Chi Square: The test for Goodness of Fit Flashcards
What does Chi Square measure in biostatistics?
The association between categorical variables
Chi Square tests whether the observed frequencies in a contingency table differ from the expected frequencies.
What is the null hypothesis in a Chi Square test?
There is no association between the categorical variables
The null hypothesis posits that the distribution of sample categorical data matches an expected distribution.
What does the Alternative Hypothesis in a Chi Square test tell you:
There is association between categorical variables
What are the two main types of Chi Square tests?
- Chi Square Goodness of Fit Test
- Chi Square Test of Independence
What does the goodness of fit test tells us
If the sample = population
Uses sample data to answer a question about the population.
What does the test of independence tell us
If two of the categories are independent.
Fill in the blank: The Chi Square statistic is calculated using the formula _______.
χ² = Σ((O - E)² / E)
O represents observed frequencies and E represents expected frequencies.
What is the significance level commonly used in Chi Square tests?
0.05
A significance level of 0.05 indicates a 5% risk of concluding that a difference exists when there is none.
True or False: The Chi Square test can be used for continuous data.
False
Chi Square tests are specifically designed for categorical data.
What are the assumptions of the Chi Square test?
- Observations are independent
- Categories are mutually exclusive
- Expected frequency should be 5 or more
These assumptions ensure the validity of the Chi Square results.
What is the role of degrees of freedom in a Chi Square test?
To determine the critical value from the Chi Square distribution
Degrees of freedom are calculated based on the number of categories minus one for goodness of fit, or (rows - 1) * (columns - 1) for independence.
Fill in the blank: A Chi Square value greater than the critical value indicates _______.
statistical significance
This means rejecting the null hypothesis.
What is the impact of sample size on the Chi Square test?
Larger sample sizes provide more reliable results and can detect smaller effects
However, very large sample sizes can lead to statistically significant results that are not practically significant.
What is a limitation of the Chi Square test?
It cannot determine the strength or direction of the association
Chi Square only indicates whether an association exists, not how strong it is.
What does the CHI Square formula primarily assess?
The CHI Square formula primarily assesses the association between categorical variables.
True or False: The CHI Square formula can only be used for two categorical variables.
False: The CHI Square formula can be used for more than two categorical variables.
Fill in the blank: The CHI Square statistic is calculated using the formula χ² = Σ (O - E)² / E, where O is ______ and E is ______.
O is the observed frequency and E is the expected frequency.
In the CHI Square formula, what does the symbol Σ represent?
The symbol Σ represents the summation of the values.
What is the significance of the degrees of freedom in the CHI Square test?
The degrees of freedom determine the distribution of the CHI Square statistic and are calculated as (number of categories - 1).
What is a parametric test?
Test only concerned with parameters and require assumptions about parameters
Exact frequency formula
n (sample size) x percentage (stated in null hypothesis)
What is the expected frequency?
value that is predicted from the (p) proportions in the null hypothesis & (n) sample size.
What does a small value for chi-square indicate?
There is a good fit between the data and the hypothesis (fail to reject H0)
A small chi-square value suggests that the observed and expected frequencies are closely aligned.
What does a large value for chi-square indicate?
There is NOT a good fit between the data and the hypothesis ( Reject H0)
