All Flashcards
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.
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 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).