Chi–Squares

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.

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.

Increase the sample size to increase all expected counts above 10.

Perform the chi-square test without modifications as small expected counts are acceptable.

Combine categories to ensure all expected counts are at least 5.

Use a t-test instead of a chi-square test to compare the proportions.

Dividing the observed frequency by the expected frequency

Calculating the standard deviation of the observed frequencies

Using the calculator to conduct a $\chi^2$ GOF test

Comparing the observed frequencies to the expected frequencies

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.

There's no association between variables, but an extreme sample leads to rejecting null hypothesis erroneously.

The variables are strongly associated, and this is reflected in high chi-square values.

The observed frequencies deviate from expected due solely to random chance.

The actual association between variables is weak and not detected by the test.

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.

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.

Determining if there is a linear correlation between height and shoe size.

Estimating the proportion of red candies in a bag based on a sample.

Testing if average test scores differ significantly before and after tutoring.

Comparing the distribution of favorite ice cream flavors among three different age groups.