Case 2 Final

Case Study 2: Team 7 Introduction and Discussion of Analysis When we are comparing two or more populations, we need to identify what type of testing we are going to use. For data that is interval, independent samples are collected, the population distribution is normal, and there are one or two factors, we use analysis of variance. We use analysis of variance when we want to analyze the sources of the variation between multiple or single samples. The analysis that we conducted is a one-way analysis of variance or one-way ANOVA. Since there is only one factor, which is the treatments (adenoidectomy, treatment with the medication Sulfafurazole, and a placebo treatment). In this case, the data follows a randomized sampling, which indicates that this follows an ANOVA assumption. This indicates that each group is independent of each other. Even though there are three different categories of treatment or response variables, each treatment is only used once, is independent and does not interact p with the other treatments. Each of the treatments, also known as response variables, are then analyzed between the episodes, visits, prescription, and days. Numerical Statistics Group 1: Surgery Episodes Visits Prescriptions Days Mean 3.3 Mean 2.16666666 7 Mean 3.35 Mean 11.48333 Standard Error 0.170244 Standard Error 0.20469995 5 Standard Error 0.191375 Standard Error 0.615933 Median 3 Median 2 Median 3 Median 11 Mode 2 Mode 2 Mode 2 Mode 11 Standard Deviation 1.318705 Standard Deviation 1.58559903 3 Standard Deviation 1.482382 Standard Deviation 4.770999 Sample Variance 1.738983 Sample Variance 2.51412429 4 Sample Variance 2.197458 Sample Variance 22.76243 Count 60 Count 60 Count 60 Count 60 Numerical statistics for the 60 surgical patients in group 1 show a mean of 3.3 episodes, 2.2 visits, 3.4 prescriptions, and 11.5 days of illness for patients who received surgery to treat otitis media. The standard deviations for these patients are 1.3 for episodes, 1.6 for visits, 1.5 for prescriptions, and 4.8 for days. The variance in episodes is 1.7, for visits is 2.5, for prescriptions is 2.2, and for days is 22.8. This group had the second highest mean for episodes, visits, prescriptions and days, after group 3. Group 1 had the highest standard deviation for

episodes, and the lowest standard deviation for prescriptions. Group 1 has the highest sample variance for episodes, and the lowest sample variance for prescriptions of all three patient groups. Group 2: Rx Sulfafurazole Episodes Visits Prescriptions Days Mean 2.966667 Mean 1.9 Mean 2.96666 7 Mean 11.05 Standard Error 0.140553 Standard Error 0.151639 Standard Error 0.22545 2 Standard Error 0.57313 9 Median 3 Median 2 Median 3 Median 10 Mode 3 Mode 1 Mode 2 Mode 7 Standard Deviation 1.08872 Standard Deviation 1.17459 Standard Deviation 1.74634 4 Standard Deviation 4.43951 8 Sample Variance 1.185311 Sample Variance 1.379661 Sample Variance 3.04971 8 Sample Variance 19.7093 2 Count 60 Count 60 Count 60 Count 60 Numerical statistics for the 60 patients in group 2 that received prescription drug, Sulfafurazole, show a mean of 2.9 episodes, 1.9 visits, 2.9 prescriptions, and 11.1 days of illness for patients who were given Sulfafurazole to treat otitis media. The standard deviation for episodes is 1.1, for visits is 1.2, is 1.7 for prescriptions, and is 4.4 for days. Sample variance for episodes is 1.2, for visits is 1.4, for prescriptions is 3, and for days is 19.7. Group 2 has the lowest means for episodes, visits, prescriptions, and days out of the three groups. Group 2 has the second highest standard deviation for episodes, visits, prescriptions after group 3 and has the lowest standard deviation out of the three groups for days. Similarly, the sample variance in group 2 is second highest of the other groups for episodes. The sample variance for visits in this group is significantly lower than it is for group 1 and group 3. Sample variance for days is the lowest in group 2 as well. Group 3: Placebo Episodes Visits Prescriptions Days Mean 3.45 Mean 2.45 Mean 3.41666 Mean 12.98333 Standard Error 0.167104 Standard Error 0.217101 Standard Error 0.239222 Standard Error 0.685809 Median 3 Median 2 Median 3 Median 12.5 Mode 3 Mode 3 Mode 3 Mode 10 Standard Deviation 1.294382 Standard Deviation 1.681656 Standard Deviation 1.853002 Standard Deviation 5.312255 Sample Variance 1.675424 Sample Variance 2.827966 Sample Variance 3.433616 Sample Variance 28.22006 Count 60 Count 60 Count 60 Count 60 Numerical statistics for the 60 placebo patients, group 3, show a mean of 3.5 episodes, 2.5 visits, 3.4 prescriptions, and 12.9 days spent ill. Standard deviation for episodes is 1.3, for visits is 1.7, for prescriptions is 1.9, and is 5.3 for days. Sample variance for episodes is 1.7, is 2.8

for visits, is 3.4 for prescriptions, and is 28.2 for days. Group three has the highest mean of the three treatment groups for episodes, visits, prescriptions, and days spent sick. It has the second highest standard deviation, after group 1, for episodes. Group 3 has the highest standard deviation for visits, prescriptions, and days. Group 3 has the second highest sample variance for episodes but has the highest sample variance for visits, prescriptions, and days. Outliers Analysis Outliers for group 1 exist only for visits and days. The single outlier for visits is 7, slightly above the mean of 2.17. Outliers for days are more elevated; with the mean of 11.48, you can see that the two outliers here are significantly higher, at 21 and 22. No lower outliers exist for episodes, visits, prescriptions, or days. Also notable in this boxplot is the wide range of data for days. The minimum and maximum are wider, the low at 5 and the high at 16, than the boxes for episodes, visits, and prescriptions. That means that the variance in days spent sick was substantial, where some patients recovered from otitis media quickly (in as little as 5 days), and others remained sick for as long as 22 days. The interquartile range (IQR) for episodes is 2-4. The IQR’s for visits is 1-3 with one outlier at 7, for prescriptions is 2-4, and for days is 7-11.5.