Expected Frequency

Definition

Expected frequency refers to the theoretical frequency of an event occurring in a statistical experiment, based on the assumption of a specific distribution of data. This concept is crucial for analyzing categorical data and helps in determining whether the observed frequencies deviate significantly from what is expected under a given hypothesis, thereby allowing for statistical testing and inference.

5 Must Know Facts For Your Next Test

1. Expected frequencies are calculated by multiplying the total sample size by the proportion of each category based on a hypothesized distribution.
2. In goodness-of-fit tests, expected frequencies are compared against observed frequencies to assess how well a model fits the data.
3. For contingency tables, expected frequencies help determine if there is a significant association between two categorical variables.
4. It’s important that expected frequencies are sufficiently large (generally at least 5) to ensure validity in statistical tests like chi-square tests.
5. When calculating expected frequencies, it's essential to use the correct total counts from your sample to avoid skewing results.

Review Questions

• How do you calculate expected frequencies for categorical data?
  • To calculate expected frequencies for categorical data, you first need the total sample size and the proportions for each category based on your hypothesis. Multiply the total number of observations by these proportions. For example, if you have a total of 100 observations and you expect 30% to fall into category A, then the expected frequency for category A would be 0.30 * 100 = 30.
• In what ways does the concept of expected frequency support hypothesis testing?
  • Expected frequency plays a vital role in hypothesis testing by providing a benchmark against which observed data can be compared. In chi-square tests, for example, researchers use expected frequencies to determine if observed deviations are significant enough to reject the null hypothesis. If observed frequencies significantly differ from expected frequencies, it suggests that the model may not adequately represent the underlying data distribution.
• Evaluate how changes in expected frequency might affect conclusions drawn from a chi-square goodness-of-fit test.
  • Changes in expected frequency can significantly impact conclusions from a chi-square goodness-of-fit test. If expected frequencies increase or decrease dramatically, it could lead to different results regarding the fit of the model. For instance, if expected frequencies become too low due to changes in sample size or distribution assumptions, it could invalidate the test's results and lead to incorrect conclusions about whether there is a significant difference between observed and expected outcomes. Therefore, ensuring that expected frequencies are calculated correctly and remain appropriate is crucial for accurate hypothesis testing.

Related terms

Chi-Square Statistic: A measure used in statistical tests to determine how expectations compare to actual observed data. It helps quantify the difference between observed and expected frequencies.

Null Hypothesis: A statement asserting that there is no effect or no difference, which is tested against the observed data. The null hypothesis often posits that the expected frequency aligns with observed frequencies.

Degrees of Freedom:

A concept used in statistics that represents the number of independent values or quantities which can be assigned to a statistical distribution. It impacts the calculation of expected frequencies and the resulting chi-square test.