Is there evidence that there are significant differences among the mean numbers
ID: 3173603 • Letter: I
Question
Is there evidence that there are significant differences among the mean numbers of species in the three groups? Describe how the three groups appear to differ, check if the conditions for conducting an ANOVA hold, and state your hypotheses. Then carry out the one-way ANOVA to compare the three population means. Make sure you get a table of the basic statistics for each groups, the results of Levene’s test for homogeneity of variance, a means plot and box plots to check for outliers. If you decide to reject the null, conduct at Tukey’s and Bonferroni’s post-hoc tests. What do you conclude?
one way Descriptives 95% Confidence Interval for Mean Mean Std. Deviation Std. Error Lower Bound Upper Bound Minimum Maximum 1 12 17.50 3.529 1.019 15.26 19.74 13 22 2 12 11.75 4.372 1.262 8.97 14.53 2 18 3 13.67 4.500 1.500 10.21 17.13 4 18 2 14.36 4.722 822 12.69 16.04 Total 33 22 Test of Homogeneity of Variances Levene Statistic df1 Sig 2 30 036 964 ANOVA Sum of df Mean Square Squares Sig 2 006 204.386 102.193 6.020 Between Groups 30 509.250 16.975 Within Groups Total 713.636 32Explanation / Answer
From the given ANOVA table, F(2,30)=6.020, p<0.05. Per rule, reject H0, if p value is less than alpha=0.05. Here, p value is 0.006, therefore, reject null hypothesis and conclude that atleast mean number of species in one group is significantly different from mean number of species in another group.
Assumption:
Assumptions of independence: The number of species in each group are random and independent samples from a population. That is number of species in in egroup cannot affect the number of species from another group. Assumption is met.
Homogeneity of variance: The assumption can be tested using Levene's test for homogeneity of variance. The p value is greater than 0.05, therefore, fail to reject null hypothesis (no difference) for the assumption of homogeneity of variance, and conclude that there is no significant difference in three groups' variances. Assumption is met.
Outliers: The assumption says that there should be no significant outliers. Bit the boxplot shows existence of a possible outlier. Assumption is not met.
The means plot shows that group 2 has lowest mean, while group1 has highest mean, but whether the difference is statistically significant one should use tests (Tukey's post Hoc) to determine if there exists statistically significant difference between specific pair of groups.
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