What are the differences between the Null Hypothesis and the Alternative Hypothesis in a GOF test?
Null Hypothesis (H0): The observed distribution matches the claimed distribution. | Alternative Hypothesis (Ha): At least one of the proportions in the null hypothesis is incorrect.
What are the differences between Observed Counts and Expected Counts?
Observed Counts: The actual data collected in each category. | Expected Counts: The values we anticipate seeing in each category if the null hypothesis is true.
What are the differences between a large chi-square value and a small chi-square value?
Large Chi-Square Value: Indicates a big difference between observed and expected counts, suggesting the null hypothesis might be false. | Small Chi-Square Value: Suggests the observed data is close to what's expected under the null hypothesis.
What are the differences between a small p-value and a large p-value?
Small p-value: Results are statistically significant, reject the null hypothesis. | Large p-value: Results are not statistically significant, fail to reject the null hypothesis.
What are the differences between conditions Random and Independence?
Random: Sample must be randomly selected. | Independence: Population must be at least 10 times the sample size (10% rule).
What is the definition of Expected Counts?
Expected counts are the values we anticipate seeing in each category if the null hypothesis is true.
What is the definition of Chi-Square Statistic?
The chi-square statistic quantifies how much our observed data deviates from our expected counts.
What is the definition of Degrees of Freedom (df)?
Degrees of freedom (df) is a parameter that determines the shape of the chi-square distribution; calculated as (Number of Categories) - 1.
What is the definition of Goodness of Fit Test?
The chi-square goodness of fit (GOF) test checks if the observed frequencies of a categorical variable match a hypothesized distribution.
What is the definition of Null Hypothesis?
The null hypothesis is the assumption we're testing – usually, it states there's no difference or relationship between variables.
What is the formula for Expected Count?
Expected Count = (Sample Size) x (Probability under Null Hypothesis)
What is the formula for Chi-Square Statistic?
\( \chi^2 = \sum \frac{(Observed - Expected)^2}{Expected} \)
What is the formula for Degrees of Freedom in a GOF test?
df = (Number of Categories) - 1
How to calculate expected count for movie series preference?
Expected Count = (Total Sample Size) * (Proportion under Null Hypothesis). E.g., for Harry Potter: 2500 * 0.33 = 825
What is the formula for calculating the chi-square statistic in the music preference example?
\( \chi^2 = \frac{(180-200)^2}{200} + \frac{(150-150)^2}{150} + \frac{(170-150)^2}{150} \)
