Week 2

Question 1

Define Descriptive / Summary Statistics (5)

Answer 1

• A quantitive description of main features of data
• A useful summary
• Before actual analysis
  
  • What are the players of the game?
  • What are the types of variables? (discrete, continuous, categorical, dummy)
• Get a feel for your data (are there any problems?)

Question 2

What to pay attention to in summary statistics? (4)

Answer 2

• Min value
• Max value
• Negative values
• Range

Question 3

What are the measures of central tendency? (3)

Answer 3

Mean, median, mode

Question 4

How do extreme values affect the mean, median, and mode

Answer 4

• Mean: Influenced by extreme values
• Median: Relatively unaffected by extreme values
• Mode: Not often affected by extreme values (unless there are identical outliers)

Question 5

Which measure of central tendency do you use for the Nominal Variable?

Answer 5

Mode:
- The numbers in nominal variables only refer to the category
- Calculating the mean would be pointless

Question 6

Which measure of central tendency do you use for the Ordinal Variable?

Answer 6

Median:
- Median splits to create further categories or creates dichotomies

Question 7

Dichotomy

Answer 7

A division of 2 things that are being represented as different or opposed.
Using the interquartile range + median of an ordinal variable would split the data into 4 categories.
Example:
x<Q1 = Small, Q1<x<Median (Q2) = Small-Medium, Median (Q2) <x< Q3 = Middle-Large, x> Q3 = Large

Question 8

Which measure of central tendency do you use for the Interval (scale) or Ratio Variables?

Answer 8

Mean or Median:
Depending on the skewness, this would indicate which central tendency to go for.
Not skewed –> Mean
Skewed –> Median

Question 9

Define Skewness

Answer 9

• Describes the shape of the distribution –> Symmetry
• Deviation from the normal bell-shape –> (a)symmetry of a distribution
• Skewness = 0 –> Symmetric, Skewness not = 0 –> Asymmetric, Skewed

Question 10

What is the name for when the skewness values go outside the -1 to +1 range?

Answer 10

Substantially skewed

Question 11

What kind of skew is a distribution with a longer right tail?

Answer 11

Positively skewed

Question 12

What is a negatively skewed distribution?

Answer 12

A distribution which has a longer tail to the left

Question 13

Kurtosis

Answer 13

• Kurtosis describes the degree to which values are found at the tails of the distribution (compared to a normal distribution)
• Can also be seen as how pointy a distribution is (peakedness or flatness)
• It is important to mention whether a value has heavy (lepotkurtic) or light (platykurtic) tails.

Question 14

Leptokurtic (kurtosis)

Answer 14

• This is where there are few values by the tails and, therefore is pointy (heavy-tailed)
• Kurtosis > 3
• Think of “lep”tokurtic as “leap” –> Tends to be more pointy (leaping upwards)

Question 15

Platykurtic (kurtosis)

Answer 15

• This is where there are more values found at the tails of the distribution, therefore more rounded and flatter (light-tailed).
• Kurtosis < 3
• Think of “plat”-ykurtic as in “platform”- this is where the distribution is more rounded and flatter.

Question 16

Mesokurtic (kurtosis)

Answer 16

This is a normal distribution.
–> Kurtosis = 3

Question 17

What is the interquartile range?

Answer 17

This is a measure of variability.
Q1: Lower Quartile (P25, 25%)
Q2: Median (P50, 50%)
Q3: Upper Quartile (P75, 75%)

Question 18

What are the measures of variablility?

Answer 18

Variance: The average of the squared differences between each data point and the mean.
Standard Deviation: The square root of variance
High standard deviation–> High dispersion of data points
Low standard deviation –> Low dispersion of data points

Question 19

Correlation significance

Answer 19

Whether the correlation in population is significantly different from zero or not.

Question 20

Directionality problem

Answer 20

A and B can be correlated because A causes B or B causes A

Question 21

Third variable problem

Answer 21

A and B can be correlated not because A causes B or B causes A. but some unmeasured third variable, C, causes both A and B

Question 22

What is the correlation coefficient?

Answer 22

This is a value with a range between -1 and +1, where it measures the association between two variables, but NOT the causation.

Question 23

𝒚(𝒊) = 𝜷(𝟎) + 𝜷(𝟏)𝒙(𝒊) + E(i)
Define these values

Answer 23

y = Dependent variable
x = Independent variable
𝜷(𝟎) = Intercept / Constant
𝜷(1) = Slope or regression coefficient for the variable ‘x’.
E = Error term –> Everything that the model does not take into account

Question 24

What does it mean to measure the coefficient of a specific variable in a multiple regression equation? (3)

Answer 24

The coefficient of each independent variable:
- Indicates change in dependent variable
- When the given independent variable changes
- But keeping all other independent variables constant (important assumption)

Question 25

What is OLS?

Answer 25

Ordinary Least Squares (OLS):
- This is a good method of showing the LINEAR relationship between x and y.
- The relationship can be found by drawing a line of best fit.

Question 26

What do you look for in regression coefficients? (3)

Answer 26

• Sign: The nature of the effect (positive/negative)
• Size: of the effect (magnitude)
• Significance: of the effect (is the coefficient statistically different from zero?)

Question 27

Give the common p-values and state when a variable becomes insignificant.

Answer 27

○ p value < 0.01 → significance at 1% level
○ p value < 0.05 → significance at 5% level
○ p value < 0.1 → significance at 10% level
○ p value > 0.1 → generally considered insignificant

Question 28

What is a regression coefficient?

Answer 28

This is an estimate of the independent variable you are measuring against the amount of change in y (DV) due to a one-unit change in x(i) while the other regressors (IVs) are held constant.
i –> In this case would refer to the independent variable we are studying.

Question 29

What is a dummy variable?

Answer 29

Dummy takes the value 1 (true) or 0 (not true) –> Indicates whether a condition is satisfied.
Generally for ‘m’ categories, you should include ‘m-1’ dummies.
The omitted one is the base/reference category.

Question 30

How do you interpret regression results for a dummy variable?

Answer 30

The same as any other variable:
- Sign: positive/negative.
- Size: the magnitude.
- Significance: depending on the p-value.
It is important to keep in mind the unit of measurement and how this may impact the dependent variable.

Question 31

How can you predict the maximum number of observations in an analysis?

Answer 31

The maximum number of observations in an analysis is always associated to the variable with the lowest number of observations.
–> When the researcher plots a regression table (model 1, 2, 3, 4, etc…) the number of observations at the bottom should not exceed the variable with the lowest number of observations in the descriptive statistics table.

Question 32

Why do regression tables have different Models?

Answer 32

This allows the researcher to separate the effect of the control variables from the main effect(s).

Question 33

How do you interpret a dummy variable in a control group on a regression table?

Answer 33

• A control group for dummy variables always has 1 dummy variable as a reference to avoid the dummy variable trap.
• When interpreting the dummy variable in a control group, the coefficient would represent a comparison between that specific dummy variable and the reference dummy.