Observed values

Definition

Observed values are the actual data points collected from an experiment or survey. They are used to compare with expected values in statistical tests.

5 Must Know Facts For Your Next Test

1. Observed values are essential for calculating the chi-square statistic in a goodness-of-fit test.
2. The difference between observed and expected values helps determine if there is a significant deviation from the expected distribution.
3. In a contingency table, observed values are the frequencies found within each cell of the table.
4. Large differences between observed and expected values can indicate that the model does not fit well.
5. Summing the squared differences between observed and expected values, divided by the expected value, gives you the chi-square statistic.

Review Questions

• What role do observed values play in calculating the chi-square statistic?
• How can large differences between observed and expected values be interpreted?
• Why are observed values important in a goodness-of-fit test?

Related terms

Expected Values: The theoretical frequencies or outcomes predicted by a statistical model based on certain assumptions.

Chi-Square Statistic:

$\chi^2$ is a measure that quantifies the difference between observed and expected frequencies in categorical data.

Goodness-of-Fit Test:

$\text{A statistical test used to determine how well sample data fit a distribution from a population with a normal distribution.}$