PS296 OC LAB 6 - Ind Samples T Test S2024 (1)
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Walden University**We aren't endorsed by this school
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PSYC 296
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Statistics
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Dec 18, 2024
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PS296 OC Lab 6 –S2024 1 PS296 Lab 6 –Independent Samples T Test Getting Started By the end of this lab, you should be able to: Perform hypothesis testing for an independent samplesttestConduct an independent samples ttest analysis on SPSSInterpret the SPSS Output for an independent samples ttestPresent the results of the analysis in proper formatResources SPSS Class Dataset Class Survey Tasks Complete the lab exercises Post your SPSS output Complete the lab quiz Notes In this lab, you will learn how to conduct and assess anindependent samples ttest on SPSS. You will complete the required steps of hypothesis testing as you interpret the SPSS output. You will also present the results of the statistical analysis in a properly formatted conclusion. Please note that all labs in this course are performed on a PC using SPSS version 28. If you are using a Mac and/or different version of SPSS, the instructions in the exercises and what you “see” on your screen might be slightly different. If you have any questions or concerns, please contact your assigned teaching assistant or lab coordinator. Tech-related issues must be directed to ICT (support@mylaurier.ca). Terminology Independent samples ttest:A statistical test that assesses the difference between two independent sample means (i.e., scores obtained from two different groups of participants). Homogeneity of variance:Occurs when the variance within different groups is equal. Heterogeneity of variance: Occurs when the variance within different groups is unequal. Pooled variance:A method used to calculate the average variance of two groups with unequal sample sizes, whereby more weight is applied to the group with the larger sample size. Levene’s test: A statistical test that assesses whether two groups have equal variances (i.e., homogeneity of variance). As you work through the exercises, you will be asked a series of questions to assess your learning. Make sure that you keep a record of your answers as you proceed through the exercises.
PS296 OC Lab 6 –S2024 2 You will post your SPSS Output for all exercises in this lab (including the On Your Ownexercises) in the Dropbox on MyLS called LAB 6 OUTPUT as one PDF document. After you have finished the lab exercises, you will also complete a short quiz. The quiz will not be visible until you have posted your SPSS Output in the Dropbox. The quiz will include questions about information presented in this lab handout, as well as your responses to the questions within the exercises. Your SPSS Output and score on the quiz will contribute to your lab credit. Remember, you only have ONE attempt at the lab quiz. If you open the quiz before you are ready to complete it, the quiz will not be reset.Introduction An independent samples ttest (akabetween samples, between groups, independent groups) is used to test whether two sample means collected from separate groups of participants are different from each other. Statistically, this test assesses whether the mean of one group is significantly different than the mean of another group. The null hypothesis is that mean of one group (μ1) is equal to the mean of the other group (μ2); in other words, the difference between the two population means from which each group/sample mean was drawn is equal to zero (μ1 - μ2= 0 or μ1 = μ2). The numerator of the formula is the difference between group/sample means (𝑥̅1− 𝑥̅2), and the denominator is the standard error of the difference between sample means (?𝑥̅1−𝑥̅2). ? = (𝑥̅1− 𝑥̅2) ?𝑥̅1−𝑥̅2When the sample sizes of the groups (i.e., n1and n2) are equal, the following computational formula can be used to calculate the tstatistic: ? = (𝑥̅1− 𝑥̅2) √?12𝑛1+?22𝑛2However, when the sample sizes are unequal, the denominator (i.e., standard error of the difference between sample means) is replaced with thepooled variance(?𝑝2), which is calculated as follows: ?𝑝2= (𝑛1− 1)?12+ (𝑛2− 1)?22𝑛1+ 𝑛2− 2The pooled variance is then substituted into the computational formula: ? = (𝑥̅1− 𝑥̅2) √?𝑝2(1𝑛1+1𝑛2)Since the sample variances of each group (?12and ?22) are used to estimate the population variances (𝜎12and 𝜎22), there are n1+ n2- 2 degrees of freedom (df) associated with this test.
PS296 OC Lab 6 –S2024 3 When the test is statistically significant, we conclude that the difference between sample means (𝑥̅1−𝑥̅2) is unlikely to have been drawn from a population with equal group means (𝜇1− 𝜇2≠ 0or 𝜇1≠ 𝜇2). This essentially means that there is a non-zerodifference between the two sets of scores (either the first set of scores is higher than the second or vice versa). Likewise, when the test is not statistically significant, we conclude the difference between sample means likely came from a population with equal group means (𝜇1− 𝜇2= 0or 𝜇1= 𝜇2). This means that there is no difference, on average, between the two sets of scores. An important assumption of the independent samples ttest is homogeneity of variance, which is assessed on SPSS with Levene’s test. When this assumption is violated, a correction is applied to the degrees of freedom. The homogeneity of variance assumption is assessed first in order to determine whether the correction is required, as well as which statistics to interpret in the SPSS Output and report in the concluding statement. Exercise 1: Identifying the research question & hypotheses On the PS296 Class Survey, students were asked to identify their personality type; that is, whether they consider themselves to be more introverted or extraverted. This variable is named Introvert_Extravert: Which better describes your personality?with 1 = Introvert and 2 = Extravert. Students also completed the Ten-Item Personality Inventory (TIPI) that is designed to assess five personality domains, one of which is emotional stability (i.e., ability to remain calm and composed when faced with stressful circumstances). This variable is named TIPI_EmotionalStabilityand higher scores represent greater emotional stability. In this exercise, you will test whether emotional stability differs depending on personality type. Do students who consider themselves to be introverted or extraverted have different levels of emotional stability?Remember to write down your answers to the questions! You will need this information to complete a quiz at the end of the lab!Q1: What is the research question? (Hint: The research question is stated at the beginning of this exercise and at the end of the paragraph above) Q2: Based on the research question, is this a one-tailedor two-tailed test? Explain your answer. (Hint: Consider whether the research question asks if the sample mean is bigger or smallerthan the population mean, or if the sample mean is different than the population mean) Q3: What is the value of the difference in population means (μ1and μ2) being tested with an independent samples ttest? (Hint: Find this value in the description at the beginning of this exercise) Now that you have identified the research question and determined whether you are conducting a one- or two- tailed test, it’s time to state the null and alternative hypotheses. Remember, hypotheses are stated with respect to the population parameter(s), which for an independent samples ttest are μ1and μ2.
PS296 OC Lab 6 –S2024 4 The null hypothesis is usually that there is no difference between the means being compared. The null hypothesis for this example in both symbols and words is as follows: H0: μ1–μ2 = 0 or μ1= μ2 Null hypothesis: Students who consider themselves to be introverted have the same level of emotional stability as extraverted students. The alternative hypothesis is the researcher’s predicted answer to the research question, and includes phrases such as different than (ordifferently), greater/higher than, or less/lower thanbased on whether the test is one- or two-tailed. Fill in the missing information in the alternative hypothesis below. In the firstand thirdblank, write one of the following symbols: =, ≠, <, or >. Note that there are two ways to present the alternative hypothesis for this test in symbols; therefore, write the appropriate symbol in the first blank following “μ2” as well as the blank following “μ1.” In the second blank, write the value of the population mean difference. In the fourth blank, write one of the following words, which should correspond to the symbol you wrote in the first blank: different, equal, higher, lower. HA: μ1–μ2___________ orμ1____μ2 Alternative hypothesis: Students who consider themselves to be introverted have a __________level of emotional stability compared to extraverted students. In this exercise, you identified the research question and developed the hypotheses. It’s now time to run the independent samples t test analysis on SPSS. Exercise 2: Running the analysis on SPSS In this exercise, you will run an independent samples ttest on SPSS. Ensure you have the PS296 Class Dataset open on SPSS and then follow the steps below. STEP 1:Go to the Analyzemenu at the top of the screen and select Compare Meansand Independent-Samples T Test. STEP 2:Move TIPI_EmotionalStabilityinto the Test Variable(s)box, and move Introvert_Extravertinto the Grouping Variablebox.
PS296 OC Lab 6 –S2024 5 STEP 3: Click on Define Groups. Type “1” beside Group 1and “2”beside Group 2. (This is the default, so leave as is.) Then click Continue. STEP 4: UncheckEstimate effect sizes. Then, click on OKto run the analysis. Remember to save your SPSS Output!
PS296 OC Lab 6 –S2024 6 In this exercise, you followed the steps to run the independent samples t test analysis on SPSS. You will now learn how to interpret the results presented in the SPSS Output. Exercise 3: Assessing the SPSS output Displayed first is the syntax record, which includes information about the analysis you just ran and your user information (e.g., name, date, time). Remember, you will need to include the SPSS Syntax Notes in any SPSS Output file that you submit for this course. In this exercise, you will learn to identify the values produced by the analysis in the tables that appear below the syntax record. 1.The first table displayed in the SPSS Output is titled Group Statisticsand includes the following information for each group/sample: number of cases included in the analysis (N), mean (Mean), standard deviation (Std. Deviation), and the standard error of the mean (Std. Error Mean). Group Statistics Grouping Variable N Mean Std. Deviation Std. Error Mean Test Variable Group 1 𝑛1𝑥̅1?1?𝑥̅1Group 2 𝑛2𝑥̅2?2?𝑥̅2The table for the Introvert_Extravert and TIPI_EmotionalStabilityvariables includes the following values: Group Statistics Introvert_Extravert N Mean Std. Deviation Std. Error Mean TIPI_Emotional Stability Introvert 243 7.64 2.692 .173 Extravert 169 8.18 2.793 .215 Helpful Hint: N for each group represents the number of particiapnts included in the analysis; therefore, the sum of n1and n2will represent the total sample size (i.e., N= 412) if all PS296 students who completed the survey provided data for the questions/items included in the analysis. Likewise, if a student did not answer all of the items included in the TIPI Emotional Stability subscale and/or did not indicate whether they were an introvert or extravert, then their data would not be included in the analysis. The number of students included in this analysis is 412 (i.e., 243 + 169); therefore, all students who completed the survey are inlcuded in this analysis. Remember to jot down your answers to the questions! You will need this information to complete a quiz at the end of the lab!Q4: What is the mean emotional stability score for students who consider themselves to be an introvert (𝑥̅1)? (Hint: Look in the Mean column along the “Introvert” row)
PS296 OC Lab 6 –S2024 7 Q5: What is the standard deviation for students who consider themselves to be an extravert (s2)? (Hint: Look in the Std. Deviation column along the “Extravert” row) Q6: How many students in the analysis consider themselves to be an extravert (n2)? (Look in the N column along the “Extravert” row) Q7: How many students’ data are included in this analysis?(Hint: Sum the values in the N column) 2.The results of the analysis are displayed in the table titled Independent Samples T Test. The first two columns of output represent the results of Levene’s Test for Equality of Variances. Recall, an important assumption of an independent samples t test is that the group variances are equal (i.e., homogeneity of variance). When the variances are not equal (i.e., heterogeneity of variance), the tstatistic is calculated differentlyto account for the violation of this assumption; specifically, an adjustment is made to the degrees of freedom. The null hypothesis of Levene’s test is that the group variances are equal, so this one test that you do not want to be significant. In the table, the value of Levene’s statistic is in the F column and the p-value associated with this statistic is located in the Sig. column. When Levene’s test is not statistically significant (i.e., p> 0.05), refer to the values along the first row labelled Equal variances assumedwhen assessing the results of the ttest. When the test is statistically significant (i.e., p< 0.05), refer to the values along the second row labelled Equal variances not assumedwhen assessing the results of the ttest. The results of the independent samples t test are displayed in the columns to the right of Levene’s test, and include the t statistic (t), degrees of freedom (df), p-value for a one- and two-tailed test (Significance One-Sided p and Two-Sided p), difference between sample means (Mean Difference), standard error of the difference between sample means (Std. Error Difference), and 95% confidence interval of the difference between sample means (Lower, Upper). Independent Samples Test Levene's Test for Equality of Variances t-test for Equality of Means F Sig. t df One-Sided p Two-Sided p Mean Difference Std. Error Difference 95% Confidence Interval of the Difference Lower Upper Test Variable Equal variances assumed Ffor Levene’sp-value for Levene’ststatistic n1+ n2- 2 p-value for ttest p-value for ttest𝑥̅1− 𝑥̅2?𝑥̅1−𝑥̅2upper limit lower limit Equal variances not assumed - - - - - - - - - - - - Corrected/adjusted values for ttest - - - - - - - - - - - - Significance
PS296 OC Lab 6 –S2024 8 The table for the Introvert_Extravert and TIPI_EmotionalStabilityvariables includes the following values: Q8: Are the variances in each group/sample equal? How do you know? (Hint: Look at the “Sig.” value for Levene’s test and determine whether it is statistically significant or not) Q9: Which row of output should you look at for the ttest? (Hint: When Levene’s test is not statistically significant, look at the top row - when it is significant, look at the bottom row) Q10: What is the value of the difference between the group/sample means? (Hint: Look in the Mean Difference column) Q11: What is the value of the tstatistic? (Hint: Look in the t column along the appropriate row) Q12: Is the tstatistic for the analysis statistically significant? Explain your answer. (Hint: Look in the One-Sided p column along the appropriate row and compare the value to α= 0.05)Q13: Based on the results of this analysis, is your decision to reject or fail to reject the null hypothesis? Explain your answer. (Hint: When the p-value is less than α = 0.05, you reject the null hypothesis, and when it is greater than α = 0.05, you fail to reject the null hypothesis)Q14: What statistic and value do you arrive at when you divide the difference between group means (“Mean Difference”) by the standard error (“Std. Error Difference”)? (Hint: Calculate the statistic by using the appropriate values in the SPSS Output table) In this exercise, you learned how to interpret the values presented in the SPSS Output tables. It’s now time to summarize the findings in an APA formatted conclusion. Independent Samples Test Levene's Test for Equality of Variances t-test for Equality of Means F Sig. t df One-Sided p Two-Sided p Mean Difference Std. Error Difference 95% Confidence Interval of the Difference Lower Upper TIPI_ Emotional Stability Equal variances assumed .855 .356 -1.971 410 .025 .049-.540 .274 -1.078 -.001 Equal variances not assumed -1.958 352.951 .026 .051 -.540 .276 -1.082 .003 Significance
PS296 OC Lab 6 –S2024 9 Exercise 4: Summarizing the results In this exercise, you will summarize the results presented in the SPSS Output in a properly formatted conclusion. The concluding statement for an independent samples ttest should include the following information: (i) One- or two-tailed test, (ii) Alpha value, (iii) Significant or non-significant, (iv) Means and standard deviations of each group, (v) t statistic in proper format, which includes the type of statistic, degrees of freedom, value of the statistic, and p-value, and (vi) Direction of the difference. 1.Fill in the missing information in the following concluding statement; specifically, replace the highlighted text/labelswith the proper information and values from the SPSS Output. Remember to round values to 2 decimal places, with the exception of the p-value, which is rounded to 3 decimal places. Also, use “M” to represent each sample mean (𝑥̅1and 𝑥̅2) and and “SD” to represent each sample standard deviation (s1and s2). Remember to jot down your answers to the questions! You will need this information to complete a quiz at the end of the lab!Based on an independent samples ttest (one or two-tailed) at α= 0.05 or 0.01, we can conclude that PS296 students who consider themselves to be introverts (M = mean of group 1, SD= standard deviation of group 1) do or do not have a significantly higher or lower or differentemotional stability level compared to those who consider themselves to be extraverts (M = mean of group 2, SD= standard deviation of group 2), t(degrees of freedom) = value of tstatistic, p-value. Note: When an analysis produces a non-significant result, the conclusion states there is a “non-significant” difference between the means, and the p-value is reported as “ns.”In this exercise, you learned how to present the results of an independent samples ttest in a properly formatted concluding statement. A well-written conclusion demonstrates your understanding of the SPSS Output, as well as the test you conducted. Now it’s time to practise what you have learned in this lab with a different variable from the PS296 Class Dataset! Exercise 5: On your own Making your bed in the morning may be one of the most important things you do each day. Take a minute to watch this short excerpt from a commencement address delivered by Admiral McRaven at the University of Texas (2014): https://www.youtube.com/watch?v=KgzLzbd-zT4 In this exercise, you will examine whether people who make their bed in the morning have lowerprocrastination scores than those who do not; specifically, Are students who make their bed each day less likely to procrastinate than those who do not make their bed?Procrastination on the class
PS296 OC Lab 6 –S2024 10 survey was assessed using the 20-item Procrastination (PRO) scale, and higher scores represent a greater likelihood to procrastinate. Conduct an independent samples t test with the following two variables in the PS296 Class Dataset: Bed_Make: Do you typically make your bed each day?and PRO_Score (calculated by summing the 20 items on the scale). Remember to jot down your answers to the questions! You will need this information to complete a quiz at the end of the lab! 1.Complete the items below:a.Identify the research question and decide whether this is a one- or two-tailed test. b.State the null and alternative hypotheses in symbols and words. c.Run the analysis on SPSS (carefully follow the instructions above –no more, and no less). d.Decide whether the results of the test are statistically significant. e.Summarize the results in a properly-formatted conclusion. 2.A portion of your lab credit is based on your SPSS Output. Post your SPSS Output for all of the analyses/exercises on SPSSthat you have conducted in this lab in the Dropbox on MyLS titled LAB 6 OUTPUTas a.pdf document. Be sure to include the Syntax Record in the Notestable format! Name your file “PS296 Lab 6 –Last Name, First Name.”In this lab, you learned how to run an independent samplesttest on SPSS. You also identified the research question, stated the hypotheses, interpreted the SPSS Output, and summarized the results in a properly-formatted conclusion. By completing the exercises in this lab, you should now feel competent in conducting and evaluating an independent samples t testanalysis on SPSS. Lab Quiz A portion of your credit for this lab is based on a quiz. This quiz is based on the information presented in this handout, as well as the exercises and questions you completed during the lab. Use the notes you created throughout the lab to answer the questions. REMEMBER, the lab quiz will not be visible until you have posted your SPSS Output in the Dropbox.You have one attemptand an enforced 15-min time limit to complete the quiz. If you did not complete the exercises and record your answers as you worked through the lab, and therefore need to complete the exercises after opening the quiz, you will run out of time. Do not open and attempt the quiz until you have completed the requirements of the lab. Lab quizzes are to be completed independently (on your own). Your TA, lab coordinator, and course instructor will not assist you with completing the quiz. Direct any concerns related to lab quizzes to the lab coordinator. Remember, do not submit your completed lab handout for grading. Your lab credit is based on the score you achieve on the quiz and your SPSS output submission.
PS296 OC Lab 6 –S2024 11 Go to the Quizzes tab and select Lab 6 Quizwhen you are ready to begin. The quiz will no longer be available after 11:59 pm on Sunday, and thequiz will not be extended, reopened, or reset. Good Luck!