Maths 2

Question 1

Types of variables

Answer 1

Categorical/Qualitative: observation belongs to one of a set of categories (numeric or non-numeric)
Quantitative: observation takes numeric value representing magnitudes (how much or how many)

Question 2

Discreet vs. Continuous

Answer 2

Discreet: possible values are operate numbers, finite, countable
Continuous: possible values form an interval, infinite, measurable

Question 3

Level of measurement

Answer 3

Non-metric
Nominal: categorical, can be distinguished (e.g.: first name)
Ordinal: qualitative, can be ordered, distinguish and compare (e.g.: grades)

Metric:
Interval: quantitative, zero point is arbituary, distinguish, compare and meaningful difference (e.g.: temperature)
Ratio: zero point is absolute, distinguish, compare, meaningful differences and ratios (e.g.: income)

Question 4

Measures of central tendency and dispersion

Answer 4

Central tendency: mean, mode, median, percentiles

Dispersion: deviation, variance, standard deviation, Range and IQR

Question 5

Interpret frequency distributions

Answer 5

1. Shape (peaks, skewed), centre (central tendency), spread (dispersion)
2. Look for outliers (striking deviations from the pattern)
3. Make statements

Question 6

Analysis single variables

Answer 6

Nominal: frequency tab, bar chart, mode
Ordinal: frequency tab, bar chart, mode, median, range, IQR
Metric: frequency tab, bar chart, median, mean, Std. Dev., range, IQR

Question 7

Crosstables

Answer 7

Describe joint distribution of two variables
For all level of measurements
Illustrate absolut and relative frequency (also conditional frequencies)

Question 8

Scatterplots

Answer 8

Quantitative variables
plotted symbols illustrate combinations of values (of the two variables)
Correlation easily visible

Question 9

Covariance and Correlation

Answer 9

Covariance
Positive –> positive correlation between variables
Negative –> negative correlation

Correlation
[0.1;0.6) –> weak positive
[0.6;1] –> strong positive
…

Pearson: two metric variables
Spearman: one or both ordinal variables

Question 10

OLS

Answer 10

Ordinary least squares –> linear regression
Residual: difference between observed value and fitted (predicted value)
Best line minimises sum of the squared distance

Question 11

Goodness of Fit

Answer 11

How good the regression line fits the data

R^2 falls between 0 and 1 –> the higher, the better the fit

Question 12

Definitions: probability, random experiment, random variable, probability distribution

Answer 12

Probability: relative possibility that an event occurs
Random experiment: process leading to occurrence of one of all possible outcomes
Random variable: variable whose value is a numerical outcome of a random phenomenon
Probability distribution: function that relates each value of random variable to its probability

Question 13

Binomial Distribution

Answer 13

Fixed number n of observations
Two possible outcomes
Probability remains the same for each observation

Question 14

Normal distribution

Answer 14

n approaches infinity –> probability of a specific event turns zero
Area under the curve corresponding to an interval is probability that variable assumes a value within this interval

Question 15

Population, Sample, Sampling methods, Finite vs infinite

Answer 15

Population: set of all elements of interest of a study
Sample: subset of the population

Simple random sampling, stratified random sampling, cluster sampling, systematic sampling, convenience sampling, judgemental sampling

Question 16

Sampling distribution and Central limit theorem

Answer 16

Each sample has different statistics –> the distribution of the different samples’ means is called sampling distribution

Central limit theorem: sampling distribution can be approximated with a normal probability distributions the sample size becomes larger

Question 17

Hypothesis Test

Answer 17

Idea: test whether a claim about a population is correct or incorrect

1. Assumption
2. Hypothesis
3. Significance level
4. Test statistics
5. P-value
6. Conclusion

Question 18

Kind of tests

Answer 18

One sample T-Test: claim - population mean is equal to particular value (H0: u = u0)
Independent samples T-Test: claim - no difference between two population means (two samples, H0: u1 = u2)
Dependent samples T-Test: claim - no difference between two population means (one sample, H0: ud = 0)
Chi-square: claim - variables are independent
Pearson/Spearman: claim - no correlation between two variables in the population (H0: p1 = 0)