Chi–Squares

Transform your data using logarithms before applying the chi-square test.

Ignore cells with low-expected counts and only analyze cells meeting assumptions.

Apply the Yates' correction for continuity or use Fisher's exact test if applicable.

Use Bonferroni correction to adjust p-values across multiple comparisons.

High expected frequencies could cause an overestimation of effect size in observed data.

Large sample sizes may decrease statistical power due to excessive variability.

Low expected frequencies can inflate the Type I error rate beyond the chosen significance level.

If expected frequencies are too low, the chi-square approximation to the distribution may not be accurate.

They are used to calculate the p-value

To be compared to the expected frequencies to calculate the chi-square statistic.

They help determine the chosen significance level

They determine the degrees of freedom for the test

Sample size being too small leading to insufficient power.

Larger variability within cells improving sensitivity and accuracy in detecting differences.

Cell counts exceeding minimum expectations reducing type I error rate artificially.

High degree of freedom enhancing robustness against violations of assumptions.

When you want to predict the sale price of homes based on their size.

When you want to determine if there is an association between gender and preference for a new product.

When you want to assess how well students scored on an exam overall.

When you want to compare the effectiveness of two medications on blood pressure.

To establish whether each category's proportion is equal across all levels of another variable.

To determine if the sample size is large enough for the chi-square test to be valid.

To calculate the degrees of freedom needed for determining the critical value.

To compare them with the observed counts to see if there is a significant association between two categorical variables.

number of rows * number of columns

(number of rows + 1) * (number of columns + 1)

number of rows + number of columns

(number of rows - 1) * (number of columns - 1)

All expected cell frequencies should be at least 5.

No expected cell frequency can equal zero.

All expected cell frequencies should be less than 20.

At least half of the expected cell frequencies should be more than 10.

Single numerical measurements taken from individual subjects within one group only.

Categorical data from two or more groups.

Ranked order data from multiple treatments in an experiment.

Continuous data measured over time from one group only.

The samples are too small to make any conclusion.

There's strong evidence that the populations have similar distributions.

Larger sample sizes are needed to decrease the p-value further.

The populations likely have different distributions.