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Power and Sample Size Question

v YourtriaI-by-trial data On each trial, your task was to report the color of the shown word (which happened to be color names). Each row below indicates the characteristics of each trial. The second column indicates the shown word. The third column indicates the color of the word font. The fourth column indicates whether the trial was part of sample 1 or sample 2. The fth column indicates if the color name and font color were congruent or incongruent. The nal column gives the time taken to identify the word color. Trial Word Font color Sample ID Word and font match Reaction time (ms) 1 BLUE Blue 1.0 Congruent 1762.0 2 GREEN Red 2.0 lnccngruent 2254.0 3 RED Green 1.0 lnccngruent 1674.0 4 GREEN Blue 2.0 lnccngruent 2660.0 5 GREEN Green 1.0 Congruent 1809.0 6 RED Blue 1.0 lnccngruent 3350.0 7 GREEN Red 2.0 lncongruent 1539.0 8 RED Red 1 .0 Congruent 1428.0 9 GREEN Red 1.0 lnccngruent 1614.0 10 GREEN Green 2.0 Congruent 1809.0 11 GREEN Green 2.0 Congruent 1233.0 12 GREEN Green 2.0 Congruent 1897.0 13 RED Red 1.0 Congruent 1115.0 14 RED Green 1.0 lncongruent 1468.0 15 GREEN Green 2.0 Congruent 1107.0 16 BLUE Red 2.0 lnccngruent 1382.0 17 BLUE Blue 2.0 Congruent 1467.0 18 BLUE Red 1.0 Inccngruent 1361.0 19 RED Blue 2.0 lnccngruent 2304.0 20 RED Blue 2.0 lnccngruent 2882.0 20 RED Blue 2.0 Incongruent 2882.0 21 RED Red 2.0 Congruent 1040.0 22 RED Red 2.0 Congruent 1464.0 23 GREEN Red 1.0 Incongruent 2184.0 24 BLUE Blue 2.0 Congruent 1499.0 25 GREEN Blue 1.0 Incongruent 1950.0 26 RED Red 2.0 Congruent 1453.0 27 BLUE Blue 2.0 Congruent 2566.0 28 GREEN Blue 2.0 Incongruent 1545.0 29 RED Red 2.0 Congruent 1459.0 30 BLUE Red 2.0 Incongruent 1420.0 31 BLUE Blue 2.0 Congruent 1979.0 32 BLUE Green 2.0 Incongruent 1107.0 33 GREEN Blue 2.0 Incongruent 2933.0 34 BLUE Blue 2.0 Congruent 1641.0 35 BLUE Blue 1.0 Congruent 1315.0 36 RED Green 1.0 Incongruent 1419.0 37 RED Blue 2.0 Incongruent 1982.0 38 GREEN Red 2.0 Incongruent 1782.0 39 GREEN Green 2.0 Congruent 1226.0 40 GREEN Green 2.0 Congruent 1567.0 41 RED Red 1.0 Congruent 1387.0 42 GREEN Green 1.0 Congruent 1496.0 43 GREEN Green 1.0 Congruent 1135.0 44 RED Red 1.0 Congruent 1201.0 45 GREEN Green 2.0 Congruent 1276.0 46 RED Green 2.0 Incongruent 2095.0 47 RED Red 2.0 Congruent 1314.0 48 RED Green 2.0 Incongruent 1289.0 49 BLUE Red 2.0 Incongruent 1179.0 50 BLUE Red 1.0 Incongruent 1724.051 GREEN Blue 2.0 Incongruent 2011.0 52 BLUE Red 2.0 Incongruent 1338.0 53 BLUE Red 1.0 Incongruent 2230.0 54 RED Red 2.0 Congruent 1513.0 55 RED Green 2.0 Incongruent 2008.0 56 BLUE Red 2.0 Incongruent 2003.0 57 BLUE Red 2.0 Incongruent 1911.0 58 BLUE Blue 1.0 Congruent 1706.0 59 BLUE Blue 2.0 Congruent 1480.0 60 BLUE Blue 2.0 Congruent 1869.0What do we predict participants will do? Why? The Stroop effect is that people are usually slower to respond when the word name is incongruent with the font color. Acommon explanation is that people cannot help but read and partly process the color name word. When the color name is incongruent with the font color, this automatic processing interferes with the color-naming task. How robust is this effect? Are there limits to this effect? The effect is quite robust and has been studied in many different situations. In the statistical analysis of this data, you are asked to run a twotailed, twosample ttest to determine if your data have a signicant difference between the response times for congruent and incongruent color name words. The null hypothesis is that the mean reaction time for congruent trials is the same as the mean reaction time for incongruent trials: Ht): \"congruent = Prncongruentu while the alternative hypothesis is that the mean reaction time for congruent trials is different from the mean reaction time for incongruent trials: Ha: \"congruent i \"incongruent- We will use cr = 0.05. This lab does not focus on the details of the hypothesis tests. After answering the questions about the mean values, it is recommended that you use an on-line calculator that will automatically compute the terms for a two-sample ttest. The trial-by-trial data have been randomly divided into two samples (1 and 2). The questions ask you to perform separate tests for the diferent samples. Most likely you will nd a larger tstatistic for the larger sample (sample 2). The properties of power can be identied by looking at the class (or global) average data. This data will onty be available to you after you answer all of the questions for the lab. The summary statistics include: - Rejection decision for sample 1 - Rejection decision for sample 2 These statistics are given a value 1 when a sample rejects the null hypothesis and a value 0 when it does not. Averaged across all students in your class (or for the global data), these statistics will report the proportion of samples that reject the null hypothesis. This proportion should be larger for sample 2 because it has a larger sample size. Answer the questions using the data below. You will often nd it helpful to sort the data and calculate values using a spreadsheet such as Microsoft Excel, Sheets from Google apps, Open Office, or Numbers (Mac only). To import the data into a spreadsheet select and copy all the cells in the trial-by-trial data table below and then paste them into an open page of the spreadsheet. Use the trial-bytrial data to answer these questions. Question Answer :l pvalue for a two-tailed testfor sample 1: :I (The difference between your answer and the correct value must be less than 0.001 .) _I Mean reaction time for comment trials in sample 2: S (The difference between your answer and the correct value must be less than 0.01.) tstatistic for sample 2: (The difference between your answer and the-correct value must be less than 0.01 .) :I :l l Mean reaction time for incongruent trials in sample 1: (The difference between your answer and the correct value must be less than 0.01.) Do you reject the null hypothesis for sample 2