Lecture 12: Popcorn Experiment Chapter 5 Popcorn Experiment Chapter 5 revisits some of the ideas presented in Chapter 3 and extends them. Response? Conditions? Experimental Material? 1 Response? 2 Conditions? Percentage of popped and unburned popcorn. Percentage of un-popped or burned popcorn. Volume of popped and unburned popcorn. Manipulate the cooking time to form treatments. 1.25 minutes 1.75 minutes 2.25 minutes 3 Experimental Material 4 Control of Outside Variables Size of bag – snack size, 1.5 oz or 42.5 g. Microwave – use only one. Power – use only one power setting. Small bags of microwave popcorn. 5 6 1 Lecture 12: Popcorn Experiment Control of Outside Variables Control Group? Brand/type – Pop Secret Home style. Procedure – Allow microwave to cool down. Wipe out moisture after every popping. If we think of the control group as bags of popcorn exposed to none of the manipulated variable (no time) a control group doesn’t make sense in this context. 7 8 Comparison Group? Replication? Bags of popcorn exposed to the recommended time given in the package directions would be a comparison group. Replication within the experiment requires that several bags be popped at each of the times. How many bags are needed? 9 10 Sample Size Sample Size Alpha: the probability of a Type I error, the chance of declaring an observed difference in sample means statistically significant when the true difference in population means is zero (there is no difference). Beta: the probability of a Type II error, the chance of missing a difference in population means when one actually exists (when there is a difference). 11 12 2 Lecture 12: Popcorn Experiment Sample Size Problem Δ : the size of the detectable difference in population means. σ : the standard deviation of the response. Most experimenters can come up with a size of a detectable difference in population means but cannot come up with the standard deviation. 13 Problem 14 Solution In order to have an idea of what the standard deviation is you need data but you are trying to figure out how much data to collect. Report the size of the detectable difference in population means in terms of the number of standard deviations: . 15 16 Sample Size Tables Resources? Number of groups: 3 Alpha = 0.05 Beta = 0.05 A one standard deviation difference in population means: = 1. n = 32 for each group or a total of 3*32 = 96 bags of microwave popcorn. Often the number arrived at using the sample size tables is too large for the available resources; time, money, experimental material. 17 18 3 Lecture 12: Popcorn Experiment Compromise Compromise Increase the chance of making an error. Alpha = 0.05, Beta = 0.10, a one standard deviation in population means: =1; n = 27, or 81 total. Increase the size of the difference in population means, Δ. Alpha = 0.05, Beta = 0.05, a two standard deviation difference in population means, = 2; n = 9 or 27 total. 19 20 Compromise Random Assignment Do both. Alpha = 0.05, Beta = 0.10, a two and one half standard deviation difference in population means, = 2.5; n = 6 or 18 total. Random assignment of treatments (times) to experimental units (bags of popcorn). 21 22 Random Assignment Random Assignment Remember that time of day is often a uncontrolled outside variable. We would also like to randomize the order in which the bags are popped. Put the 18 bags of microwave popcorn in a bowl. Mix thoroughly. Put 18 poker chips; 6 red, 6 white and 6 blue, in another bowl mix thoroughly. 23 24 4 Lecture 12: Popcorn Experiment Treatments Random Assignment Blue = 1.25 minutes Red = 1.75 minutes White = 2.25 minutes Draw a bag from the bowl, without replacement. Draw a chip from the other bowl without replacement. 25 Random Assignment 26 Random Assignment Not only are treatments (times) assigned at random to experimental units (bags) but the order of popping and measuring are also randomized over time. Pop that bag at the time indicated by the color of the chip. Measure the volume of popped but unburnt kernels. 27 28 Random Selection? Repeating? Because microwave popcorn is packaged using a continuously running production line when we buy packages of popcorn we are probably not getting a random selection from the population. We could always repeat the entire experiment using different bags, maybe even a different brand or type. 29 30 5