Manual Calculations: First, plot the data for the two sample graphically in form of a scatter-plot and mark the sample means. Follow these step-by-step instructions to fill the terms of an ANOVA table.

cases [i]	Sample1	Sample2		(Yi-)	(Yi-)2	Both Samples		(Yi-)	(Yi-)2
1	-1.02					-1.02
2	1.42					1.42
3	-0.26					-0.26
4	-0.05					-0.05
5	1.86					1.86
6	0.68					0.68
7	0.05					0.05
8	0.27					0.27
9	2.47					2.47
10	-1.39					-1.39
11		-0.84				-0.84
12		0.12				0.12
13		-0.57				-0.57
14		-1.09				-1.09
15		0.21				0.21
16		-0.13				-0.13
17		0.94				0.94
18		0.87				0.87
19		-0.35				-0.35
20		-0.40				-0.40
Σ =

Items from Sample 1

• Count the number of cases for sample 1: n₁ =
• Calculate the sum of all Y in sample 1: ΣY_i =
• Calculate the mean for Y in sample 1: ₁ = ΣY_i / n₁ =
  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 =
• Calculate the sum of all Y in sample 2: ΣY_i=
• Calculate the mean for Y in sample 2: ₂ = ΣY_i / n₂ =
  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 =
• Calculate the sum of all Y: ΣY_i =
• Calculate the mean for all Y (i.e., the mean of means):  = ΣY_i / n =
  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 =
• The error sums of squares: SS_E = Σ(Y_i-)² =
• The model sums of squares: SS_M = SS_T - SS_E =
• The degrees of freedom for the model term: df_M = the number of samples - 1 =
• The degrees of freedom for the total term: df_T = n - 1 =
• The degrees of freedom for the error term: df_E = df_T - df_M =
• 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 =

To double-check your solution, compare with these results