ANOVA Questions and Answers 2023-2024 Verified
What is an ANOVA?
ANOVA is an analysis of variance between groups (or levels of a factor) or within
groups (or error) Whereas t-tests compare
only two sample distributions, ANOVA is capable of comparing many. We partition the
total variance into how group means differ from the grand mean and how individual
observations within groups differ from their group's mean
What are the three assumptions of ANOVA?
1. independence of observations 2. normality 3. homogeneity of variance
What is the null hypothesis?
All means are equal
μ1 = μ2 = μ3 = μ4
What is the Alternative (one way) hypothesis?
μ1≠ μ2≠ μ3≠ μ4
(There is at least ONE difference between groups)
What is the F statistic or F ratio?
An F statistic is a value you get when you run an ANOVA test or a regression analysis
to find out if the means between two populations are significantly different. It's similar to
a T statistic from a T-Test; A-T test will tell you if a single variable is statistically
significant and an F test will tell you if a group of variables are jointly significant.
Sum of squares
The residual sum of squares is used to help you decide if a statistical model is a good fit
for your data. It measures the overall difference between your data and the values
predicted by your estimation model (a "residual" is a measure of the distance from a
data point to a regression line). The sum of the squared deviations, (X-Xbar)², is also
called the sum of squares or more simply SS. SS represents the sum of squared
differences from the mean and is an extremely important term in statistics. Variance.
The sum of squares gives rise to variance. In statistical data analysis the total sum of
squares (TSS or SST) is a quantity that appears as part of a standard way of presenting
results of such analyses. It is defined as being the sum, over all observations, of the
squared differences of each observation from the overall mean. Can calculate the sums
of squares TOTAL, WITHIN, and BETWEEN
What is the mean square formula?
Mean Square=
Sum of Squares divided by its degrees of freedom
In ANOVA, mean squares are used to determine whether factors (treatments) are
significant.
Represents the variation between the sample means.
What is the purpose of a post-hoc test?
Purpose: Discover which pairs of scores are significantly different
-Preserves FAMILY-WISE PROTECTION against Type I error
When do you look at post-hoc tests?
ONLY IF overall F value is significant
, What is a 2 way ANOVA?
2 independent variables
What are the # of levels?
Ex:
You want to know how gait speed varies based on age and gender.
Define IV, DV, and levels.
# of groups within each independent variable
DV: Gait speed
IV: Age and Gender
3 levels (groups) for age
2 levels (groups) for gender
You want to test for sex differences in gait velocity among 3 age groups used
earlier.
What is the "main effect"?
Average effect for each independent variable.
Main effect for sex (combing all ages)
"What is the effect of sex on gait speed? Is there a difference in gait speed if you're
male versus female? Do men and women have different gaits speeds?"
Main effect for age (combining both genders)?
"Does gait speed depend on age?"
What is the interaction ?
Is there an interaction BETWEEN the independent variables?
Analyze all subgroups for significant differences
What do main effect and interaction effect have in common?
Assessing effect of the IV
You want to test for sex differences in gait velocity among 3 age groups used
earlier.
What is the interaction asking?
Does the effect of gender (on gait speed) DEPEND on how old you are?
Does the effect of age (on gait speed) DEPEND on sex?
or: For gait speed, is there a different trend of increasing age for women versus men?
What does a SIGNIFICANT INTERACTION tell us?
This tells us that any main effects may be MISLEADING or MEANINGLESS
You want to test for sex differences in gait velocity among 3 age groups used
earlier.
What is the null hypothesis for each main effect?
What is an ANOVA?
ANOVA is an analysis of variance between groups (or levels of a factor) or within
groups (or error) Whereas t-tests compare
only two sample distributions, ANOVA is capable of comparing many. We partition the
total variance into how group means differ from the grand mean and how individual
observations within groups differ from their group's mean
What are the three assumptions of ANOVA?
1. independence of observations 2. normality 3. homogeneity of variance
What is the null hypothesis?
All means are equal
μ1 = μ2 = μ3 = μ4
What is the Alternative (one way) hypothesis?
μ1≠ μ2≠ μ3≠ μ4
(There is at least ONE difference between groups)
What is the F statistic or F ratio?
An F statistic is a value you get when you run an ANOVA test or a regression analysis
to find out if the means between two populations are significantly different. It's similar to
a T statistic from a T-Test; A-T test will tell you if a single variable is statistically
significant and an F test will tell you if a group of variables are jointly significant.
Sum of squares
The residual sum of squares is used to help you decide if a statistical model is a good fit
for your data. It measures the overall difference between your data and the values
predicted by your estimation model (a "residual" is a measure of the distance from a
data point to a regression line). The sum of the squared deviations, (X-Xbar)², is also
called the sum of squares or more simply SS. SS represents the sum of squared
differences from the mean and is an extremely important term in statistics. Variance.
The sum of squares gives rise to variance. In statistical data analysis the total sum of
squares (TSS or SST) is a quantity that appears as part of a standard way of presenting
results of such analyses. It is defined as being the sum, over all observations, of the
squared differences of each observation from the overall mean. Can calculate the sums
of squares TOTAL, WITHIN, and BETWEEN
What is the mean square formula?
Mean Square=
Sum of Squares divided by its degrees of freedom
In ANOVA, mean squares are used to determine whether factors (treatments) are
significant.
Represents the variation between the sample means.
What is the purpose of a post-hoc test?
Purpose: Discover which pairs of scores are significantly different
-Preserves FAMILY-WISE PROTECTION against Type I error
When do you look at post-hoc tests?
ONLY IF overall F value is significant
, What is a 2 way ANOVA?
2 independent variables
What are the # of levels?
Ex:
You want to know how gait speed varies based on age and gender.
Define IV, DV, and levels.
# of groups within each independent variable
DV: Gait speed
IV: Age and Gender
3 levels (groups) for age
2 levels (groups) for gender
You want to test for sex differences in gait velocity among 3 age groups used
earlier.
What is the "main effect"?
Average effect for each independent variable.
Main effect for sex (combing all ages)
"What is the effect of sex on gait speed? Is there a difference in gait speed if you're
male versus female? Do men and women have different gaits speeds?"
Main effect for age (combining both genders)?
"Does gait speed depend on age?"
What is the interaction ?
Is there an interaction BETWEEN the independent variables?
Analyze all subgroups for significant differences
What do main effect and interaction effect have in common?
Assessing effect of the IV
You want to test for sex differences in gait velocity among 3 age groups used
earlier.
What is the interaction asking?
Does the effect of gender (on gait speed) DEPEND on how old you are?
Does the effect of age (on gait speed) DEPEND on sex?
or: For gait speed, is there a different trend of increasing age for women versus men?
What does a SIGNIFICANT INTERACTION tell us?
This tells us that any main effects may be MISLEADING or MEANINGLESS
You want to test for sex differences in gait velocity among 3 age groups used
earlier.
What is the null hypothesis for each main effect?
