# Hypothesis Testing - Chi Squared Test

The Chi-Square test statistic is useful for measuring how close** counts of categorical variables** are to what we would expect under some assumption (which we will call the Null Hypothesis).

## accept or reject the null hypothesis ..

### Chi Square Test | P Value | Statistical Hypothesis Testing

In this case, the observed numbers were so different from the expected 1:1 ratio that Yates correction made little difference - it only reduced the X^{2 }value from 13.34 to 12.67. But there would be other cases where Yates correction would make the difference between acceptance or rejection of the null hypothesis.

### Null hypothesis for a chi-square goodness of fit test

The resulting F_{1} offspring from this OH88119 x 6.8068 all showed resistance to bacterial spot. These were then allowed to self-pollinate and a hypothesis was devised to describe the mode of inheritance for the Rx-4 gene. The breeders’ hypothesis was that Rx-4 expression is due to a single gene with complete dominance. The results in the F_{2} generation though, deviated from what the researchers in that there were more susceptible F_{2} plants than they anticipated. The question remains, as to how far can observed results deviate from what was expected before they should be considered significant? In other words, is the difference in the number of susceptible plants seen and those expected simply due to chance or is something else going on such as a wrong genetic hypothesis, high influence of the environment, etc.? An example of differences due to chance in this tomato example might be a plant that didn’t get inoculated properly, a worker accidentally hoed out a plant, an incorrectly categorized phenotypic observation etc. So these would be random events which impact results, but are unrelated to the Rx-4 gene. This is where statistics, and in this case study, chi-square comes into play - to help plant breeders accurately interpret results.