Statistics VII - Exam Questions I

Question 1

What is the difference between 1-way ANOVA and 2-way ANOVA?

Answer 1

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 2

What does ANOVA mean?

Answer 2

Analysis of Variance

Question 3

What is an interaction term?

Answer 3

If two predictor variables affect the outcome
variable in a way that is non-additive, we
need to include an interaction term in the
model to capture this effect.

Question 4

What’s a Bonferroni correction?

Answer 4

The Bonferroni correction is a multiple-comparison correction used when several dependent or independent statistical tests are being performed simultaneously.

Question 5

How to do a Bonferroni correction?

Answer 5

To perform a Bonferroni correction, divide the critical P value (α) by the number of comparisons being made. For example, if 10 hypotheses are being tested, the new critical P value would be α/10. The statistical power of the study is then calculated based on this modified P value.

Question 6

Interpret the following regression formula:

y = 0.8 + 1.5 x

Answer 6

There is a positive correlation between x and y.

Question 7

What does a correlation coefficient of 0.6 mean?

Answer 7

There is a positive correlation.

Question 8

Example with 3 variables and 2 group measures á: What multivariate test can we use for testing the group means?

Answer 8

MANOVA

Question 9

Example with 3 variables and 2 group measures á: What univariate test can we use for testing the group means?

Answer 9

Student’s t-test

Question 10

Can we do a PCA when all given eigenvalues are nearly equal?

Answer 10

no, because that would mean that it’s isotrop and the variance is in all direction the same and there is no direction of a largest variance.

Question 11

What are common / specific factors in the context of factor analysis?

Answer 11

Common factors have influence on several variables, specific factors influence only one variable.

Question 12

What is the difference multiple and multivariate regression?

Answer 12

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

Question 13

What is the first principal component?

Answer 13

The first principal component is defined as the direction of the greatest variance.

Question 14

What does it mean to standardize a variable and when should one do so?

Answer 14

It means to center the variable around its mean and using SD as a unit. In this way, variables with different units can be compared. This is for example done in the calculation of the correlation.

Question 15

What is the difference between covariance and correlation?

Answer 15

Covariance can only be used with variables in the same units. Correlation uses standardized variables.

Question 16

A normally distributed variable has a mean of 8.3 and a variance of 4.1. One specimen has the value 14.6 for this variable. How many standard deviations away from the mean is this specimen? How to interpret this?

Answer 16

(14.6 - 8.3) / √4.1

Question 17

What is Mahalanobis distance?

Answer 17

Mahalanobis distance is like a multivariate version of the z-score: it provides a way to measure distances that takes into account the scale of the data.
The Mahalanobis distance has the following properties:
It accounts for the fact that the variances in each direction are different.
It accounts for the covariance between variables.
It reduces to the familiar Euclidean distance for uncorrelated variables with unit variance.

Question 18

What is quadratic classification?

Answer 18

A quadratic classifier is used in machine learning and statistical classification to separate measurements of two or more classes of objects or events by a quadric surface. It is a more general version of the linear classifier.

Question 19

What are the assumptions of discriminant function analysis?

Answer 19

The assumptions of discriminant analysis are the same as those for MANOVA:

• Multivariate normality
• Homogenity of variance/covariance
• Multicolinearity
• Independence

Question 20

What is a leave-one-out cross validation?

Answer 20

(LOOCV) involves using a single observation from the original sample as the validation data, and the remaining observations as the training data. This is repeated such that each observation in the sample is used once as the validation data. This is the same as a K-fold cross-validation with K being equal to the number of observations in the original sampling.

Question 21

How long is the vector v = (2, 5, 3, 1)?

Answer 21

||v|| = √(4 + 25 + 9 +1) = √39

Question 22

Transform the vector v = (2, 8, 7) into a unit vector (Einheitsvektor)!

Answer 22

||v|| = √117
->
v0 = (2/√117, 8/√117, 7/√117)

Question 23

The first PC is the direction of the greatest variance. What is the definition for the second PC?

Answer 23

It is the direction of the second greatest variance and it is orthogonal to the first PC.

Question 24

In a PCA the 3 eigenvalues of the covariance matrix are I1 = 1120.3, I2 = 3.7, I3 = 1.1.
How much variance in the data set is explained by the first, second and third PC?

Answer 24

PC1: 1120.3/1125.1 = 99.57 %
PC2: 3.7/1125.1 = 0.3 %
PC3: 1.1/1125.1 = …

Question 25

In a PCA one can either work with the correlation matrix or the covariance matrix. If we have the following variables: body height, body weight, blood oxygen level and height of hometown above sea level - would one use the correlation or the covariance matrix?

Answer 25

The correlation matrix, because the units differ.

Question 26

A data set consists of 21 variables investigated in 120 subjects. How many PC can one get?

Answer 26

21

Question 27

What is parametric statistics?

Answer 27

A branch of statistics that assumes that the data has come from a type of a probability distribution.