module 9

Question 1

Expected contingency tables

Answer 1

The contingency table of expected frequencies under the null hypothesis. They are the reference we compare categorical data for the hypothesis test.

Question 2

How many columns does a one way contingency table have?

Answer 2

Two. One for the list of categories and one for the data of each category

Question 3

How many columns does a two way contingency table have?

Answer 3

Three. One for the list of categories, one for the data of the first variable, and one for the data of the second variable.

Question 4

Independent (contingency tables)

Answer 4

In the context of expected contingency tables, independence refers to the cells in the table having equal relative proportions across the levels of each variable.

Question 5

Equally (contingency tables)

Answer 5

In the context of expected contingency tables, equality refers to all cells in the table having the same expected frequency.

Question 6

Interaction (contingency tables)

Answer 6

In the context of expected contingency tables, an interaction refers to the cells in the table not having equal relative proportions across the levels of each variable.

Question 7

how to make an expected one way contingency table

Answer 7

• add up the total of the numerical column and divide it by how many rows there are, the number should be the same for each value

Question 8

To calculate the expected contingency table, you first need to calculate the _____________

Answer 8

marginal distributions as proportions

Question 9

how to find two way expected contingency table

Answer 9

multiply the total sum of all numbers in the table by the marginal distributions of the row and column

Question 10

For 1-way contingency tables, the null hypothesis is that the counts are distributed ______ among the cells whereas for 2-way contingency tables, the null hypothesis is that the counts are distributed ______ among the cells.

Answer 10

equally, independently

Question 11

_________ is the null distribution for hypothesis testing but with categorical data

Answer 11

chi-squared distribution

Question 12

Ch-squared score

Answer 12

• aka x^2
• measures the distance between observed and expected contingency tables
• calculates the square difference between tables on a cell by cell basis

Question 13

what are the steps for a chi-squared test

Answer 13

• subtract each observed and expected cell
• square the difference
• divide by the expected value
• add up all the cells

Question 14

what is Oi in the chi square test equation

Answer 14

observed count in the i’s cell of observed table

Question 15

what is Ei in the chi square test equation

Answer 15

Expected count on the i’s cell

Question 16

what is n in the chi square test equation

Answer 16

total number of cells

Question 17

what is 𝝨 in the chi square test equation

Answer 17

all the cells added together

Question 18

t or f: the x^2 score is a measure of the distance between your sample and the null hypothesis

Answer 18

true

Question 19

For 1-way tables, the degrees of freedom are the number of cells minus ____

Answer 19

1

Question 20

For 2-way tables, the degrees of freedom are the number of rows minus one multiplied by the _________

Answer 20

number of column

Question 21

what do chi-squared distributions describe?

Answer 21

the likely variation in chi-squared scores that are due to sampling error alone

Question 22

what are the four steps in a chi-squared test

Answer 22

• define the null and alternative hypotheses
• establish the null distribution
• conduct the stat test
• draw scientific conclusions

Question 23

_______ the null hypothesis if the observed score is greater than the critical score (i.e., ꭓ2o>ꭓ2c) or if the p-value is smaller than the Type I error rate (i.e., p<⍺).

Answer 23

reject

Question 24

_______ the null hypothesis if the observed score is less than or equal to the critical score (i.e., ꭓ2o≤ꭓ2c) or if the p-value is larger or equal to the Type I error rate (i.e., p≥⍺).

Answer 24

fail to reject

Question 25

Unlike other hypothesis tests, the chi-squared test is always _______

Answer 25

directional

Question 26

Type I error rate and p-value always go on the ______ hand side

Answer 26

right

Question 27

for one way tables, confusions are if the counts are _____ among the cells and for two way its if the counts are ____ of each other

Answer 27

equal, independent

Question 28

chi square tests should involve all but this in the conclusion:

a) the null and alternative hypotheses in simplified form
b) short name of the test (i.e., ꭓ2)
c) degrees of freedom
c) total count in the observed table
d) observed chi-squared value (two decimal places)
d) p-value (three decimal places)

Answer 28

a)

Question 29

t or f: Since the null distribution is based on the chi-squared score, it cannot contain all the necessary information about the distance between the observed and expected table under the null hypothesis.

Answer 29

false