module 9 Flashcards
Expected contingency tables
The contingency table of expected frequencies under the null hypothesis. They are the reference we compare categorical data for the hypothesis test.
How many columns does a one way contingency table have?
Two. One for the list of categories and one for the data of each category
How many columns does a two way contingency table have?
Three. One for the list of categories, one for the data of the first variable, and one for the data of the second variable.
Independent (contingency tables)
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.
Equally (contingency tables)
In the context of expected contingency tables, equality refers to all cells in the table having the same expected frequency.
Interaction (contingency tables)
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.
how to make an expected one way contingency table
- 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
To calculate the expected contingency table, you first need to calculate the _____________
marginal distributions as proportions
how to find two way expected contingency table
multiply the total sum of all numbers in the table by the marginal distributions of the row and column
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.
equally, independently
_________ is the null distribution for hypothesis testing but with categorical data
chi-squared distribution
Ch-squared score
- aka x^2
- measures the distance between observed and expected contingency tables
- calculates the square difference between tables on a cell by cell basis
what are the steps for a chi-squared test
- subtract each observed and expected cell
- square the difference
- divide by the expected value
- add up all the cells
what is Oi in the chi square test equation
observed count in the i’s cell of observed table
what is Ei in the chi square test equation
Expected count on the i’s cell
what is n in the chi square test equation
total number of cells
what is 𝝨 in the chi square test equation
all the cells added together
t or f: the x^2 score is a measure of the distance between your sample and the null hypothesis
true
For 1-way tables, the degrees of freedom are the number of cells minus ____
1
For 2-way tables, the degrees of freedom are the number of rows minus one multiplied by the _________
number of column
what do chi-squared distributions describe?
the likely variation in chi-squared scores that are due to sampling error alone
what are the four steps in a chi-squared test
- define the null and alternative hypotheses
- establish the null distribution
- conduct the stat test
- draw scientific conclusions
_______ 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<⍺).
reject
_______ 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≥⍺).
fail to reject
Unlike other hypothesis tests, the chi-squared test is always _______
directional
Type I error rate and p-value always go on the ______ hand side
right
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
equal, independent
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)
a)
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.
false
