Expected values

Definition

Expected values are the theoretical frequencies of outcomes in a statistical experiment, based on a given distribution. They are used to compare observed data with what is theoretically expected.

5 Must Know Facts For Your Next Test

1. Expected values are essential for conducting a Chi-Square Goodness-of-Fit test.
2. They are calculated by multiplying the total number of observations by the probability of each category.
3. Expected values help determine how well the observed data fits the expected distribution.
4. When actual data closely matches expected values, it suggests that the model being tested is a good fit.
5. Deviation between observed and expected values can be analyzed using the Chi-Square statistic.

Review Questions

• How do you calculate expected values for a given category?
• Why are expected values important in statistical tests like Chi-Square?
• What does it mean if there is a large difference between observed and expected values?

Related terms

Chi-Square Statistic:

A measure used in statistics to assess how much observed frequencies deviate from expected frequencies.

Goodness-of-Fit Test:

A statistical test used to determine if sample data fits a distribution from a population with a normal distribution.

$p$-Value: $p$-Value quantifies the evidence against a null hypothesis; lower $p$-values suggest stronger evidence against the null hypothesis.