Understanding Chi-Square Test in Statistics
Chi-square test is a non-parametric test used to measure the association between categorical variables. It can assess goodness of fit and test for independence between observed and expected frequencies. No specific assumptions are needed for the variables in this test. Chi-square frequency tables help analyze how observations are distributed among different groups, aiding in hypothesis testing related to proportions in populations.
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Chi-square Test www.kent.ac.uk/student-learning-advisory-service 1
Chi-square Test We will introduce chi square test, in particular we will cover: What a chi square test is Chi square test in SPSS This presentation is intended for students in initial stages of Statistics. No previous knowledge is required. 2
Chi-square Test A non-parametric test that is used to measure the association between two categorical variables. We use it when we have observed frequencies of a categorial variable (e.g., male vs female, healthy vs sick). 3
Chi-square Test There are 2 types of chi-square tests: The chi-square goodness of fit test is used to compare the observed frequencies in a data sample with the frequencies based on some prior expectation either empirical or theoretical. The chi-square test of independence assesses whether observed frequencies are dependent on (i.e., contingent on) certain conditions. 4
Chi Chi- -square frequency tables square frequency tables A frequency distribution table / contingency table shows how observations are distributed between different groups (i.e., the number of observations in each group). A chi-square goodness of fit test can test whether these observed frequencies are significantly different from what was expected, such as equal frequencies. Null hypothesis (H0): The bird species visit the feeder in the same proportions as the average over the past five years. Alternative hypothesis (H1): The bird species visit the feeder in different proportions from the average over the past five years. 5 https://www.scribbr.com/statistics/chi-square-tests/
Chi Chi- -square frequency tables square frequency tables A frequency distribution table / contingency table shows how observations are distributed between different groups (i.e., the number of observations in each group). A chi-square test of independence can test whether these observed frequencies are significantly different from the frequencies expected if handedness is unrelated to nationality. Null hypothesis (H0): The proportion of people who are left-handed is the same for Americans and Canadians. Alternative hypothesis (H1): The proportion of people who are left- handed differs between nationalities. 6 https://www.scribbr.com/statistics/chi-square-tests/
Assumptions of the Chi Assumptions of the Chi- -square square Since we only require that the two variables are categorical, there are no assumptions required on the variables in the Chi-Square test. 7
The X The X2 2 statistic statistic Both of Pearson s chi-square tests use the same formula to calculate the chi-square (X2) statistic: Where: X2 is the chi-square statistic is the summation operator (i.e., it takes the sum of ) O is the observed frequency E is the expected frequency The larger the difference between the observations and expectations (O E in the equation), the bigger the chi-square statistic will be. The chi-square statistic gets compared with a critical value using a chi-square critical value table or statistical software. 8 https://www.scribbr.com/statistics/chi-square-tests/
Chi Chi- -square test of Independence in square test of Independence in SPSS SPSS 1. Go to: http://www.discoveringstatistics.com/docs/ds_d ata_files/SPSS%20Data%20Files/ 2. Download the Cats.sav file Then follow along! To do this, you will need to install SPSS: https://www.kent.ac.uk/software/spss -statistics 9
Upcoming workshops Upcoming workshops www.kent.ac.uk/student-learning-advisory- service maths/stats appointments available! maths/stats appointments available! 10
