Module 9 Flashcards
What are expected contingency tables?
the contingency table you expect from a populaion where the null hypothesis is true
hypothesis testing with categorical data is based on comparing the observed contingency tavle against an expected contingency table
What is the expected contingency table for a 1-way contingency table?
it is one where the counts are distributed equally among all levels
How is the expected contingency always given?
given as counts
What is the sum of all the counts in the observed contingency table?
the same as the sum of all counts in the observed contingency table
How is the expected contigency table data typically shown as?
has a fractinoal values because it repersents the average from a statistical population
What does it mean if there is no interaction between the variables?
then the variables are considered independent of each other
What is interaction for a expected contingency table?
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.
What is the null hypothesis of independence for expected contingency tables?
one where the counts are distributed independently among all lebels.
independence does not mean the cells alll have equal expected counts. rather it means that the relative proportion accross the levels of one variable is the same accross all levels of the other.
How to calculated the expected contingency table?
- calculate the marginal distributions as proportios
- the expected value for each cell is then calculated as the product of the row and column marginal distributions that go wth each cell, multiplied by the total table count
What si the chi-squared score (X^2)?
a measure of the distance between two contingency tables. If the contingency tables are an observed and expected table, then is measures the distance between sample data and the null hypothesis.
How do you calculate a chi-squared score for any observed and expected table?
- take the difference between each observed and expected cell
- square the difference
- divide by the expected value
- sum over all cells in the table
What is the null distribution for any hypothesis test?
is the sampling distribution that we get from repeatedly sampling an imaginary statistical population where the null hypothesis is true
What is the chi squared score a measure of?
a measure of the distance between your sample and the null hypothesis
What is the chi squared distribution?
is the distribution of chi-squared scores expected from repeatedly sampling a statistical population where the null hypothesis was true. It is the null distribution for hypothesis testing with categorical data.
Why are only positive values possibe for the chi squared score?
because the chi squared score is a measure of absolute distance between observed and expected table
What is the degrees of freedom for a 1 way table chi squared distribution?
the number of cells minus one
what is the degrees of freedom for a 2-way table for a chi squared distribution?
the number of rows minus one, multiplied by the number of columns, minus one (df=(c-1)(r-1))
How does the hypothesis test work for the chi squared test?
- locating the critical x2 score that corresponds to the type I error rate on the chi squared distribution
- and comapre that to the observed X2 score
- the statistical decision can be made either by comparing the observed and critical X2 scores, or by comparing the corresponding p-value and Type I error rate
how do you make the statistical decision for chi squared test?
- reject the null hypothesis if the observed score is greater than the critical score or if the p value is smaller than the Type I error rate
- fail to reject the null hypothesis if the observed score is less than or equal to the critical score or if the p value is larger or equal to the Type I error rate
Why is the chi squared test always directional
becuase the chi squared score is a measure of absolute distance, and we are only interested in the furthest distance from the null hypothesis
as such, the type I error rate and p value always go on the right hand side
What are the scientific conclusions for the chi squared test for a one way table?
- reject the null hypothesis and conclude that there is evidence to support that the counts are not equal among cells
- fail to reject the null hypothesis and conclude that there is no evidence to support that the counts are not equal among cells
What are the scientific conclusions for the chi squared test for a two way table?
- reject the null hypothesis and conclude that there is evidence to support that the variables are not independent of each other
- fail to reject the null hypothesis and conclude that there is no evidence to support that the variables are not independent of each other
What should the reporting of a chi square testing include
- short 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)
