AP Biology chi-square flashcards

What is the chi-square test used for?

To determine if there is a significant difference between observed and expected frequencies in categorical data.

Chi-square formula

\displaystyle \frac{(O - E)^2}{E}, where O = observed frequency, E = expected frequency.

True or false: Chi-square can be used for continuous data.

False, because chi-square is used only for categorical data.

Difference between observed and expected frequencies

Observed frequencies are collected data; expected frequencies are predicted by a hypothesis.

What does a high chi-square value indicate?

It suggests a significant difference between observed and expected data.

Degrees of freedom formula for chi-square

$\displaystyle df = n - 1$, where n is the number of categories.

What is the significance level commonly used in chi-square tests?

The 0.05 significance level is commonly used to determine statistical significance.

True or false: Chi-square tests require normally distributed data.

False, because chi-square tests do not require normality.

Fill in the blank: A chi-square value above the critical value indicates ____.

a significant difference in data.

Observed frequency example

If 30 out of 100 plants are tall, the observed frequency is 30.

Expected frequency calculation

If the ratio is 1:1, the expected frequency for tall plants in 100 trials is 50.

True or false: A chi-square test can confirm a hypothesis.

False, because chi-square tests only assess data compatibility with a hypothesis.

Difference between goodness-of-fit and test of independence

Goodness-of-fit tests one variable; test of independence examines two variables.

What do p-values represent in chi-square tests?

The probability that the observed data could occur under the null hypothesis.

What is the null hypothesis in chi-square tests?

The assumption that there is no significant difference between observed and expected frequencies.

Chi-square test limitations

Requires a minimum expected frequency of 5 in each category for validity.

What does a p-value less than 0.05 indicate?

It suggests that the observed data significantly differs from the expected data.