Question

Some individuals believe that there is a link between mobile phone use and brain tumors. The basic idea is that mobile phones emit microwaves, and so holding one next to your brain for large parts of the day is a bit like sticking your brain in a microwave oven and selecting the ‘cook until well done’ button. (Please note: this claim has been refuted. But if it were supported, the study described below would not be a realistic or ethical way to test this claim.) Hypothetically, if researchers were to test this experimentally, they could get six groups of people and strap a mobile phone to their heads (that they can’t remove). Then, by remote control, they turn the phones on for a certain amount of time each day. After 6 months, they could measure the size of any tumor (in mm2 ) close to the site of the phone. The six groups experienced 0, 1, 2, 3, 4, or 5 hours per day of phone microwaves for 6 months.

1.) State the null and alternative hypothesis for this study. Do so as both a sentence and using the appropriate mathematical representation (uncommon symbols to copy and edit as needed: σµ 2 ).

2.) Using the procedure for conducting a one-way ANOVA, run the analysis placing the independent and dependent variables in their appropriate dialog boxes. In addition to the one-way ANOVA, conduct a Tukey’s HSD post-hoc test. That data will be used to answer question 3. Copy and paste the output of your ANOVA in your MSWord document (under #1).

3.) Although an ANOVA can tell us whether at least one group differs from all other groups, it does not tell us which groups are different. To determine this outcome we use a post-hoc test. Based on the results of your Tukey’s HSD post-hoc comparison, indicate which groups, if any, were significantly different from one another in this analysis.

4.) Based on a significance level of α = 0.05, report your results in APA format.

5.) In a couple of sentences, explain what the results of this study mean. Think of it as if you were trying to explain the meaning of the statistical analysis to your grandparents. How would you describe the results to them?

First Column: Usage

Second Column: Tumor

.00   .04
.00   .02
.00   .03
.00   .03
.00   .06
.00   .06
.00   .03
.00   .05
.00   .02
.00   .03
.00   .03
.00   .04
.00   .05
.00   .04
.00   .03
.00   .06
.00   .05
.00   .04
.00   .03
.00   .03
1.00   .79
1.00   .76
1.00   .24
1.00   .96
1.00   .64
1.00   .35
1.00   .49
1.00   .80
1.00   .78
1.00   .05
1.00   .95
1.00   .41
1.00   .64
1.00   .50
1.00   .17
1.00   .74
1.00   .40
1.00   .29
1.00   .02
1.00   .71
2.00   1.31
2.00   1.10
2.00   1.09
2.00   .50
2.00   1.28
2.00   .54
2.00   .66
2.00   1.71
2.00   1.87
2.00   1.24
2.00   1.71
2.00   2.36
2.00   1.56
2.00   1.89
2.00   .85
2.00   1.00
2.00   1.00
2.00   1.41
2.00   1.65
2.00   .89
3.00   4.33
3.00   2.49
3.00   2.06
3.00   3.34
3.00   3.20
3.00   2.26
3.00   3.82
3.00   2.88
3.00   2.60
3.00   4.11
3.00   3.53
3.00   3.04
3.00   3.65
3.00   4.16
3.00   2.84
3.00   1.79
3.00   2.58
3.00   3.61
3.00   2.66
3.00   1.86
4.00   4.67
4.00   5.18
4.00   4.08
4.00   4.63
4.00   5.34
4.00   4.86
4.00   5.22
4.00   5.42
4.00   3.06
4.00   4.75
4.00   5.20
4.00   5.11
4.00   5.67
4.00   3.85
4.00   4.90
4.00   5.23
4.00   5.32
4.00   6.07
4.00   4.15
4.00   5.44
5.00   5.19
5.00   5.05
5.00   6.16
5.00   4.92
5.00   4.67
5.00   3.90
5.00   5.27
5.00   2.72
5.00   5.33
5.00   5.38
5.00   5.45
5.00   4.45
5.00   4.85
5.00   4.15
5.00   4.07
5.00   3.69
5.00   4.45
5.00   4.64
5.00   5.13
5.00   5.57

Answer 1

null hypothesis: there is no significant difference between the five groups ie.,

alternative hypothesis: at least one of the groups differ from others ie.,

#1
ANOVA
VAR00003
	Sum of Squares	df	Mean Square	F	Sig.
Between Groups	450.694	5	90.139	269.660	.000
Within Groups	38.107	114	.334
Total	488.800	119

Multiple Comparisons
Dependent Variable: VAR00003
(I) VAR00002			Mean Difference (I-J)	Std. Error	Sig.	95% Confidence Interval
						Lower Bound	Upper Bound
Tukey HSD	.00	1	-.49600	.18283	.081	-1.0260	.0340
		2.00	-1.24250*	.18283	.000	-1.7725	-.7125
		3.00	-3.00200*	.18283	.000	-3.5320	-2.4720
		4.00	-4.86900*	.18283	.000	-5.3990	-4.3390
		5.00	-4.71350*	.18283	.000	-5.2435	-4.1835
	1.00	.00	.49600	.18283	.081	-.0340	1.0260
		2.00	-.74650*	.18283	.001	-1.2765	-.2165
		3.00	-2.50600*	.18283	.000	-3.0360	-1.9760
		4.00	-4.37300*	.18283	.000	-4.9030	-3.8430
		5.00	-4.21750*	.18283	.000	-4.7475	-3.6875
	2.00	.00	1.24250*	.18283	.000	.7125	1.7725
		1.00	.74650*	.18283	.001	.2165	1.2765
		3.00	-1.75950*	.18283	.000	-2.2895	-1.2295
		4.00	-3.62650*	.18283	.000	-4.1565	-3.0965
		5.00	-3.47100*	.18283	.000	-4.0010	-2.9410
	3.00	.00	3.00200*	.18283	.000	2.4720	3.5320
		1.00	2.50600*	.18283	.000	1.9760	3.0360
		2.00	1.75950*	.18283	.000	1.2295	2.2895
		4.00	-1.86700*	.18283	.000	-2.3970	-1.3370
		5.00	-1.71150*	.18283	.000	-2.2415	-1.1815
	4.00	.00	4.86900*	.18283	.000	4.3390	5.3990
		1.00	4.37300*	.18283	.000	3.8430	4.9030
		2.00	3.62650*	.18283	.000	3.0965	4.1565
		3.00	1.86700*	.18283	.000	1.3370	2.3970
		5.00	.15550	.18283	.957	-.3745	.6855
	5.00	.00	4.71350*	.18283	.000	4.1835	5.2435
		1.00	4.21750*	.18283	.000	3.6875	4.7475
		2.00	3.47100*	.18283	.000	2.9410	4.0010
		3.00	1.71150*	.18283	.000	1.1815	2.2415
		4.00	-.15550	.18283	.957	-.6855	.3745
*. The mean difference is significant at the 0.05 level.

if p value is greater than 0.05 we accept null hypothesis otherwise reject null hypothesis

from the first table p-value is 0.000 which is less than 0.05

hence we reject null hypothesis and conclude that atleast one of the groups differ from other group at 0.05 level of significance

post hoc test

significant values under tuckeys hsd test

group(0,1)=.081>0.05: there is no significant difference between group 0 and group 1 at 5% level of significance

group(0,2)=0.00<0.05: the two groups differ from each other at 5% level of significance

group(0,3)=0.00<0.05: the two groups ie., group 0 and group 3 differ from each other at 5% level of significance

group(0,4)=0.00<0.05: the two groups ie., group 0 and group 4 differ from each other at 5% level of significance

group(0,5)=0.00<0.05: the two groups ie., group 0 and group 5 differ from each other at 5% level of significance

group(1,2)=0.001<0.05:the two groups ie., group 1 and group 2 differ from each other at 5% level of significance

group(1,3)=0.000<0.05:the two groups ie., group 1 and group 3 differ from each other at 5% level of significance

group(1,4)=0.000<0.05:the two groups ie., group 1 and group 4 differ from each other at 5% level of significance

group(1,5)=0.000<0.05: the two groups ie., group 1 and group 5 differ from each other at 5% level of significance

group(2,3)=0.000<0.05: the two groups ie., group 2 and group 3 differ from each other at 5% level of significance

group(2,4)=0.000<0.05: the two groups ie., group 2 and group 4 differ from each other at 5% level of significance

group(2,5)=0.000<0.05: the two groups ie., group 2 and group 5 differ from each other at 5% level of significance

group(3,4)=0.000<0.05: the two groups ie., group 3 and group 4 differ from each other at 5% level of significance

group(3,5)=0.000<0.05: the two groups ie., group 3 and group 5 differ from each other at 5% level of significance

group(4,5)=0.957>0.05: there is no significant difference between group 4 and group at 5% level of significance

so there is no significant difference between groups (0,1) and (4,5) at 5% level of significance

through anova, we have found that at least the size of tumours of one group differs from another group

through tuckeys hsd, we have found that the size of tumours for the groups one and two are equal ie., the tumour size is the same when a person received microwaves for 0,1 hours per day. also, the size of tumours for the groups four and five are equal ie., the tumour size is the same when a person received microwaves for 4,5 hours per day

so if we use phone for one hour it is equivalent to not using it. also, the tumour size is more when they experience microwaves 4 to 5 hours per day