Session 6 - Crosstabulations Flashcards
Cross tabulation used for, AKA
Used for 2 categorical variables (can be binary)
Also known as a contingency table, or cross-tabulation
Can calculate row, column %s and look for trends
Chi-squared test for association
Chi - squared - Find for each CELL the frequency expected if H0 were true - using the row and column totals then distributing evenly
Chi squared - Expected frequency calculation if H0 true
(Row total x column total) / grand total
Looking for evidence for (or against) ANY association
Comparing observed and expected frequencies in chi-squared table
Sum of all squares the (observed frequency-expected frequency)squared / expected frequency
ch-squared distribution
graph of probability densities - shape depends upon degrees of freedom
allows identification of 5% cut off for statistical significance
How may degrees of freedom for a contingency table? (chi squared)
(number of rows-1)x(number of columns-1)
Observation from a chi-squared distribution is denoted as
χ2 (also often mention degrees of freedom)
Significance of χ2
Use table of degrees of freedom vs probablility that tabulated value is exceeded, to compute if χ2 is significant (<0.05 probability) or not
Computer will do this
Chi squared test considerations
Is NOT an index of the strength of association - if we double the frequencies, the χ2 will double, but strenght is unchanged
It is a test for large samples - the smaller the expected values, the more dubious the results
chi-squared is valid if…
At least 80% of the expected frequencies exceed 5
AND
All the expected frequencies exceed 1
2 options if assumptions not met for chi-squared
combine or delete rows / columns
or
uses fisher’s exact test
Fisher’s exact test
Calculate the probability of every possible table
with the given row and column totals
Only used to be used for small samples in 2 by 2
tables, because of computing problems but can
be used with any sample size (no assumptions!)
Will give a p-value
Like chi-squared - tests for ‘any association’
Chi-squared test for Linear Association used if
IF there is a natural ordering to categories - looks for a trend from one end of the table to the other
eg categories of improvement
Linear by linear association test on SPSS is…
Mantel-Haenszel linear-by-linear association chi-squared test
Assumptions for linear by linear chi-squared
At least 30 observations
Both variables have meaningful, ordered categories
