Question

Analysis of Variance results:

Responses: Self-esteem
Factors: handedness

Response statistics by factor

handedness	n	Mean	Std. Dev.	Std. Error
left	7	4.2857143	3.0937725	1.1693361
mixed	4	8	2.1602469	1.0801234
right	9	5.4444444	3.4681087	1.1560362

ANOVA table

Source	DF	SS	MS	F-Stat	P-value
handedness	2	35.299206	17.649603	1.7896918	0.1971
Error	17	167.65079	9.8618114
Total	19	202.95

Tukey HSD results (95% level)

left subtracted from

	Difference	Lower	Upper	P-value
mixed	3.7142857	-1.3351574	8.7637289	0.1728
right	1.1587302	-2.9011749	5.2186352	0.7481

mixed subtracted from

	Difference	Lower	Upper	P-value
right	-2.5555556	-7.3966838	2.2855727	0.386

A ANOVA was run to test the hypothesis to determine if there would be significant difference in self-esteem scores of participants who are left handed, right handed or mixed.

Give a report on the findings.

Was there any significance in difference?

Run a post hoc test even if findings are not significant.

Answer 1

From the ANOVA table, an F value of 1.7896918 was calculated. At df1 = 2 and df2 = 17, the p value was calculated as 0.1971. The decision value being that since the p value was > (0.05), we fail to reject the null hypothesis, that is the differences were not significant.

The ANOVA Table

Source	SS	DF	Mean Square	F	Fcv	p
Between	35.299206	2.0	17.649603	1.788000	3.5915	0.1974
Within/Error	167.797625	17.0	9.870449
Total	203.10	19.0

The post Hoc Test

Left	4.2857143
Mixed	8
Right	5.4444444
	Difference	1 / ni + 1/nj	MSE	q critical	ME	Left	Right
Left - Mixed	3.7142857	0.39285714	9.87	2.567185	5.055139	-1.34085	8.769425
Left - Right	1.1587301	0.25396825	9.87	2.567185	4.064485	-2.90575	5.223215
Mixed - Right	6.8412699	0.36111111	9.87	2.567185	4.846589	1.994681	11.68786

A Tukeys post Hoc test was conducted, and the method used was the method of Confidence Interval, whic is given by

Difference (q critical / sqrt(2) )* Sqrt(MSE * [(1 / ni + 1 / nj)]

Please not: We take the absolute value of the difference

Where q critical is tukeys q critical found from tukeys table for the level of significance where on the horizontal we have k = number of treatments and df error on the vertical.

Here = 0.05, df error = 17 and number of treatments = 3 (since df1 = k - 1 = 2)

Therefore tukeys critical = 3.63

MSE = 9.8618114

If the confidence interval comes up with different signs, then the differences are not significant as is the case we see for left subtracted from mixed, left subtracted from right , where the confidence interval for each has different signs, but for mix subtracted from right, the signs are the same, which means that there is a statistical difference between these 2 values.

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