Question

Researchers want to examine the effect of scent on memory. A total of 9 people were recruited for the study. Each person randomly assigned to one of the three experimental groups. Each person was asked to read a passage from a book. A week later, each study participant was asked to recall as much information as they could from the previously read passage.  Researchers determined a score for each subject representing the facts that have been correctly recalled. The data are available in Table 1.

Group 1: Scent is present during a passage reading and during the passage recall

Group 2: No scent is present in either the passage reading or the passage recall

Group 3: Scent is present during the passage reading only

The purpose of this study is to identify whether there are differences between the mean number of facts recalled by the experimental group one week after reading the original passage (α = 0.05).

For this question, conduct a one-way ANOVA by hand (showing all your calculations) to compare the means of these three samples. Remember to follow the steps of hypothesis testing and show your calculations. Also, create a one-way ANOVA summary table showing your results of the analysis (see table 2 for an example).

Make sure to take a photo/scan your work and paste the scanned work or photo to your Word document.

Table 1.

Passage recall scores by group, individual group means, and overall mean.

Group 1(=3)	Group 2(=3)	Group 3(=3)
22	30	27
33	20	18
29	14	17
	(N=9)

Table 2.

One-way ANOVA Summary Table

Source	SS	DF	MS	Fc	Fα
Between
Within
Total

Answer 1

Following table shows the group total:

	G1	G2	G3
	22	30	27
	33	20	18
	29	14	17
Total	84	64	62

Following table shows the grand total and total of square values:

	G	G^2
	22	484
	33	1089
	29	841
	30	900
	20	400
	14	196
	27	729
	18	324
	17	289
Total	210	5252

From above table,

Now

Now

Since there are 3 different groups so we have k=3. Therefore degree of freedoms are:

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Now

F test statistics is

The critical value of F using excel function "=FINV(0.05,2,6)" is 5.143.

Since F < 5.143 e reject the null hypothesis. There is no evidence to conclude that there are differences between the mean number of facts recalled by the experimental group one week after reading the original passage

Following is the completed ANOVA:

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