Unit 8( Chi-square) & Unit 9(Slopes)
Chi-Square GOF
Chi-Square Two-Way Test
A one-way table is a frequency count table for a single categorical variable
- Observed Counts: The actual counts/value from the study
- Expected Counts: The expected counts/value if Ho is true
Chi-Square formulas
Expected counts: 
T-Statistic: 
Degrees of freedom: 
As df decreases, the distribution becomes more right skewed
Chi-square is not a normal distribution, it's right skewed and it's always positive
State
- Ho: The distribution of [. ] is same as [. ]
- Ha: The distribution of [. ] is different than [. ]
Plan(Conditions) - Random
- Independence
- Large counts: All expected counts are at least 5
- All conditions met, perform chi square test for GOF
Do - find t-stat and use x^2cdf
- Or use Ti-84 and find X^2 GOF Test
Conclude - Reject/fail to reject Ho. Convincing/not convincing
Two Way Table: A table that display frequencies counts for two different categories collected from a single group of people
Homogeneity(Two way table) (Two samples)
State
- Ho: The distribution of var. A is the same as for var. B
- Ha: The distribution of var A. is different as for var. B
Independence(Refers to association) (One sample)
State:
- Ho: There is no association between var A. and var. B (var. A and var. B are independent)
- Ha: There is an association between var. A and var. B (var A and var B are not independent)
Expected Count:
- (column Total* Row Total)/ table total
- Ti-84-> 2nd matrix(perform X^2 first then find expected count by going back to 2nd matrix)
Do
- use t-stats formula and use x^2cdf
- Ti-84->perform X^2 Test
Confidence Interval for slopes
Test for slopes
Least Square Regression analysis data:
Far Bottom Left=Slope
B interpretation: For every increase of[ ], the predicted[. ] increase/decrease by [. ]
Far Top left=y intercept
a interpretation: When the [varA] is at 0, the predicted [varB] is [. ]
S=standard deviation
S interpretation: The actual [var A] typically varies by [. ] from the mean
Far Bottom of SE Coef=SEb
SEb interpretation: On average, the actual slope is typically off by[. ]
Conditions for Slopes
- Linear: scatterplot needs to show linear relationship and residual plot doesn't have leftover curved pattern
- Independence: Assume at least n*10
- Normality: Dot plot of residuals cannot show strong skewness or outliers
- Equal SD: Residual plot does not show a clear sideways Christmas tree pattern
- Random:Random Sample
Df=n-2
Formula: 
-Conclude
We are % confident that the interval of[. ] capture the true slope of linear regression for [var A] and [var B]
State:
- Ho: B=0
- Ha: B>,<,≠ 0
Positive relationship: B > 0
Negative relationship: B < 0
T-statistic formula: 
Procedure: Linear regression t-test for slope
Ti-84: LinRegTTest
State
Estimate the true slope of the regression line with % confidence level