Week Six - Chi-Square

Question 1

What is a Univariate Design

Answer 1

One variable

Question 2

What is a Factorial Design

Answer 2

Two or more variables

Question 3

Explain Degrees of Freedom

Answer 3

In statistics, the number of degrees of freedom is the number of values in the calculation of a final statistic that are free to vary.

Example: If three numbers sum to 30, how many degrees of freedom are there? How many numbers can be chosen at random?
- 2

Question 4

What are inferential stats?

Answer 4

Inferential statistics answer questions about whether statistics from a sample generalise to a population.

Question 5

What do Descriptive stats do?

Answer 5

[Descriptive] statistics summarise data

Question 6

What is an Effect Size

Answer 6

A [usually standardised] measure of the strength of relationship or magnitude of difference among a set of statistics.

Allows an assessment of practical significance

Question 7

Chi-square tests can only be used with what type of data?

Answer 7

CHI-SQUARE TESTS CAN ONLY BE USED WITH CATEGORICAL (OR ORDINAL) DATA.

Question 8

A Chi-Square Goodness of Fit is what kind of test?

Answer 8

univariate

Question 9

What are we doing when conducting a CSGOF? i.e., What does it test?

Answer 9

When conducting a Chi-square Goodness-of-Fit test, we are examining a single variable and testing whether the counts (or percentages) in the different categories for
that variable differs significantly from a uniform distribution.

Question 10

What is the Null Hypothesis for CSGOF?

Answer 10

Default assumption for null hypothesis is that the population is uniformly distributed across categories.
Proportions are equal for all levels of the variable.

Question 11

What are the 3 Chi-Square Data Assumptions?

Answer 11

Counts in each category (cell) must be independent
A single observation cannot contribute to more than one category

Data must be counts (categorical or ordinal variable)
Number of observations in each category

Sample size must be large enough
Expected frequencies (counts) in all cells should be at least 5
Observed frequencies can be less than 5.

Question 12

How do you calculate degrees of freedom for a chi-square goodness of fit?

Answer 12

Number of cells - 1

Question 13

What does a Chi-square measure?

Answer 13

CHI-SQUARE MEASURES HOW WELL THE DATA MATCH (FIT) THE EXPECTED DISTRIBUTION

Question 14

Small chi square stat means? and is dependent on?

Answer 14

good fit
0 = good fit and closer to null

Magnitude of Chi-square statistic is dependent on
Sample size
Degrees of freedom

Question 15

Chi-square formula is

Answer 15

X^2 = sum of all cells (observed count-expected count)^2/expected count

Question 16

What does Cramer’s V do?

Answer 16

Tells us how big the difference is between the observed data and the null hypothesised expected data.

Question 17

Cramer’s V =

Answer 17

Square root of X2(chi stat)/N(k-1)

• N = total sample size
• K = levels of variable

Question 18

Cramer’s V stats

Answer 18

> .5 = large
.3-.5 = medium
.1 - .3 = small
0 -.1 = trivial

Question 19

Chi-Square GOF write up looks like

Answer 19

χ 2 (dof, N = (sample size)) = STAT (CS result), p = , Cramer’s V = ..

Question 20

Chi-Square Test of Independence Tests what

Answer 20

whether two categorical variables are independent

When we conduct a chi-square test of independence, we’re comparing groups in terms of some outcome variable. For example, you might be comparing two groups of students (those who ate breakfast and those who didn’t) in terms of propensity to fall asleep in class.

Question 21

The Null Hypothesis for CSTOI

Answer 21

Do the proportions within the levels of one or more categories deviate significantly from the total proportions

Expected proportions will be equal

NULL = There is no relationship between the variables

Question 22

Calculation for Expected Frequencies

Answer 22

Expected Frequency = (Rowtotal x Columntotal)/Ntotal

Question 23

For a Chi-square Test-of-Independence expected degrees of freedom are calculated using what formula?

Answer 23

df = (R-1) x (C-1)

Question 24

What test do we use if expected frequencies are bloew 5

Answer 24

USE FISHER’S EXACT TEST OR ROBUST IF BELOW 5

Question 25

A test becomes robust when?

Answer 25

fewer than 20% of cells have small expected frequencies