ANOVA CNSL 503 QUESTIONS WITH
CORRECT ANSWERS 2025
What is an ANOVA? - CORRECT ANSWER -
ANOVA is an analysis of variance between groups (or levels of a factor) or within groups (or error) Wherea
s t-tests compare
only two sample distributions, ANOVA is capable of comparingkmany. We partition the total variance into
how group means differ from the grand mean and how individual observations within groups differ from t
heir group's mean
Whatkare the three assumptions of ANOVA? - CORRECT ANSWER -
1. independence of observations 2. normality 3. homogeneity of variance
What is the null hypothesis? - CORRECT ANSWER -All meanskare equal
μ1 = μ2 = μ3 = μ4
Whatkis the Alternative (one way) hypothesis? - CORRECT ANSWER -μ1≠ μ2≠ μ3≠ μ4
(There is at least ONE difference between groups)
What is the F statistic or F ratio? - CORRECT ANSWER -
An F statistic is a value you get when you run an ANOVA test or a regression analysis to find out if the mea
ns between two populations are significantly different. It's similar to a T statistickfrom 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 variabl
es are jointly significant.
Sum of squares - CORRECT ANSWER -
The residual sum of squares is used to help you decide if a statistical model is a good fit for your data. It m
easures the overall difference between your data and the values predicted by your estimation model (a "r
esidual" is a measure of the distance from a data point to a regression line). The sum of the squared devia
tions, (X-
Xbar)², is also called the sum of squares or more simply SS. SS represents the sum of squared differences f
rom the mean and is an extremely important term in statistics. Variance. The sum of squares gives rise to
variance. In statistical data analysiskthe total sum of squares (TSS or SST) is a quantity that appears as partk
of a standard way of presentingkresults of such analyses. It is defined as being the sum, over all observatio
ns, of the squared differences of each observation from the overall mean. Can calculate the sums of squar
es TOTAL, WITHIN, and BETWEEN
, What is the mean square formula? - CORRECT ANSWER -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.
Whatkis the purpose of a post-hoc test? - CORRECT ANSWER -
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? - CORRECT ANSWER -ONLY IF overall F value is significant
Whatkis a 2 way ANOVA? -kCORRECT ANSWER -2 independent variables
Whatkare the # of levels?
Ex:
You want to know how gait speed varies based on age and gender.
Define IV, DV, and levels. - CORRECT ANSWER -# 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.
CORRECT ANSWERS 2025
What is an ANOVA? - CORRECT ANSWER -
ANOVA is an analysis of variance between groups (or levels of a factor) or within groups (or error) Wherea
s t-tests compare
only two sample distributions, ANOVA is capable of comparingkmany. We partition the total variance into
how group means differ from the grand mean and how individual observations within groups differ from t
heir group's mean
Whatkare the three assumptions of ANOVA? - CORRECT ANSWER -
1. independence of observations 2. normality 3. homogeneity of variance
What is the null hypothesis? - CORRECT ANSWER -All meanskare equal
μ1 = μ2 = μ3 = μ4
Whatkis the Alternative (one way) hypothesis? - CORRECT ANSWER -μ1≠ μ2≠ μ3≠ μ4
(There is at least ONE difference between groups)
What is the F statistic or F ratio? - CORRECT ANSWER -
An F statistic is a value you get when you run an ANOVA test or a regression analysis to find out if the mea
ns between two populations are significantly different. It's similar to a T statistickfrom 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 variabl
es are jointly significant.
Sum of squares - CORRECT ANSWER -
The residual sum of squares is used to help you decide if a statistical model is a good fit for your data. It m
easures the overall difference between your data and the values predicted by your estimation model (a "r
esidual" is a measure of the distance from a data point to a regression line). The sum of the squared devia
tions, (X-
Xbar)², is also called the sum of squares or more simply SS. SS represents the sum of squared differences f
rom the mean and is an extremely important term in statistics. Variance. The sum of squares gives rise to
variance. In statistical data analysiskthe total sum of squares (TSS or SST) is a quantity that appears as partk
of a standard way of presentingkresults of such analyses. It is defined as being the sum, over all observatio
ns, of the squared differences of each observation from the overall mean. Can calculate the sums of squar
es TOTAL, WITHIN, and BETWEEN
, What is the mean square formula? - CORRECT ANSWER -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.
Whatkis the purpose of a post-hoc test? - CORRECT ANSWER -
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? - CORRECT ANSWER -ONLY IF overall F value is significant
Whatkis a 2 way ANOVA? -kCORRECT ANSWER -2 independent variables
Whatkare the # of levels?
Ex:
You want to know how gait speed varies based on age and gender.
Define IV, DV, and levels. - CORRECT ANSWER -# 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.
