Spring 2010 Discussion Exercise 10 Name Matthew B Marck Section 0101 Paired vs Unpaired Studies We have talked about paired and unpaired studies Unpaired studies assign experimental units to treatments using randomization with no further design structure When the means of 2 treatments are compared in an unpaired study we analyze the data using a 2 sample t test if the data meet the assumptions of normality For paired studies you create groups of 2 experimental units that are similar for some factor that you think might influence your study and you want to block out not quantify So within a pair EUs should be similar but there can be large differences from 1 pair to another e g one pair might be females one pair might be males if you think gender is important to the results Pairs contain 1 experimental unit per treatment being tested Within a pair experimental units are assigned to a treatment using randomization Paired studies with 2 treatments are analyzed using a paired t test if data meet normality assumptions Paired studies help remove the impact of some extraneous variability If all your experimental units are ALL similar there is no point in pairing your EUs and an unpaired approach should be used instead For the examples below decide whether the study should be run as a paired study or an unpaired study 1pt each 1 You want to look at the impact of 2 drugs in lower a person s cholesterol and you have twins 2 You want to look at the impact of 2 drugs to control a certain hormone in rats and have a available to use in the experiment Paired study Unpaired study colony of genetically similar rats to use in your study Paired study Unpaired study 3 You want to study how 2 different strains of soybean grow in a field that has areas of high soil moisture and areas of low soil moisture but you don t want to quantify the effect of soil moisture Paired study Unpaired study 4 You want to look at how people respond to a new medication and have absolutely no idea what other factors might influence drug response before the start of the study Unpaired study Paired study Data analysis 2 sample t test 6 You hypothesize that men will have a larger hand span than women Hand span is the maximum distance between thumb and little finger when a hand is spread out on a flat surface As a discussion group measure the hand span of all the men in the class and the hand span of all the women in class in cm Use these sample data as an estimate of the population values for the entire Biom 301 class Give the data to your Instructor who will calculate the following for you to record 6pts Mean hand span of women 20 0 cm Mean hand span of men 22 1 cm Sample size men 11 Standard deviation of hand span in women 0 59 cm Standard deviation of hand span in men 1 07 cm Sample size women 7 Test whether men have a larger hand span than women in the Biom 301 class Assume data meet the assumption of normality and use 0 05 a State the question ID the population Is the mean hand span of men in the class larger than the hand span of women in the class b State your null and alternative hypotheses define symbols Ho men women Ha men women mean hand span c Analyze your data statistically t 22 1 20 0 sqrt 1 072 11 0 592 7 5 35 tcritical for df 6 0 05 in 1 tail 1 94 p value 0 05 d Provide a statement of conclusion that includes the statistical evidence and makes inference back to the population Mean class male hand span is significantly larger than that of the mean female hand span t 5 35 p 0 05 n1 11 n2 7 Data analysis paired t test 7 Now you want to know if the hand span of dominant hands the one you write with is on average larger than the hand span of the non dominant hand for students in Biom 301 Since hand span will vary with people you decide to create a pair of experimental units within a person and compare a person s dominant hand to their non dominant hand Collect data for each person in the discussion group This time you want to know the difference between the width of the dominant hand and the width of the non dominant hand We will calculate the difference as dominant non dominant Record your result below Dominant Hand span 23 0 cm Non dominant hand span 22 9 cm Difference 0 1 cm Give the data to your Instructor who will calculate the following for you to record Mean difference in handspan 0 12 cm Standard deviation of the differences 0 32 cm Sample number of differences 18 Test whether the dominant hand has a larger handspan than the non dominant hand for students in the Biom 301 class Assume data meet the assumption of normality and use 0 05 a State the question ID the population 6pts Is the dominant hand larger than the non dominant hand for students in class b State your null and alternative hypotheses define symbols Ho dominant non dominant Ha dominant non dominant mean hand span c Analyze your data statistically t 0 12 0 32 sqrt 18 1 59 tcritical for df 17 0 05 in 1 tail 1 74 p value 0 05 d Provide a statement of conclusion that includes the statistical evidence and makes inference back to the population Mean dominant hand span is not significantly larger than the mean non dominant hand span t 1 59 p 0 05 n 17