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STAT151 University Studies Lakeland College ONE-WAY ANALYSIS OF VARIANCE The One-Way ANOVA procedure in StatCrunch performs a one-way analysis of variance for a quantitative dependent variable by a single independent variable (factor). The one-way analysis of variance F-test is used to test the hypothesis that several population means are equal. The test is valid if the assumption of independence (within and across samples), normality and equal standard deviations for the populations are satisfied. The normality assumption is likely to be violated if the graphical methods show extreme skew for the response variable. The F test works quite well as long as the largest group standard deviation is no more than twice the smallest standard deviation. In this assignment you will compare the mean lengths of the cuckoo’s eggs that were found in nests of various other host birds. In particular, you will use analysis of variance to see whether the size of the egg varies depending on the host bird. It is strongly recommended that you get familiar with Lab 5 Instructions before you start working on the assignment. Cuckoo Birds Cuckoos lay their eggs in the nests of other (host) birds. The eggs are then adopted and hatched by the host birds. Usually one egg is laid by in one nest but some cuckoos may lay 2 eggs or even more. As soon as the young Cuckoo hatches, it pushes out many of its foster parent's eggs or young which tend to be smaller than Cuckoos. In consequence, the host birds raise only the young cuckoos and lose their own clutch. It is hypothesized that each female Cuckoo specializes in one species of host and will produce eggs which are very similar to the true eggs of that species. This behaviour is supposed to reduce the risk of the foster parents recognizing the foreign egg and ejecting it. In this lab assignment you will use one-factor analysis of variance to determine if there is a relationship between the size of a cuckoo's egg and the type of nest where the egg was laid. More precisely, you will determine whether significant differences exist among the mean lengths of cuckoo eggs laid in various host nests. The data set that will be used in the lab assignment contains the lengths of cuckoo eggs that were found in nests of various other host birds. The data come from the text by L.H.C. Tippett, The Methods of Statistics, 4th Edition, John Wiley and Sons, Inc., 1952, p. 176. The following host birds are represented in the data set: the Tree Pipit, Hedge Sparrow, Robin, Pied Wagtail, and Wren. All data are lengths in millimeters. For the purpose of this assignment assume that the data were obtained by a scientist who wandered around the countryside looking in birds nests to find cuckoo eggs and found a total of 120 cuckoo eggs in various host species. The lengths of the eggs were obtained with digital calipers by another scientist not directly involved in the study. The data are available in the StatCrunch file lab5data.xlsx
. The data are not to be printed
in your lab report submission. The following is the description of the two variables in the data file: Column Variable Name Description of Variable 1
HOST Meadow Pipit, Tree Pipit, Hedge Sparrow, Robin, Pied Wagtail, and Wren; 2
LENGTH Egg’s length (in millimeters).
Answer the following questions using the data:
