Question

Suppose we wanted to compare the somatic complaints (as measured on a scale known as the Physical Symptom Scale or PSS) of three groups of people: non-smokers, smokers, and people who recently quit smoking.   Using the following data for the PSS score, do a one-way ANOVA to evaluate smoking and PSS scores:

                            Nonsmokers                   Smokers                     Quitters

                                    19                                31                                30

                                    28                                29                                22

                                    17                                22                                29

                                    20                                29                                29

                                    25                                28                                34

                        Analysis of Variance results:

Data stored in separate columns.

Column statistics

Column	n	Mean	Std. Dev.	Std. Error
Nonsmokers	5	21.8	4.5497253	2.034699
Smokers	5	27.8	3.4205263	1.5297059
Quitters	5	28.8	4.3243497	1.933908

ANOVA table

Source	DF	SS	MS	F-Stat	P-value
Columns	2	143.33333	71.666667	4.2074364	0.0412
Error	12	204.4	17.033333
Total	14	347.73333

Using StatCrunch, determine the means for the three groups and compute the sums of squares, degrees of freedom, and mean squares for these data. What is the value of F? Using an alpha of 0.05, is the F statistic significant? Why? What hypothesis did you test? Did you accept or reject your hypothesis and why? Copy and Paste your work from StatCrunch into your Word document submission

Answer 1

Answer

Using the ANOVA table output

F statistic is 4.2074 with p value = 0.0412

yes,it is significant because the p value is less than 0.05 significance level

We tested the hypothesis

Null hypothesis:- there is no difference between mean pairs

Alternate hypothesis:- at least one pair of means is different

We reject the null hypothesis because p value is less than 0.05 level