What does ANOVA stand for?
Analysis of Variance
ANOVA is a statistical method used to compare means among three or more groups.
What are the two types of ANOVA mentioned?
- One-factor ANOVA
- Two-factor ANOVA
The type of experimental design determines the type of ANOVA performed.
What is the purpose of ANOVA?
To compare more than two groups and identify differences in their means
It extends the test for the difference between the mean of two groups.
What is a factor in the context of ANOVA?
A characteristic thought to influence the measured observations
A level is a value of the factor.
When should you use a one-factor ANOVA?
When there is one categorical independent variable and one quantitative dependent variable with at least three levels
It is used in a completely randomised design.
What are the hypotheses for ANOVA?
- H1: µ1=µ2=µ3=…
- H0: At least two means differ
What are the three key assumptions for one-way ANOVA?
- Observations are independent and random
- Population at each factor level is approximately normally distributed
- Normal populations have a common variance
What are the title in the source table for all ANOVA tests?
Source, SS, v, MS, F
What is the formula for the Mean of Squares, MS?
MS=SS/v
What is the formula for the F ratio, F?
F=MS(B)/MS(E)
Mean squares between divided by mean squares error
What is a blocking factor in two-way ANOVA?
A second factor that places subjects into homogenous groups called blocks
It helps control for variability in the experimental design.
What is the significance level typically used in hypothesis testing for ANOVA?
5%
This level is commonly used to determine statistical significance.
True or false: ANOVA can only be performed with two groups.
FALSE
If there are onlt two groups to be tested, the two sample z or t test would be appropriate
What is the mean square (MS) in ANOVA?
The sum of squares divided by the degrees of freedom
It is used to calculate the F ratio.
What is the F ratio in ANOVA?
Mean square between groups divided by mean square within groups
This is used as the test statistic in an ANOVA
Fill in the blank: A level is a _______ of the factor.
value
Levels are specific values that a factor can take in an experiment.
What is the total in ANOVA?
The overall sum of squares from all sources of variation
It includes both between-group and within-group variations.
Which experimental design is associated with one-factor ANOVA?
Completely randomised design
Which experimental design is associated with two-factor ANOVA?
Randomised block design
How could you comment on any difference found in an ANOVA hypothesis test?
Calculate the mean of each level in the factor mentioned and compare these.
How do you test if a blocking factor is effective?
Use the F ratio for the blocking factor and test against the CV for that factor, if the F ratio is significant then the blocking factor was effective
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0 Foundations of Statistics31
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1 Numerical Measures, Graphs and Diagrams72
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2 Probability22
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3 Populations and Samples45
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4 Introduction to Probability Distributions21
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5 Binomial Distribution17
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6 Normal Distribution20
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7 Correlation and Regression33
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8 Introduction to Hypothesis Testing54
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9 Contingency Tables21
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10 Non-Parametric Tests22
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11 Bayes' Theorem15
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12 Linear Combinations21
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13 Experimental Design23
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14 Estimates and Confidence Intervals24
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15 Errors and Power27
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16 One and Two Sample Hypothesis Tests23
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17 Paired Tests10
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18 Poisson and Exponential Distributions21
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19 Goodness of Fit30
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20 ANOVA21
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21 Effect Size16
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Identify the test48
