Week 9, 10, 11, 12

Question 1

Expected contingency table

Answer 1

The contingency table you expect from a population where the null hypothesis is true.

Question 2

Hypothesis testing for categorical data is based on __

Answer 2

contingency tables

Question 3

Difference between 1 way and 2 way expected contingency tables

Answer 3

1 way contingency looks at if there are differences in the counts between levels of a variable
-Expectation: Counts are distributed equally among cells - take total count and divide by amount of levels

2 way contingency looks at if the counts are independent between the variables
-Expectation: Counts are distributed independently among cells

Question 4

How to calculate independence for 2 way tables

Answer 4

Calculating independence requires first calculating the marginal distribution as proportions
The expected table is the product of the row and column proportions for each cell, multiplied by the table total

Question 5

What does the chi-square score measure

Answer 5

Measures the distance between observed and expected contingency tables. It works by calculating the squared difference between the two tables on a cell-by-cell basis

Question 6

The four steps in calculating the chi-square score

Answer 6

Take the difference between each observed and expected cell

Square the difference

Divide by the expected value

Sum over all cells in the table

Question 7

Chi Square Distribution

Answer 7

The null distribution for hypothesis testing with categorical data

It is the distribution of chi-square scores you would get from sampling an imaginary statistical population where the null hypothesis was true

ONLY POSITIVE VALUES

Question 8

Degrees of freedom for 1 way tables vs 2 way tables

Answer 8

1 way: df=k-1
Number of cells minus 1

2 way: df=(r-1)(c-1)
(rows-1 multiplied by columns-1)

Question 9

Statistical test conclusions for chi square scores

Answer 9

-Reject null hypothesis if X^2 observed> X^2 critical or is p<alpha

Fail to reject the null hypothesis if X^2 observed< X^2 critical or is p>alpha

Question 10

Reports for chi square tests should include:

Answer 10

Name of Test
Degrees of freedom
Total count in the observed table
The observed chi-squared value (two decimal places)
P-value (three decimal places)

Question 11

Write out the formula for the t-observed for correlation

Answer 11

Refer to formula sheet

Question 12

Reporting of correlation test should include

Answer 12

Symbol for the test
Degrees of freedom
Observed correlation value
P-value (three decimal places)

Question 13

Correlation

Answer 13

Evaluate the association between two numerical variables (looking for a pattern)
No implied causation between the variables
Both variables are assumed to have variation
Not used for prediction
Pearson’s correlation coefficient (r, p) measures the strength of the association

Question 14

Write out the formula for r

Answer 14

refer to formula sheet

Question 15

Difference between correlation and linear regression

Answer 15

Correlation cannot predict, linear regression can (experimental studies)

Question 16

What is the linear equation? Describe the components

Answer 16

y=a+b(Xi)

Slope (b):
-Amount that the response variable (y) increases of decreases for every unit change in the predictor variable (x)

Intercept (a)
-The value of the response variable (y) when the predictor variable (x) is at 0

Question 17

Statistical Model
-3 componentS

Answer 17

Systematic Component: describes the mathematical function used for predictions
Linear equation

Random component: describes the probability distribution for sampling error (linear regression is Normal Distribution)
Error distribution
Only occurs in response variable

Link Function: connects the systematic component to the random component

Question 18

How to calculate the sum of squares

Answer 18

1. Calculate the residual for each data point
2. Take the square of each residual
3. Sum the squared residuals across all data points
4. Divide by the degrees of freedom

Question 19

Null and alternative hypothesis for linear regression

Answer 19

Intercept:How does the intercept (a) relate to a reference value (Ba)

Slope:How does the slop (b) relate to a reference value (Bb)

Question 20

What is the null distribution in linear regression hypothesis tests

Answer 20

a t-distribution

Question 21

What are the 4 main assumptions of linear regression

Answer 21

1. Linearity
   - Response variable a linear combination of the predictor variable
   Y=a+bx is a straight line
2. Independence
   The residuals along the predictor variable should be independent of each other
   Evaluated qualitatively using a plot of residuals against the predictor variable
3. Normality
   Residual variation should be Normally distributed
   Evaluated using the Shapiro-Wilks Test
4. Homoscedasticity
   The residual variation should be similar across the range of the predictor variable

Question 22

F test

Answer 22

evaluate the difference in variance between two groups

Question 23

Null and alternative hypothesis of F-test

Answer 23

Ho= ratio of variances is one

Ha= ration of variances is not 1

Question 24

What to report for F-score

Answer 24

Mean, sd, sample size for each group
Observed F score
Degrees of freedom for each group
P-value

Question 25

Single Factor ANOVA

Answer 25

Used to work with numerical and categorical variables

Group variation: the variation among means of the categorical levels

Residual variation: the variation among sampling units within a categorical variable

ANOVA evaluates whether there is a difference in means among categorical levels

Question 26

Post-Hoc tests

Answer 26

Secondary statistical test designed to indicate which groups have different means
ONly used if the ANOVA F-test indicates to reject the null hypothesis

Question 27

Two Factor ANOVA

Answer 27

Two categorical variables and their interaction

Question 28

Two factor ANOVA is used to anser 3 questions

Answer 28

Main effects A
-Differences among the levels of factor A averaging across the levels of factor B

Main effects B
Differences among the levels of factor B averaging across the levels of factor A

Interactions
Differences among the levels of one factor within each level of the other factor
Cell by cell comparisons

Question 29

Interactions are deviations from____

Answer 29

additivity: When the effect of the levels are their simple sum