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In order to compare observed data with data we used Chi-square test. Let we see an example according to Mendel’s laws, we expected 12 of 25 offspring from a cross to make and the actual observed number was 9 males, then we want to know about the goodness to fit between observed and expected. By using Chi-square test we can determine a significant difference between the expected frequencies and the observe frequencies in one or more options. In order to examine different with categorical variables we use Chi-square test. In social world there are a number of features like religion, political preference, etc. We use Chi-square test to examine hypotheses using such variables.
Chi-square test requirements in quantitative data, one or more categories of variables, independent observation, adequate sample size (at least 10), simple random sample, data in frequency form, all observations must be used. If we find any value for Chi-square test, we determine whether the observed frequencydiffer significantly from the expected frequencies. We can find expected frequencies for Chi-square test by using three ways: - First we hypothesize that all frequencies are equal in each category or group. Let us see an example we might expect that half of the students are enteringthe second year class of 100 at tech school will be identified as girls and half as the boys. Here expected frequency we get divided by 2 of strength of students. In the class there are 100 students entering in the second year class and there are two categories, girls and boys, so we divided number of students 100 by 2 and the number of categories to get 50 (expected frequencies) in each category. Our expected frequency of girls and boys is 50. We determine the expected frequencies on the basis of prior knowledge about the data.
Let’s use the school example again, here we have prior knowledge about the frequencies of girls and boys in both categories girls and boys category from last year’s entering class, when 40% of the students are girls and 60% of the total students is boys. Now we can find expected frequencies by using given data girls are 40% and boys are 60%. If the total students are 100 then number of girls in school is 40 and the number of boys in school is 60. Let us find expected frequencies by using the Chi - square test. Let we see Chi-square test formula used for data is X^2 = summation of (O – E) ^2 / E, Here O = Observed frequency in each category, E = Expected frequency in the corresponding category, x^2 is Chi-square. Let we summarize the Chi-square test steps: - first we writingthe observed frequencies now we figure expected frequencies and write them. Now we use the formula to find the Chi-square values. Now we find the difference between observed frequencies and expected frequency (O – E). According to the formula we get Square of different observed frequencies and expected family and divided by expected frequency. Find the table.
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