All Flashcards
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.
Explain the concept of a P-value in the context of a Chi-Square test.
The p-value tells us the probability of getting our observed results (or more extreme) if the null hypothesis were true. A small p-value (typically < 0.05) means our results are statistically significant, and we reject the null hypothesis.
Explain the concept of Chi-Square Distributions.
Chi-square distributions are always positive and skewed to the right. The shape is determined by the degrees of freedom; as df increases, the distribution becomes more symmetrical.
Explain the concept of the Large Counts condition for a GOF test.
The Large Counts condition requires that all expected counts must be at least 5. This ensures the chi-square statistic is approximately chi-square distributed.
Explain the purpose of the Random condition in a GOF test.
The sample must be randomly selected to ensure that the sample is representative of the population, which is a requirement for the GOF test to be valid.
Explain the purpose of the Independence condition in a GOF test.
The population must be at least 10 times the sample size (10% rule). This ensures that the observations are independent of each other.