Question

For the question below, state what your null and alternative hypotheses are and select the appropriate test. Assess assumptions and do whatever needs to be done depending on your results (ie, doing a transformation of data or selecting a non-parametric if data violate assumptions). If you decide to run a Kruskal-Wallis test, you can assume the data satisfy those assumptions. Recall that it is generally considered ok to violate one assumption, especially if sample size is not too small. Perform the test and report the p value with the biological interpretation of your data. Finally, make a plot of the data that DOES NOT have a title, but does have proper x and y axis labels (can do it in excel or SPSS).

1)

You are interested in the connection between vitamin C and bone health. You expose guinea pigs to three different doses of vitamin C and then you record tooth growth following the doses. You collect the following data which are measures of tooth length in mm.

Dose 0.5	Dose 1.0	Dose 2.0
4.2	16.5	23.6
11.5	16.5	18.5
7.3	15.2	33.9
5.8	17.3	25.5
6.4	22.5	26.4
10	17.3	32.5
11.2	13.6	26.7
11.2	14.5	21.5
5.2	18.8	23.3
7	15.5	29.5

Answer 1

For the question below, state what your null and alternative hypotheses are and select the appropriate test. Assess assumptions and do whatever needs to be done depending on your results (ie, doing a transformation of data or selecting a non-parametric if data violate assumptions). If you decide to run a Kruskal-Wallis test, you can assume the data satisfy those assumptions. Recall that it is generally considered ok to violate one assumption, especially if sample size is not too small. Perform the test and report the p value with the biological interpretation of your data. Finally, make a plot of the data that DOES NOT have a title, but does have proper x and y axis labels (can do it in excel or SPSS).

Test for assumptions.

Test for normality shows that Kolmogorov-Smirnov test p values for the 3 groups are 0.20 which is > 0.05 level of significance. This shows that the normality assumption is not violated.

Tests of Normality
	Group	Kolmogorov-Smirnova			Shapiro-Wilk
		Statistic	df	Sig.	Statistic	df	Sig.
Tooth length	Dose 0.5	.198	10	.200*	.890	10	.170
	Dose 1.0	.217	10	.200*	.908	10	.270
	Dose 2.0	.154	10	.200*	.973	10	.919
*. This is a lower bound of the true significance.
a. Lilliefors Significance Correction

1)

You are interested in the connection between vitamin C and bone health. You expose guinea pigs to three different doses of vitamin C and then you record tooth growth following the doses. You collect the following data which are measures of tooth length in mm.

ANOVA used to compare the means of the three groups.

Descriptives
Tooth length
	N	Mean	Std. Deviation	Std. Error	95% Confidence Interval for Mean		Minimum	Maximum
					Lower Bound	Upper Bound
Dose 0.5	10	7.9800	2.74663	.86856	6.0152	9.9448	4.20	11.50
Dose 1.0	10	16.7700	2.51531	.79541	14.9707	18.5693	13.60	22.50
Dose 2.0	10	26.1400	4.79773	1.51718	22.7079	29.5721	18.50	33.90
Total	30	16.9633	8.26603	1.50916	13.8767	20.0499	4.20	33.90

ANOVA
Tooth length
	Sum of Squares	df	Mean Square	F	Sig.
Between Groups	1649.489	2	824.744	67.072	.000
Within Groups	332.001	27	12.296
Total	1981.490	29

Calculated F(2,27) = 67.072, P=0.000 which is < 0.05 level of significance. Ho is rejected. We conclude that three group means are different. We conclude that there is a connection between vitamin C and bone health.