Quantitative Data Analysis

Question 1

Income (€); Temperature (C)

-> Interval

Answer 1

Quantitative - Continuous

*Continuous variables: Includes numbers with commas.

Question 2

Number of cars (1,2,3); Employees

-> Isolated values

Answer 2

Quantitative - Discrete

*Discrete variables: NO numbers with commas, the value must be clear.

Question 3

Small; Medium; Large

-> Ordered Categories

Answer 3

Qualitative - Ordinal

Question 4

Employed/Unemployed

-> Unordered Categories

Answer 4

Qualitative - Nominal

Question 5

Limitations of r (3)

Answer 5

• Only linear relation
• No information about causality
• Not valid measure when other variables have effects

Question 6

Standard normal distribution (variance and mean)

Answer 6

mean = 0
variance = 1

Question 7

How to write rejcetion region

Answer 7

t < t alpha/2

Question 8

Paired samples t-test

Answer 8

compares the means of two variables for single group.

Question 9

Independent sample t-test

Answer 9

samples are independent does not use the same matrix

Question 10

Alpha (3)

Answer 10

-> is the same as significance level; or p-value; can be found in the t-table
-> Error one | defines a false positive conclusion (Alpha)
-> 1–α = the probability of choosing H0 correctly

Question 11

Beta

Answer 11

-> is the same as power, or effect size
-> Error two || defines false negative conclusion (Beta)
-> β = the probability of making a type II error
-> 1–β = the probability of choosing H1 correctly = power

Question 12

How to lower Beta (4)

Answer 12

▪ when α would be chosen bigger
▪ when n would be larger
▪ when σ would be smaller
▪ when μ would be more in line with H1 and less with H0

Question 13

Cohens´d: Effect size (def.)

Answer 13

-> Effect size: Cohens d is a standardized effect size for measuring the difference between two group

Question 14

Levens test (def. and interpretation)

Answer 14

-> the lower the p-value the more the variances differ (significant if it is lower than 5%)

-> Choose equal variances, because Levene’s test p-value = 0.422>0.10

Question 15

p^

Answer 15

probability in the sample (actually occurring)

Question 16

P

Answer 16

probability in the population (to be tested)

Question 17

Conditions chi square: (2)

Answer 17

(1) Random sample
(2) no cells have E below 1; max. 20% of cells have E below 5

Question 18

Hypothesis chi-square test (2)

Answer 18

H0: the variables are independent (not associated)

H1: the variables are dependent (associated)

Question 19

Kendall’s tau-b

Answer 19

rows = columns -> square tables

-> Strength and direction of association between two variables

-> HOW STRONG the association of categorical variables is

-> ONLY if both variables are ordinal or higher

Question 20

Kendall’s tau-c

Answer 20

rows ≠ columns -> rectangular tables

-> HOW STRONG the association of categorical variables is

-> ONLY if both variables are ordinal or higher

Question 21

Cramers V

Answer 21

measures also positive or negative association; not linear relation

-> If ONE or more variables are nominal

Question 22

When non-normality / requirements are not met

Answer 22

1. Transformation (apply t-test)
2. Bootstrapping (simulate sampling)
3. Non-parametric test (not sensitive to non-normality and outliers)
4. Bigger sample (if possible)

Question 23

Hypothesis of Shapiro-Wilk and kolmogorov-smirnov test

Answer 23

H0: the variable is normally distributed

H1: the variable is not normally distributed

-> p value > 10 % -> normality