STAT 310 Final Exam Review Topics
One-way ANOVA
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One variable that researchers are manipulating to see the effects on the response
H0: group/treatment means are equal
Ha: at least two of the groups means differ
Assumptions:
o Independent observations – random assignment
o Normal distribution – bell-shaped & symmetric histogram, points fall on reference line
in normal quantile plot
o Constant variance – no fan/wedge shape
Statistical model: yij = μ + τi + εij
Predicting
Randomized Complete Block Design
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Blocks are created to reduce unwanted variability. That is, a source of variation you’re not
interested in measuring the effects of that you can control.
There is one factor in which researchers are manipulating to see the effects on the response
Assumptions:
o Normality
o Constant variance
o Interaction between treatment and block – assumed to hold without actually checking
Statistical model: yij = μ + τI + βj + εij
predicting
Two-way ANOVA (Factorial Treatment Design)
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Two variables that researchers are manipulating to see the effects on the response
Statistical model: yijk = μ + αi + βj + αβij + εijk
Analysis:
o First check to see if interaction is significant
 If yes, look at simple effects
 If no, look at main effects
o Look at main effects (if needed) to determine whether each is significant or not
Assumptions:
o Normality
o Constant variance
o Independent observations
Predicting
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Two-way ANOVA in a Randomized Complete Block Design
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Two variables that researchers are manipulating to see the effects on the response.
Blocks are also created to reduce unwanted variability
Statistical model: yijk = μ + αi + βj + αβij + ρk + εijk
Assumptions:
o Normality
o Constant variance
o Independent observations
o No treatment and block interaction
Analysis:
o First check to see if interaction is significant
 If yes, look at simple effects
 If no, look at main effects
o Look at main effects (if needed) to determine whether each is significant or not
Predicting
Two Numeric Variables
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Correlation
o -1 ≤ r ≤ 1
o Strongest linear relationship ±1
o Weakest linear relationship 0
Simple Linear Regression
o Fitted regression equation from JMP output
o Testing whether regression is useful
o Interpreting intercept and slope
o Interpreting/identifying R2
o Assumptions:
 Linear
 Constant variance
 Independent observations
 Normality
 Outliers
o Predicting
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Multiple Numeric variables
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Correlation matrix
Scatterplot matrix
Multiple Linear Regression
o Fitted regression equation from JMP output
o Testing whether regression is useful
o Interpreting intercept and slope coefficients
o Assumptions:
 Linearity
 Constant variance
 Independence
 Normality
 Outliers
o Backward elimination
ANOCOVA
o Used when you want to adjust for particular quantitative variables
o Testing for unequal slopes model (interaction term present)
o Testing for equal slopes model (no interaction term)
o Estimated regression equations from JMP output
o Predicting
Goodness of Fit Tests
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One categorical variable with 2 outcomes
o H0: p = 0.30
Ha: p ≠ 0.30
o Expected counts ≥ 5
o Chi-square test
o Test statistic
o Make conclusion in terms of Ha
One categorical variable with more than 2 outcomes
o H0: pA = 0.40 pB = 0.20
pC= 0.10
Ha: Two or more differ
o Expected counts ≥ 5
o Chi-square test
o Test statistic
o Make conclusions in terms of Ha
pD = 0.30
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Comparing Two Proportions
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Chi-square test
o H0: pA = pB
Ha: pA ≠ pB
o Expected counts ≥ 5
o Test statistic
o Make conclusion in terms of Ha
Fisher’s Exact Test
o H0: pA ≤ pB
or
Ha: pA > pB
o No expected counts
o No test statistic
o Make conclusion in terms of Ha
H0: pA ≥ pB
Ha: pA < pB
Chi-square Test of Independence
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When there are more than two outcomes for at least one of the categorical variables
H0: the two variables are independent (i.e. no relationship)
Ha: the two variables are not independent (i.e. relationship exists)
Expected counts ≥ 5
Chi-square test
Test statistic
Make conclusion in terms of Ha
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