. The datacontains pH measurements for four different lakes in the Adirondacks t
ID: 3173604 • Letter: #
Question
. The datacontains pH measurements for four different lakes in the Adirondacks that were acidified by acid rain and that are now making a slow recovery. We would like to determine if there are any significant differences in mean pH amongst the four lakes. We understand that the data were taken at different times over a period of years, but we have good prior support that our analysis will still be meaningful. Do the analyses to answer the question, make sure you get a table of the basic statistics for each group, the results of Levene’s test for homogeneity of variance, a boxplot check for outliers a means plot. Briefly explain what your output results mean, and succinctly state your conclusions, if your initial results warrant a post-hoc comparison, then carry out the Bonferroni and Tukey post-hoc tests
Oneway Descriptives pH air eq 95% Confidence Interval for Mean Mean Std. Deviation Std. Error Lower Bound Upper Bound Minimum Maximum 11.00 4.35 4.5639 4.6775 29 4.6207 14943 02775 4.92 2.00 29 5.5893 .74081 13756 5.3075 5.8711 459 6.86 300 29 5.7721 ,71314 13243 5.5008 6.0433 4.46 6.74 400 24 5.1000 19627 04006 5.0171 5.1829 473 5.54 4.35 70257 06669 5.4104 Total 5.1460 111 5.2782 6.86 Test of Homogeneity of Variances pH air eq Levene Statistic Sig 3 107 31.570 000 ANOVA pH air eq Sum of Mean Square df Sig Squares 3 7.727 26.568 23.180 Between Groups 000 107 .291 Within Groups 31.117 110 Total 54.297Explanation / Answer
The dependent variable is Ph air eq which is supposedly continuou sin nature and the observations that is Ph measurements of each lake is independent of another. In other words, Ph level of one lake does not influence Ph level of another lake.
Assumptions: Observations are independent and random in nature.
The Levene's test shows a F value of 31.570, and p value is less than 0.05. the null hypothesis (of no difference) is not retained. Therefore, the assumption for homogeneity of variance is not met.
[Note: H0: sigma1^2=sigma2^2=sigma3^2=sigma4^2 (the variance pH for four lakes is equal), H1:atleast one lake has different variance pH, reject H0, if p value from Levene's test is less than 0.05, and conclude assumptions not met]
The boxplot shows that there is no outlier. Therefore assumption for no outlier is met.
The Means Plot shows that Lake 1 has lowest pH and Lake 3 has highest pH. But to decide, whether the difference for pH levels for the lakes are significnat or not, one should proceed with one-way ANOVA. The ANOVA table shows that F(3, 107)=26.568, p<0.05. The p value is less than 0.05, therefore, reject null [H0:mu1=mu2=mu3=mu4 (there is no difference in mean pH levels for four lakes)], and conclude that atleast mean pH of one lake is significantly different from mean pH level of another lake.
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