02_Basic statistic characteristics

Question 1

What is descriptive, inductive statistics and hypothesis testing?

Answer 1

descriptive: distinction of different scale levels and understanding of respective analysis constraints + calculation of different measures

Inductive: Concept of sampling error, fundamental characteristics of theoretical distributions, estimating and testing

hypothesis testing: univariate and bivariate parametric and non-parametric statistical tests

Question 2

What are the two things needed to analyze a relationship?

Answer 2

operationalization: represents the development of scales for measuring characteristic values of a particular concept/variable

Scale of measurement: defines the mathematical characteristics of a scale and thereby of the data to be gathered

Question 3

what are the 4 measurement scales?

Answer 3

1. Nominal scale: Assignment of objects to categories (Sex: male, female)
2. Ordinal scale: Ranking (counting and ordering,
3. Interval scale: constant units –>inferences about distance (no natural zero point)
4. Ratio scale: constant units, fixed and multiplications possible

Question 4

What is the likert scale?

Answer 4

Likert scale: ordinal scale with mostly 5 to 7 scale points
(from Fully disagree to fully agree)

Question 5

What is a quasi-metric ordinal scale=

Answer 5

Ordinal scale with the assumption: equal distances between scale points, –>treated just like Interrval scale (5 to 7 scale points, so that measures such a mean and variance are meaningful

Question 6

What is a percentile?

Answer 6

Percentiles are generalizations of the median: observations are arranged according to their size and a percentile divides them in two groups.

–>The pth percentile: value such that p percent of the observations fall at or below

Question 7

What is the mode?

Answer 7

= the value that *most frequently occurs in a data set

Question 8

Interpretation of standard deviation

Answer 8

Standard deviation measures the amount of variation

low value: data points close to mean, mean is informative
high value: data points further away from the mean, not informative

Question 9

What is the intuition behind the “coefficent of variation?

Answer 9

coefficient of variation:is a measure that expresses the relative variability of a set of data points compared to their mean (average)

–>independent of scale of the data, thus makes comparision between two variable on different scals possible

When comparing CVs, asmaller value implies greater consistency relative to the mean, while a larger value implies greater variability

Question 10

What is the meaning of Skewness?

Answer 10

Measures for the symmetry of a distribution

–>symmetric Skewness=0
”< 0 –>left skewed
>0 –>right-skewed

Question 11

What is the sampling error?
(Why do we have one)

Answer 11

By taking samples from a population, we have uncertainity because there are different samples possible

Sampling error: provideds information about the standard deviation of a variable when drawing several sample of the size n

Standard error= 0.17 –>If several samples would be drawn, the standard deviation of their mean/variable x would be 0.17

Question 12

Confidence intervall interpretation
CI (95%) = (1.6, 2.26)

Answer 12

Confidence intervall: (1-alpha) probability that the true parameter lies within the confidence interval

Ex: average CS is between 1.6 and 2.26 in 95% of repeated samples

Question 13

What is the margin of error?

Answer 13

Margin of error= 1/2 of the confidence intervall

Question 14

What does the confidence intervall depent on?

Answer 14

1. significance level (1-alpha): larger –>decreases the CI
2. Sample size:
   - Larger –>lower standard error–>decreasing CI
   - Smaller –>higher standard error–>increasing CI

3.Standard deviation:

Question 15

What is the intuition behind the H0 and H1 hypothesis?

Answer 15

H0: observered result, completly explained by standard error (chance)
H1: accounting for standard error, the results are still significant

Question 16

What are the two error types?

Answer 16

Alpha-error (type 1): Reject H(0) even though H0 is true

Beta-error: (type 2): Don´t rejects H0, but H0 is not true –>Statistical power

Question 17

cal pow

What is the statistical power?

Answer 17

The statistical power (1-beta) of a significance test is the long-term probability, given the population effect size, significance criterion and sample size of rejection of H0.

–>Statistical Power: The probability that a statistical test will correctly reject a false null hypothesis, or in other words, the probability of detecting a true effec

Question 18

What are the three drivers of statistical power?

Answer 18

drivers of statistical power:
- Effect size expressed in alternative hypothesis: stronger effects are easier to detect
- Chosen significance level: decrease in alpha error decreases statistical power (1-beta)
- Sample size: larger n increaases power of the test (1-beta)

Question 19

Possilble outcomes: Test and interpretion –>No rejection of H0 (related to statistical power)

Answer 19

No rejection of H0
high statistical power:
- Evidence for H0
- Refutation of the substantial testing hypothesis (H1)
–>the study successfully avoids making a Type I error (false positive) by not incorrectly rejecting a true null hypothesis

low statistical power:
- Inconclusive status, neither support for H1 nor for H0
- Danger of seemingly contracdictory research findings –>type 2 error

Question 20

Possible outcomes: Test and Interpretation: rejection of H0 (high/low statistical power)

Answer 20

Rejection of H0:

high statistical power:
- Danger that very small effects will be statistically significant
- Practical relevance of the finndings need to be established

Low statistical power:
- support for H1

Question 21

What does the MAD measure?

Answer 21

The MAD (Mean Absolute Deviation) = average of the absolute deviation from a measure of certainty (mean or median)

MAD from the mean is never smaller than the mean absolute deviation from the median

Question 22

What are the 3 assumptions of the t-test for two populations means?

Answer 22

T- test for two population means

Assumptions:
- independent samples
- both variables are normally distributed in the population
- the variance of observed variables are equal

Question 23

When can we use the paired t-test?

Answer 23

When data is not independent —> two related groups or repeated measuring

cannot be used with aggregated data

Question 24

For the chi square test of goodness of fit, what is the prerequisite and the ho and h1

Answer 24

—> are preferences of males equally distributed across all 3 functions ( one sample)

For every category i = n*p >= 5 if not

— merge adjacent categories
— ignore corresponding category ( if merge not possible)