Nominal measures of association

when can nominal variables of association be used?

when there’s at least one nominal variable and it can’t determine direction; only strength (0-1)

what is chi-squared and when can it be used?

χ2 = chi squared

it’s only used with frequencies (numbers and not percentages), used in 2 by 2 tables,

what does the formula for chi-squared mean?

fo = observed frequencies (frequencies in table)

fe = expected frequencies (frequencies would expect if no relationship between variables)

greater the difference between fo and fe, the stronger the association

the formula for fe is row marginal x column marginal/N for each number

what is row marginal?

Row marginal refers to the total counts or frequencies for each row in a contingency table, representing the sum of the values across all columns for that row. → look down

what is column marginal?

Column marginal refers to the total counts or frequencies for each column in a contingency table, representing the sum of the values across all rows for that column. → look right

when can cramer’s v be used?

only with frequencies (numbers not percentages), and used with tables of any size to measure the strength of association between two nominal variables.

what is the difference between cramer’s v and chi?

same procedure but the difference is the denominator: multiply x by whatever is less either the number of rows - 1 or number of columns - 1

what does x² mean?

to find x² make a little table of fo, fe, fo - fe, fo-fe² and fo-fe² / fe and sum it upto find the chi-square statistic, create a table of observed frequencies (fo), expected frequencies (fe), the difference (fo - fe), the squared difference (fo - fe)², and the ratio of the squared difference to the expected frequency, then sum the last column.

what is lambda?

a PRE measure it predicts by how much errors in predicting the dependent variable will be reduced if we know the relationship and it’s an asymmetrical measure that assesses the strength of association between two nominal variables, unlike symmetrical measures such as Cramer's V. Lambda is specifically useful for understanding predictive capabilities in contingency tables.

what is E₁ and E_2?

E₁ is the number of errors we will make predicting the dependent variable if we know nothing about the independent

E₂ is the number of errors we will make predicting the dependent variable if we know the independent

what is the formula for E₁?

N - the largest marginal of the dependent variable (the largest number after N)

what is the formula for E₂?

marginal for each value of the independent (the columns going down so the largest number going down) - largest marginal of the dependent variable

look at the columns going down and minus the total from the second largest number in the column and do that for all the columns and add them up at the end

what is the finding for PRE?

we will make x% of fewer errors predicting the dependent if we know about the independent than if we knew nothing about the independent