(PM) Statistics - Method Selection

Question 1

Testing one mean and the standard deviation of the population is given.

Answer 1

One-Sample Z-test

Question 2

Testing one mean and the standard deviation of the population is NOT given.

Answer 2

One-Sample T-test

Question 3

Testing one proportion

Answer 3

One-Sample Proportion test

Question 4

Testing one variance

Answer 4

One-Sample Variance test

Question 5

Comparing two independent means, with equal variances

Answer 5

Independent Sample T-test. T~(N1+N2-2)

Question 6

Comparing two independent means, with UNequal variances

Answer 6

Independent Sample T-test. T~(m)

Question 7

T~(m)

Answer 7

Value of the smallest sample size minus 1

Question 8

Comparing two dependent means on equality

Answer 8

Matched Pairs T-test. H0: P1 - P2 = 0

Question 9

Comparing two dependent means with hinge

Answer 9

Matched Pairs T-test. H0: P1 - P2 = h

Question 10

Comparing two variances on equality

Answer 10

Two-Sample Variance test. H0: Variance(1) / Variance(2) = 1

Question 11

Comparing to variances with hinge

Answer 11

Two-Sample Variance test. H0: Variance(1) / Variance(2) = h

Question 12

… Model with one independent variable

Answer 12

Simpel lineair regression model

Question 13

… Model with two or more independent variables

Answer 13

Multiple lineair regression model

Question 14

What are the four regression assumptions?

Answer 14

1. The residuals are 0 on average
2. The residuals are normally distributed
3. The residuals are independent from each other
4. The residuals are equally spread, they are homoscedastic

Question 15

What is the first regression assumption?

Answer 15

The residuals are zero on average, their expectation (E) is zero (0).

This assumption is violated if a strong lineair correlation (collinearity) between the independent variables is observed. You can detect this by seeing if there’s a 0.8 or higher correlation between independent variables

Question 16

What is the second regression assumption?

Answer 16

The residuals are distributed normally.

This assumption is violated if the residuals are not normally distributed. You can detect this using a residual plot or a histogram and check for normal distribution or for outliers

Question 17

What is the third regression assumption?

Answer 17

The residuals are independent from each other.

This assumption has two violations.

1 - This assumption is violated if the value of the residuals is dependent on the value of previous residuals. You can test for this by performing a Durbin Watson test for autocorrelation.

2- This assumption is violated if the relation between dependent and independent variables is not lineair. You can check this by plotting the residuals and predicted values on a graph. If the resulting graph has a curve, a rounding or other form this assumption is violated

Question 18

What is the fourth regression assumption?

Answer 18

The residuals have equal spreading, they are homoscedastic.

This assumption is violated of the residuals differ, if they are is heteroscedastic. You can detect this by plotting the residuals and predicted variables on a graph. Here, you have to check whether the spread from left to right is the same.

Question 19

How to determine the rejection region for the positive autocorrelation?

Answer 19

If D ≤ D(a,L), then: conclude H1
If D(a,U) < D < D(a,L), then: ‘no conclusion’
If D ≥ D(a,U), then: conclude H0

Question 20

How to determine the rejection region for the negative autocorrelation?

Answer 20

If D ≥ 4 - D(a,L), then: conclude H1
If 4 - D(a,L) < D < 4 - D(a,U), then: ‘no conclusion’
If D ≤ 4 - D(a,U), then: conclude H0

Question 21

How to determine the rejection region for omnidirectional autocorrelation?

Answer 21

If D ≤ D(a/2,L) OR if D ≥ 4 - D(a/2,L), then: conclude H1

If D(a/2,L) < D < D(a/2,U), OF if 4 - D(a/2,U) < D < 4 - D(a/2,L), then: ‘no conclusion’

If D ≥ D(a/2,U) OR if D ≤ 4 - D(a/2,U), then: conclude H0

Question 22

What are the conditions for a function to be a probability density function?

Answer 22

1. The chance of X is not below 0 for the entire range of X.

2. The sum of the probabilities for x are 1.

Question 23

What to write when asked to fill the basic assumption?

Answer 23

Write down the formula and fill in the variable names, not it’s values

E.g. Y = B0 + B1 * D(age) + e(residuals), with E(e) = 0

Question 24

What to write when asked to fill the sample regression equation?

Answer 24

Write down the formula and fill in the variables, not variable names.

E.g. ŷ = 0.8345 - 0.3451 * X

Question 25

How should you generally treat the left side of a test?

Answer 25

Use the negative of the value from the table. Except for the F-test.

Question 26

What is the order of the positive Durbin Watson outcomes spread?

Answer 26

Left: H1, there is positive autocorrelation
Middle: Inconclusive
Right: H0, no positive autocorrelation

Question 27

What is the order of the negative Durbin Watson outcomes spread?

Answer 27

Left: H0, no negative autocorrelation
Middle: Inconclusive
Right: H1, there is negative autocorrelation

Question 28

What is the order of the two-sided Durbin Watson outcomes spread?

Answer 28

Left: H1, there is autocorrelation
Second to left: Inconclusive

Middle: H0, there is no autocorrelation

Second to right: Inconclusive
Right: H1, there is autocorrelation

Question 29

Give a couple options on to solve the issue of autocorelation

Answer 29

1. Include time itself in the model. Meaning, regress Y on X1, X2, etc, and on X(t)
2. Use the differences between the values of Y and X(i) over time, instead of using the absolute values themselves.

Question 30

How to calculate X-bar rejection?

Answer 30

Mu + Z(a) * Standard error

With Standard error is the calculation below the divider

Question 31

How to determine type II error?

Answer 31

1. Calculate the X-bar for the rejection region
2. Fill the X-bar in the Z formula
3. Find the P-value in the Z-table