# The Chi-Squared Test

The Chi-Squared Test

Overview

• The Chi-Squared Test is a statistical test used to determine if there is a significant difference between the observed results and the results expected due to chance.
• It’s used to test the hypothesis that the observed and expected results are independent, often employed in genetics to verify inheritance patterns.

Purpose in Genetics

• Employed in genetic investigations to compare the observed ratios of phenotypes or genotypes with those expected from a certain model of inheritance.
• Determines whether any observed deviations from expected values could be due to chance or whether they indicate that the expected model of inheritance is incorrect.

Calculation

• The Chi-Square formula is: Χ² = Σ [ (O-E)² / E ], where O stands for the observed frequency, E stands for the expected frequency, and Σ is the summation symbol, indicating that this calculation is done for each category of data.
• A lower chi-square value suggests that the deviations from the expected ratios are likely due to random sample variation (chance), whereas a larger chi-square value indicates that another factor could be influencing the outcome.

Degrees of Freedom

• The degrees of freedom (df) must be calculated for the test and is given by the formula: df = n - 1, where n is the number of categories.
• In the context of genetics, if we are looking at a monohybrid cross, df = 2 - 1 = 1, because there are two categories of outcomes (dominant and recessive).

Significance

• The chi-square value is compared to a chi-square distribution table to determine the probability that the observed deviations could have occurred due to chance.
• A p-value is derived from this comparison. If the p-value is less than the chosen significance level (often 0.05), then the difference between observed and expected is considered statistically significant.
• This means that in a genetic context, the assumed inheritance pattern does not fit the observed data, and the hypothesis is potentially incorrect.

Possible Limitations

• The Chi-Square Test assumes that each observation is independent of the others.
• Not accurate when expected frequencies are very low, so usually each expected frequency should be 5 or more. For small samples, a different statistical test might be more appropriate.
• Tells only if there is a significant difference, not what the difference is or why it might be occurring. It is crucial to critically evaluate these results in the context of our biological understanding.