Setting Up a Chi Square Goodness of Fit Test
Ava Garcia
8 min read
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Study Guide Overview
This guide covers chi-square tests, focusing on the goodness-of-fit (GOF) test. It explains expected counts, the chi-square statistic, chi-square distributions, and degrees of freedom. The guide also details GOF test conditions (random, independence, large counts), provides example problems and practice questions, and offers exam tips.
#AP Statistics: Chi-Square Tests - Your Ultimate Study Guide π
Hey there, future AP Stats superstar! Let's get you prepped and confident for the exam with this super-focused guide on Chi-Square tests. We'll break down the concepts, highlight key points, and make sure you're ready to ace it!
#Expected Counts: What to Expect? π€
In a nutshell, expected counts are what we anticipate seeing in each category if the null hypothesis is true. Think of it as the baseline we're comparing our actual results against.
- Null Hypothesis: This is the assumption we're testing β usually, it states there's no difference or relationship between variables.
- Calculation:
Expected Count = (Sample Size) x (Probability under Null Hypothesis)- Example: If you survey 100 people and expect a 50/50 split, the expected count for each category is 50. * Why they matter: They help us determine if our observed data is significantly different from what we'd expect by chance.
#Chi-Square Statistic: Measuring the Difference π
The chi-square statistic quantifies how much our observed data deviates from our expected counts.
- Formula:
- We sum the squared differences between observed and expected counts, divided by the expected counts, for each category.
- Interpretation:
- A large chi-square value means a big difference between observed and expected, suggesting the null hypothesis might be false.
- A small chi-square value suggests the observed data is close to what's expected under the null hypothesis.
- P-value: We use the chi-square statistic to calculate a p-value, which 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.
#Chi-Square Distributions: The Shape of Things π
Chi-square distributions are always positive and skewed to the right.
- Degrees of Freedom (df): This parameter determines the shape of the distribution.
df = (Number of Categories) - 1- As df increases, the distribution becomes more symmetrical.
- Visual: 
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