Hypothesized Distribution

Definition

The hypothesized distribution refers to the theoretical or expected distribution of a variable under the null hypothesis in a statistical analysis, particularly in the context of a chi-square goodness-of-fit test. It represents the distribution that the researcher believes the data should follow if the null hypothesis is true.

5 Must Know Facts For Your Next Test

1. The hypothesized distribution is the theoretical or expected distribution of the variable under the null hypothesis in a chi-square goodness-of-fit test.
2. The chi-square goodness-of-fit test is used to determine if the observed data follows the hypothesized distribution.
3. The test statistic in a chi-square goodness-of-fit test measures the discrepancy between the observed frequencies and the expected frequencies based on the hypothesized distribution.
4. If the test statistic is sufficiently large, the null hypothesis is rejected, indicating that the observed data does not follow the hypothesized distribution.
5. The hypothesized distribution is an important component in evaluating the fit of the data to the proposed model or theory being tested.

Review Questions

• Explain the role of the hypothesized distribution in a chi-square goodness-of-fit test.
  • In a chi-square goodness-of-fit test, the hypothesized distribution represents the theoretical or expected distribution of the variable under the null hypothesis. The test compares the observed frequencies of the data to the expected frequencies based on the hypothesized distribution. If the observed data significantly deviates from the hypothesized distribution, the null hypothesis is rejected, indicating that the data does not follow the proposed distribution.
• Describe how the hypothesized distribution is used to calculate the expected frequencies in a chi-square goodness-of-fit test.
  • The hypothesized distribution provides the expected or theoretical frequencies for each category or bin in the data. These expected frequencies are calculated based on the parameters of the hypothesized distribution and the total sample size. The chi-square test statistic is then computed by comparing the observed frequencies in the data to the expected frequencies derived from the hypothesized distribution. This allows researchers to determine if the observed data significantly deviates from the expected distribution under the null hypothesis.
• Analyze the importance of the hypothesized distribution in the interpretation and validity of a chi-square goodness-of-fit test.
  • The hypothesized distribution is crucial in the interpretation and validity of a chi-square goodness-of-fit test. If the hypothesized distribution is not appropriate or does not accurately reflect the true underlying distribution of the variable, the results of the chi-square test may be misleading or invalid. The researcher must carefully select the hypothesized distribution based on theoretical considerations, prior research, or assumptions about the data-generating process. The validity of the test depends on the appropriateness of the hypothesized distribution, as it serves as the benchmark for evaluating the fit of the observed data.

Related terms

Null Hypothesis: The null hypothesis is a statement that there is no significant difference or relationship between the variables being studied. It is the hypothesis that the researcher aims to test in a statistical analysis.

Chi-Square Goodness-of-Fit Test:

A statistical test used to determine whether a sample of data fits a specified probability distribution. It compares the observed frequencies of the data to the expected frequencies based on the hypothesized distribution.

Observed Frequencies:

The actual frequencies or counts of the data observed in a sample or experiment. These are compared to the expected frequencies based on the hypothesized distribution.