables in 2 groups á 50 cases. For each of these variables a t-test was used to search for differences of the means. The authors of the study found no significant univariate t-test. Could there still be a (multivariate) difference between the two groups?

Answer 20

Yes, MANOVA or Hotelling’s T2 could help.

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Question 21

As with other parametric tests, we make the following assumptions when using two-way ANOVA:

Answer 21

• The population from which the sample are obtained must be normally distributed.
• Sampling is done correctly. Observations for within and between groups must be independent.
• The variance among populations must be equal (homoscedastic).
• Data are interval or nominal

Question 22

What is the trace of a matrix?

Answer 22

The sum of all (main) diagonal fields.

Question 23

What does cross-validation mean?

Answer 23

Testing the classification with a sample that was not used for the computation of classification rules.