Chi Square Formula
Chi square formula is the tool to calculate chi square statistic required in the chi square test. The formula and its applications will be further discussed.
Definition: When the task of comparing two or more than two statistical data sets is given then the chi square formula is used. It uses data that has variables spread across various categories. The chi square formula is used to identify the difference between the expected frequency and the observed frequency present so as to understand the relationship between different categorical variables. Karl Pearson introduced this test in 1900.
Formula: x2 = ∑ (Oi – Ei)2/ Ei where, Oi= Actual given value
Ei = Value expected
Also, statistic derived from the chi square test is the P-value. The P-value implies the value of probability in this test. This value determines how probable it is to get a same result or a result that is more extreme as compared to the actual data given. It is basically the chances relating to occurrence or repetitions of a given event. The main point of significance of this value is the fact that it helps to understand how valid the hypothesis is and whether it can be accepted or rejected. The lower the P-value it means the alternative hypothesis relating to the observed and expected frequency is more likely to be accepted. When the P-value is equal to or lower than 0.5 it indicates that the hypothesis is rejected. However, when the P-value is greater than 0.5 the hypothesis is accepted and is very likely.
Solved example:
According to the survey on number of children in each family in a village the data has been provided in the table given below.
Number of Children | Oi | Ei |
1 child | 20 | 15.6 |
2 children | 16 | 17.1 |
3 children | 4 | 3.2 |
Total | 40 |
Solution:
Number Of Children | Oi | Ei | (Oi – Ei)2 | (Oi – Ei)2/ Ei |
1 child | 20 | 15.6 | 19.36 | 1.241 |
2 children | 16 | 17.1 | 1.21 | 0.070 |
3 children | 4 | 3.2 | 0.64 | 0.200 |
Total | 40 | 1.511 |
Hence, x2 = ∑ (Oi – Ei)2/ Ei = 1.511
Therefore, Chi squared = 1.511