Analysis of Scientific Data - Summer Semester, 2020 Week 7 Tutorial Part A - ONE WAY ANOVA Early developmental experiences, such as incubation conditions, can have important consequences for post-hatching fitness in birds. A paper reported on a study where wood duck eggs were collected from nest boxes and experimentally incubated at various fixed temperatures, each falling within the range of temperatures of naturally incubated wood duck nests. The response variables recorded included egg mass (g) at the time of hatching. A one-way analysis of variance of egg mass by temperature in R gave the following results: Df Sum Sq Temperature 3 117.1 Residual 23 312.5 Total 26 429.6 a) How many fixed temperatures were used in this design? DF for Temperature = K -1 where Kis no. of fixed temperatures K - 1 = 3, => K = 4 (i. e. no. of categories) b) How many eggs were included in this analysis? n-1=26 => n= 27 There were 27 eggs. c) The paper reported that the mean egg mass for the 6 eggs at 35 ? was "44.7 + 1.88 g" where they indicated that "1.88" was the standard error of the mean (SEM). Based on this statement, what was the sample standard deviation of the egg mass for those 6 eggs? SEM = 1.88 - n =6 (given) - 5 = 1.88 x 6 5 = 1.88 - 5 56 = 1.88 - $ = 4.605 15 d) What is the R2 value for this model? =>R2=117.1 429.6 =>R = 0.27 R2 = SS Temp SS Total 27% of variability in egg mass is explained by temperature. e) What is the F statistic used to test for the difference in mean egg mass between the different temperatures? Esta+ = 117-1/3 Fstat = 2.87 312.5/23 f) What is the p-value for this test? What do you conclude? p-value = P(F3,23>2.87) = 0.0584 Using R function 1 -Pf (2-ST, d+1=3, d+2=23)
Part B - TWO WAY ANOVA Studies suggest that relieving sad memories leads to a reduction in blood oxytocin. In an exploration of 'pet therapy', a student project within the Islands investigated if dogs or cats had a greater feel-good effect by comparing the increase of oxytocin after petting a cat and after petting a dog. A sample of 40 subjects, ages ranging from 21 to 40 years, were randomly split into two equal groups of 20 and both groups were subjected to relieving sad memories. One group then petted cats while the other group petted dogs, each of 10 minutes. Blood was collected to measure oxytocin levels (pg/ml) for baseline, post sad and post-pet treatment. a) The table below shows the observed sample means and standard deviations of oxytocin increase for the 10 subjects in each combination of animal and sex. Animal Cat Sex n Male 10 Female 10 Mean 0.013 0.984 SD 0.116 0.166 Dog Male 10 Female 10 0.008 0.171 0.702 0.348 Draw an interaction effects plot for this data. Use Y axis to represent