Question

A professor compared differences in class grades between students in their freshman, sophomore, junior, and senior years of college. If different participants were in each group, then what type of statistical design is appropriate for this study?(a) a two-independent sample t test(b) a one-way between-subjects ANOVA(c) a two-way between-subjects ANOVA(d) both a two-independent sample t test and a one-way between-subjects ANOVA

Answer 1

(b) a one-way between-subjects ANOVA

That's the correct option since we have one factor (class grade) and we have more than two groups.

Explanation:

(a) a two-independent sample t test

We can't apply a two independnet t test since we are comparing more than two groups (Freshman, sophomore, Junior and senior). And for this case when we have more than two groups, the most powerful method is the one way ANOVA between subjects.

(b) a one-way between-subjects ANOVA

That's the correct option since we have one factor (class grade) and we have more than two groups.

One way Analysis of variance (ANOVA) "is used to analyze the differences among group means in a sample".

The sum of squares "is the sum of the square of variation, where variation is defined as the spread between each individual value and the grand mean"

If we assume that we have
`p` groups and on each group from
`j=1,\dots,p` we have
`n_j` individuals on each group we can define the following formulas of variation:

`SS_(total)=\sum_(j=1)^p \sum_(i=1)^(n_j) (x_(ij)-\bar x)^2`

`SS_(between)=SS_(model)=\sum_(j=1)^p n_j (\bar x_(j)-\bar x)^2`

`SS_(within)=SS_(error)=\sum_(j=1)^p \sum_(i=1)^(n_j) (x_(ij)-\bar x_j)^2`

And we have this property

`SST=SS_(between)+SS_(within)`

(c) a two-way between-subjects ANOVA

We can't apply a two way ANOVA since we have just one factor (or variable of interest) the class grades measured with a score. So then is not appropiate use this method for this case.

(d) both a two-independent sample t test and a one-way between-subjects ANOVA

False since we can't apply the two way ANOVA, that's not correct.