Teachers told their students that they would either receive praise, candy, or money after completing their homework on time. Below you will find a table of the number of homework completed by 15 children in one week. In addition, you will find the Means, Totals, and Sum of Squares values below each column for each treatment. Is there enough evidence to show that the type of reward affects the number of homework completed? Compute a one-way ANOVA following the steps below. Treatment: Praise Candy Money 0 2 2 0 4 3 2 0 1 1 1 4 2 3 5 M1= 1 M2= 2 M3= 3 T= 5 T=10 T= 15 SS1= 4 SS2=10 SS3=10 Compute the following values: N = # of total scores = G = ∑T= grand total of all scores= ∑X2= k = # of conditions = n = # per group = For the data above in the table, calculate SSTotal: SStotal = ΣX2 – (G2/N) = Now, calculate SSwithin: SSwithin = ΣSSeach treatment = Finally, calculate SSbetween: SSbetween = Σ(T2/n) – G2/N OR SStotal – SSwithin = Calculate the degrees of freedom: dftotal= N-1 = dfwithin= N- k = dfbetween= k-1 = Calculate the between and within treatments variance: MSbetween= SSbetween/dfbetween = MSwithin= SSwithin/dfwithin= Finally, calculate the F -statistic F = MSbetween/MSwithin= Can we reject the null hypothesis at the alpha of .05 level? Find the F-critical value using the correct degrees of freedom, then compare your F-calcluated to the F-critical to make a statistical decision. Fcritical = Fcritical(dfbetween, dfwithin) =
Teachers told their students that they would either receive praise, candy, or money after completing their homework on time. Below you will find a table of the number of homework completed by 15 children in one week. In addition, you will find the Means, Totals, and Sum of Squares values below each column for each treatment. Is there enough evidence to show that the type of reward affects the number of homework completed? Compute a one-way ANOVA following the steps below.
Treatment:
|
Praise |
Candy |
Money |
|
0 |
2 |
2 |
|
0 |
4 |
3 |
|
2 |
0 |
1 |
|
1 |
1 |
4 |
|
2 |
3 |
5 |
M1= 1 M2= 2 M3= 3
T= 5 T=10 T= 15
SS1= 4 SS2=10 SS3=10
Compute the following values:
N = # of total scores =
G = ∑T= grand total of all scores=
∑X2=
k = # of conditions =
n = # per group =
For the data above in the table, calculate SSTotal:
SStotal = ΣX2 – (G2/N) =
Now, calculate SSwithin:
SSwithin = ΣSSeach treatment =
Finally, calculate SSbetween:
SSbetween = Σ(T2/n) – G2/N OR SStotal – SSwithin =
Calculate the degrees of freedom:
dftotal= N-1 =
dfwithin= N- k =
dfbetween= k-1 =
Calculate the between and within treatments variance:
MSbetween= SSbetween/dfbetween =
MSwithin= SSwithin/dfwithin=
- Finally, calculate the F -statistic
F = MSbetween/MSwithin=
Can we reject the null hypothesis at the alpha of .05 level? Find the F-critical value using the correct degrees of freedom, then compare your F-calcluated to the F-critical to make a statistical decision.
Fcritical = Fcritical(dfbetween, dfwithin) =
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