Minimum Expected Frequency

Definition

Minimum expected frequency refers to the smallest number of observations that should be expected in each cell of a contingency table for the Chi-square test to be valid. It ensures that the assumptions of the Chi-square test are met, allowing for accurate statistical inference regarding relationships between categorical variables.

5 Must Know Facts For Your Next Test

1. The minimum expected frequency should be at least 5 in each cell of a contingency table to ensure the validity of the Chi-square test.
2. If any cell has an expected frequency less than 5, it may indicate that the sample size is too small or that categories should be combined.
3. In cases where minimum expected frequencies are not met, alternative tests such as Fisher's Exact Test may be more appropriate.
4. The concept of minimum expected frequency helps to minimize Type I and Type II errors by ensuring sufficient data for analysis.
5. It is essential to calculate expected frequencies based on the marginal totals of the contingency table before conducting a Chi-square test.

Review Questions

• Why is maintaining a minimum expected frequency important when conducting a Chi-square test?
  • Maintaining a minimum expected frequency is crucial because it ensures that the assumptions of the Chi-square test are met, leading to valid results. Specifically, if expected frequencies are too low, it can distort the Chi-square statistic and increase the risk of Type I and Type II errors. A minimum expected frequency of 5 per cell is commonly recommended to provide reliable estimates of the relationship between categorical variables.
• How do you calculate the expected frequencies in a contingency table, and why is this step important for determining minimum expected frequency?
  • To calculate expected frequencies in a contingency table, you multiply the total number of observations by the proportion of each category's marginal total divided by the overall total. This step is important for determining minimum expected frequency because it provides a baseline for comparison against observed frequencies. By ensuring that each cell meets or exceeds the minimum expected frequency threshold, researchers can confidently apply the Chi-square test and interpret its results.
• Evaluate how failing to adhere to the minimum expected frequency requirement could impact research conclusions drawn from a Chi-square test.
  • Failing to adhere to the minimum expected frequency requirement can significantly compromise research conclusions derived from a Chi-square test. When some cells have low expected frequencies, it can lead to inaccurate test statistics, resulting in misleading p-values and potential misinterpretation of relationships between variables. This might cause researchers to falsely accept or reject hypotheses about associations, ultimately affecting decision-making processes based on flawed statistical analysis. Therefore, researchers must carefully check and address any violations of this assumption to maintain integrity in their findings.

Related terms

Chi-square Test: A statistical test used to determine if there is a significant association between two categorical variables by comparing observed frequencies to expected frequencies.

Contingency Table: A table that displays the frequency distribution of variables, used to analyze the relationship between two categorical variables.

Degrees of Freedom: A parameter that indicates the number of values in a calculation that are free to vary, often used in Chi-square tests to determine the distribution of the test statistic.