Worksheat: Analysis of Variance

Results:

cases [i]	Sample1	Sample2		(Yi-)2	Both Samples		(Yi-)2
1	-1.02		0.403	2.025	-1.02	0.1395	1.344
2	1.42		0.403	1.034	1.42	0.1395	1.640
3	-0.26		0.403	0.440	-0.26	0.1395	0.160
4	-0.05		0.403	0.205	-0.05	0.1395	0.036
5	1.86		0.403	2.123	1.86	0.1395	2.960
6	0.68		0.403	0.077	0.68	0.1395	0.292
7	0.05		0.403	0.125	0.05	0.1395	0.008
8	0.27		0.403	0.018	0.27	0.1395	0.017
9	2.47		0.403	4.272	2.47	0.1395	5.431
10	-1.39		0.403	3.215	-1.39	0.1395	2.339
11		-0.84	-0.124	0.513	-0.84	0.1395	0.959
12		0.12	-0.124	0.060	0.12	0.1395	0.000
13		-0.57	-0.124	0.199	-0.57	0.1395	0.503
14		-1.09	-0.124	0.933	-1.09	0.1395	1.512
15		0.21	-0.124	0.112	0.21	0.1395	0.005
16		-0.13	-0.124	0.000	-0.13	0.1395	0.073
17		0.94	-0.124	1.132	0.94	0.1395	0.641
18		0.87	-0.124	0.988	0.87	0.1395	0.534
19		-0.35	-0.124	0.051	-0.35	0.1395	0.240
20		-0.40	-0.124	0.076	-0.40	0.1395	0.291
Σ =	4.03	-1.24		17.5965			18.9851

Items from Sample 1

• Count the number of cases for sample 1: n₁ = 10
• Calculate the sum of all Y in sample 1: ΣY_i = 4.03
• Calculate the mean for Y in sample 1: ₁ = ΣY_i / n₁ = 0.403 and fill in measures from example 1
• Calculate for each case the squared deviation from its respective sample mean (Y_i-)² and fill column

Items from Sample 2

• Count the number of cases for sample 2: n₂ = 10
• Calculate the sum of all Y in sample 2: ΣY_i= -1.24
• Calculate the mean for Y in sample 2: ₂ = ΣY_i / n₂ = -0.124 and fill in measures from example 2
• Calculate for each case the squared deviation from its respective sample mean (Y_i-)² and fill column

All Items

• Count the total number of cases: n = 20
• Calculate the sum of all Y: ΣY_i = 2.79
• Calculate the mean for all Y (i.e., the mean of means):  = ΣY_i / n = 0.1395 and fill for all measures
• Fill the column for each case with squared deviations from its respective sample mean (Y_i-)² and fill column

Fill ANOVA table

• Sum the two columns that contain the squared deviations
• The total sums of squares: SS_T = Σ(Y_i-)² = 18.9851
• The error sums of squares: SS_E = Σ(Y_i-)² = 17.5965
• The model sums of squares: SS_M = SS_T - SS_E = 1.3887
• The degrees of freedom for the model term: df_M = the number of samples - 1 = 1
• The degrees of freedom for the total term: df_T = n - 1 = 19
• The degrees of freedom for the error term: df_E = df_T - df_M = 18
• Fill the model variance (MS_M) term by dividing the model sums of squares (SS_M) term with its respective degrees of freedom: MS_M =
• Fill the error variance (MS_E) term by dividing the error sums of squares (SS_E) term with its respective degrees of freedom: MS_E =
• Obtain the ratio of the model MS over the error MS: F =
• Look up p-value for the statistic in an F distribution with df_M and df_E degrees of freedom (F[df_M, df_E]): p =