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Title of Resource Stats Lab: Single-sample t-test with Caramel Apple PopsTM Author(s) Maya G. Sen Institution Northern Michigan University This hands-on activity has students collect data that they analyze (by hand and with SPSS) using a single-sample t-test. They compare the weights of a Brief Description: sample of Caramel Apple PopsTM to the population mean (i.e., the advertised weight). Keywords: Single-sample t-test, SPSS calculation, interpretation of findings Author Contact [email protected], www.mayasen.com Information: Additional Information: TeachPsychScience.org is made possible with grant support from the Association for Psychological Science (APS) Fund for Teaching and Public Understanding of Psychological Science to the site creators Gary Lewandowski, Natalie Ciarocco, and David Strohmetz. All materials on this site have been subjected to a peer review process. We welcome additional resources (www.teachpsychscience.org/submissions). © 2013 by Maya G. Sen . All Rights Reserved. This material may be used for noncommercial educational purposes. All other uses require the written consent of the authors. Instructors: Please provide any instructions/tips/suggestions that would help instructors use this resource more effectively. If possible, please also provide your best estimate of how long the resource will take in class. Please paste your resource on the start of the next page. Thanks! Notes I have found some packages with advertised weights of 17.0g, and others post the weight as 17.7g. I have done this lab several times in class, and each time the average weight was significantly higher than advertised. If I feel that the class has mastered calculating sums of squares, I will calculate that for them. If it’s a group that is still struggling, I will have them calculate it for more practice. Once I have sent them the data, I wander around the classroom to give help as needed. We then go over the results as a class, so they can check their calculations against mine. This activity takes approximately one 50-minute class period (although I sometimes have to go a little over – my classes are 100 minutes). Materials Needed Enough Caramel Apple PopsTM for everyone (including you!). o You can substitute other candy that has its weight listed on the individual pieces, but Caramel Apple PopsTM are very popular with the students. o http://www.amazon.com/Caramel-Apple-Pops-48-CountPackage/dp/B0015AWU7U/ A small scale, e.g., http://www.amazon.com/gp/product/B0012N1NAA/ Single-sample t-test Lab Notes I have found some packages with advertised weights of 17.0g, and others post the weight as 17.7g. I have done this lab several times in class, and each time the average weight was significantly higher than advertised. If I feel that the class has mastered calculating sums of squares, I will calculate that for them. If it’s a group that is still struggling, I will have them calculate it for more practice. Once I have sent them the data, I wander around the classroom to give help as needed. We then go over the results as a class, so they can check their calculations against mine. This activity takes approximately one 50-minute class period (although I sometimes have to go a little over – my classes are 100 minutes). Materials Needed Enough Caramel Apple PopsTM for everyone (including you!). o You can substitute other candy that has its weight listed on the individual pieces, but Caramel Apple PopsTM are very popular with the students. o http://www.amazon.com/Caramel-Apple-Pops-48-CountPackage/dp/B0015AWU7U/ A small scale, e.g., http://www.amazon.com/gp/product/B0012N1NAA/ Single-sample t-test Lab Goals: The goals of this lab are 1) to give you experience collecting and analyzing data using the single-sample t-test, and 2) to help you understand the purpose and appropriate use of the single-sample t-test. Background: The single-sample test is used when a researcher has data from one sample, and is comparing that sample to a population mean (remember, the population standard deviation is unknown for t-tests, and therefore must be estimated based on the sample’s SD). In this lab, we will compare the weights of a sample of Caramel Apple PopsTM to their advertised weight (17.0g), which we will treat as the population mean. (We’ll assume that the company weighed a population’s-worth of their candy, and that the advertised weight is that population mean.) Instructions: Go to the front of the classroom, grab a Caramel Apple Pop TM, and weigh it. Tell me its weight so that I can enter it into the spreadsheet. Note: I will subtract 1g from each weight to account for the weight of the wrapper and the stick (previous years’ students have weighed numerous sticks + wrappers, and they have averaged 1g). To save time, we will not weigh the stick and wrapper from each individual. While the rest of the class weighs their candy and I prepare the spreadsheet, get started on the steps of the hypothesis-testing procedure (the parts you can do without our data). Work in pairs or groups of three. When the data are collected, I will send you a spreadsheet. Complete the hand calculations to test your hypothesis. Once you are done, redo the calculations in SPSS to double-check your work. Step 1: Identify the correct comparison distribution and statistical analysis to use: Analysis: Single-sample t-test Comparison Distribution: Step 2: State the research hypothesis and null hypothesis for a two-tailed test. State your H1: State your H0: Step 3: Determine the characteristics of the comparison distribution. a. Mean of comparison distribution (NOT the mean of your sample) = b. Calculate the standard deviation of the comparison distribution as follows: Estimated population standard deviation s= Standard deviation of the distribution of means c. The shape is a t distribution with sM = degrees of freedom (df). Step 4: Determine the critical value(s) on the comparison distribution. a. Set the significance level at 0.05. This is a two-tailed test. b. The appropriate cut-off scores (tcrit) are: Step 5: Calculate your t-test. tobt = Step 6: Decide whether to reject H0. REJECT or FAIL TO REJECT H0? (circle the correct one) Step 7: Calculate effect size, and circle the strength of the effect size. d= The effect size is [none, small, medium, large]. Step 8: Write a summary statement. Fill in the blanks and circle where appropriate. A single sample t-test was performed to determine whether the mean weight of the Caramel Apple PopsTM differed from the advertised weight of 17.0g. The mean weight [did/ did not] differ significantly from the advertised weight, t( with a effect size (d = )= ). How do you think the company would respond to these results? Why? ,p 0.05, Step 9: Now, run the analysis in SPSS to double-check your answers. Be sure to look carefully at your output to ensure you understand where to find the relevant information. Copy and paste your data from Excel into SPSS (the “Data View” tab). On the “Variable View” tab, label your variable, set the decimal places to “1,” and select “Scale.” Select Analyze > Compare Means > One-Sample T Test… Move your variable from the box on the left to the right using the center arrow key. Set the Test Value to 17.0 (the population mean). Click OK. Your output should look like the example below (although the numbers will be different). You should be able to find several numbers that match the numbers you calculated. Remember, since SPSS can more easily keep track of many decimal places than we can, that the number may not be identical. They should, however, be close. Look for the following: o N, Mean, s, sM, t, df, and p o Do your results match SPSS’s results? Single-sample t-test Lab KEY Goals: The goals of this lab are 1) to give you experience collecting and analyzing data using the single-sample t-test, and 2) to help you understand the purpose and appropriate use of the single-sample t-test. Background: The single-sample test is used when a researcher has data from one sample, and is comparing that sample to a population mean (remember, the population standard deviation is unknown for t-tests, and therefore must be estimated based on the sample’s SD). In this lab, we will compare the weights of a sample of Caramel Apple PopsTM to their advertised weight (17.0g), which we will treat as the population mean. (We’ll assume that the company weighed a population’s-worth of their candy, and that the advertised weight is that population mean.) Instructions: Go to the front of the classroom, grab a Caramel Apple PopTM, and weigh it. Tell me its weight so that I can enter it into the spreadsheet. Note: I will subtract 1g from each weight to account for the weight of the wrapper and the stick (previous years’ students have weighed numerous sticks + wrappers, and they have averaged 1g). To save time, we will not weigh the stick and wrapper from each individual. While the rest of the class weighs their candy and I prepare the spreadsheet, get started on the steps of the hypothesis-testing procedure (the parts you can do without our data). Work in pairs or groups of three. When the data are collected, I will send you a spreadsheet. Complete the hand calculations to test your hypothesis. Once you are done, redo the calculations in SPSS to double-check your work. Step 1: Identify the correct comparison distribution and statistical analysis to use: Analysis: Single-sample t-test Comparison Distribution: sampling distribution of the mean Step 2: State the research hypothesis and null hypothesis for a two-tailed test. State your H1: Our sample of CA Pops will weigh more or less than the advertised weight (17.0g). M≠μ State your H0: The weight of our CA pops will not differ from the advertised weight (17.0g). M=μ Step 3: Determine the characteristics of the comparison distribution. a. Mean of comparison distribution (NOT the mean of your sample) = 17.0 b. Calculate the standard deviation of the comparison distribution as follows: Estimated population standard deviation s= Standard deviation of the distribution of means c. The shape is a t distribution with 20 0.468 sM = 0.102 degrees of freedom (df). Step 4: Determine the critical value(s) on the comparison distribution. a. Set the significance level at 0.05. This is a two-tailed test. b. The appropriate cut-off scores (tcrit) are: ±2.086 Step 5: Calculate your t-test. tobt = (18.181-17)/0.102 = 11.58 Step 6: Decide whether to reject H0. REJECT or FAIL TO REJECT H0? (circle the correct one) Step 7: Calculate effect size, and circle the strength of the effect size. d = (18.181-17)/0.468 = 2.53 The effect size is [none, small, medium, large]. Step 8: Write a summary statement. Fill in the blanks and circle where appropriate. A single sample t-test was performed to determine whether the mean weight of the Caramel Apple PopsTM differed from the advertised weight of 17.0g. The mean weight [did/ did not] differ significantly from the advertised weight, t( 20 ) = 11.58, p < 0.05, with a large effect size (d = 2.53). How do you think the company would respond to these results? Why? They may be pleased because the sample we studied weighed more than the advertised weight, indicating that they are not cheating their customers. However, the company may prefer that we had found no significant difference from the advertised weight, so that they are not using more ingredients than necessary, which would cost them extra money. Step 9: Now, run the analysis in SPSS to double-check your answers. Be sure to look carefully at your output to ensure you understand where to find the relevant information. Copy and paste your data from Excel into SPSS (the “Data View” tab). On the “Variable View” tab, label your variable, set the decimal places to “1,” and select “Scale.” Select Analyze > Compare Means > One-Sample T Test… Move your variable from the box on the left to the right using the center arrow key. Set the Test Value to 17.0 (the population mean). Click OK. Your output should look like the example below (although the numbers will be different). You should be able to find several numbers that match the numbers you calculated. Remember, since SPSS can more easily keep track of many decimal places than we can, that the number may not be identical. They should, however, be close. Look for the following: o N, Mean, s, sM, t, df, and p o Do your results match SPSS’s results? (The one below is the example. The next page has the answers for our data.)