Flashcards
Chi-Squared Test
Flashcards do conjunto (22)
- 1What is a contingency table?A method of showing bi-variate data, also known as a two-way table
- 2—
- 3What do we call the data collected in the table?Observed values
- 4How do we test for independence?Test the observed values against the values that are expected in each of the cells
- 5How do we calculate the expected values?(row total x column total) / grand total
Note this is for each individual cell - 6Create an expected values table for this observed value table:
- 7The expected values don't need to be....Whole numbers
- 8What is the formula to work out the test statistic?Σ(oi - Ei)^2 / Ei
(Oi = observed frequency , Ei = expected frequency)
Note: This is for corresponding cells - 9Create a test statistic table from the tables above:
- 10The greater the values in the (o - E)^2 / E cells correspond to the cells that have the greatest.....Influence on association
- 11What is Chi-squared distribution?The distribution of the sum of the squares of set n, independent random variable
- 12How is Chi-squared denoted?χ^2
- 13The number of independent random variables is called....Degrees of freedom (nu / v)
- 14For the contingency table m x n , how do we calculate the degrees of freedom?v = (m-1)(n-1)
- 15the test statistic calculated from a contingency table is approximately χ^2 distribution:Σ(oi - Ei)^2 / Ei ~ χ^2
- 16Chi-squared test for association between category A and category B :1. State null and alternative hypothesis in context
2. Complete contingency tables for observed and expected values
3. Calculate approximate χ^2 statistic using Σ(oi - Ei)^2 / Ei
4. State degrees of freedom using
v = (m-1)(n-1)
5. Determine critical value using χ^2 table for given significance level
6. Compare χ^2 statistic with critical value from table and conclude - 17For any Chi-squared test, what are our null and alternative hypothesis' ?H0 : No association between A and B
H1 : Association between A and B - 18What are our conclusions for Chi-squared distribution?χ^2 statistic < critical value : accept H0
χ^2 statistic > critical value : reject H0
Remember to write conclusion is context - 19If the expected value in any cell is too small, it increases chance of.....Error in the test
- 20We should not run a χ^2 test for association if any cell has an expected value of less than or equal to....5
- 21How could we attempt to fix the problem above?Combine category's (e.g. if bike, run and walk, combine to bike, on-foot)
- 22Chi-squared table: (Use only 0.9 and above)
