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Unit 8( Chi-square) & Unit 9(Slopes) - Coggle Diagram
Unit 8( Chi-square) & Unit 9(Slopes)
Chi-Square GOF
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 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
Chi-Square Two-Way Test
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
Chi-Square formulas
Expected counts:
T-Statistic:
Degrees of freedom:
As df decreases, the distribution becomes more right skewed
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
