Chi-squared

Question 1

What are the steps of analysis?

Answer 1

Obtain Data, from which we calculate…
. . .
A test statistic that represents the relationship of interest, which we compare to…
. . .
The distribution of that test statistic under the null hypothesis to get…
. . .
The probability p of getting a test statistic as large as the one we have (or larger) if the null hypothesis is true so that we can…
. . .
Evaluate our competing hypotheses using a previously decided 𝛼 level.

Question 2

What are we calculating when we calculate a test statistic?

Answer 2

How different are the observed counts from the expected counts?

Question 3

Define the term “Observed counts”

Answer 3

The number of occurrences in each category observed in the sample

Question 4

Define the term “Expected counts”

Answer 4

The number of occurrences in each category expected under the null hypothesis

Question 5

What is the 𝜒^2 distribution?

Answer 5

The sum of squared normal distributions

Question 6

What two things do degrees of freedom determine?

Answer 6

The distribution’s shape and proportions

Question 7

What does 𝜒^2 quantify?

Answer 7

How different a set of observed frequencies are from expected frequencies

Question 8

What is a Goodness of Fit Test?

Answer 8

Tests whether a sample of frequency data came from a population with a specific, known distribution

Question 9

What is continuous data?

Answer 9

Represent some measurement or score on a scale
Examples = Reaction time to press a button, mean anxiety score
Answers the question: how much?

Question 10

What is categorical data?

Answer 10

Represent membership in a particular group or condition
Examples = control vs experimental group, year of uni
Answers the question: which one?

Question 11

What is a statistical assumption?

Answer 11

A precondition that must be true in order for a statistical test to work as expected. If these assumptions are violated (i.e.not true), then the test may give inaccurate or misleading estimates or results.

Question 12

What is an assumption of the chi-squared test?
What test do we use instead if this assumption is not met?

Answer 12

One of the assumptions of 𝜒^2 is that all expected frequencies are greater than 5
Otherwise this test can give you a drastically wrong answer
In this case, use Fisher’s exact test (fisher.test()) instead