please follow the instructions in the assighnment file. use spss and follow the proceedures
PSYC 207 Assignment #3 (27 marks) Differences between means: t-tests, One-Way and Factorial Two-Way ANOVA INTRODUCTION A substantial part of quantitative statistics is assessing whether or not there are significant differences between two or more groups on a specific variable of interest (e.g. income, intelligence, oxygen consumption, etc.), often (but not always) after exposure to some form of intervention (e.g. government program, behavioral therapy, exercise regimen, etc.). The same can be said for relationships or associations between two groups. 1. Differences between means For example, a researcher might be interested in how the administration of a drug might help to lower blood cholesterol levels in a specific population. There are a number of options as to how the researcher might do this, depending on the research design: 1. Compare two independent groups from the same population. One gets the drug (intervention group) and one does not (control group). 2. Compare the same group against each other. The group’s blood cholesterol level is measured (pre-test), and then after the administration of the drug, measured again (post-test). The pre-test and post-test findings compared against each other to see if there is a difference. 3. The researcher might want to compare different levels of the drug to see what minimum levels are effective enough at lowering blood cholesterol (there are always side effects to medication and it is desirable to minimize those). If the researcher wanted to use three (3) different levels of the drug (say, 100mg, 250mg and 500mg) then s/he would need four groups: Group 1 (Control – no drug), Group 2 (100mg), Group 3 (250mg), and Group 4 (500mg). 4. Carrying on from (3), the researcher might also think that there is an adjuvant effect with the combination of drugs plus medication – i.e. that drugs to lower blood cholesterol levels might be enhanced with added exercise. In each of these cases, the researcher needs to use the appropriate statistical test. In class, we learned that a t-test is required to assess the difference between two means and two means ONLY. If the groups are independent, then an independent t-test is used. If a group is compared against itself, then a dependent t-test is used. If the researcher is comparing more than two means, a one-way ANOVA (Analysis of Variance) has to be used. If two independent variables are assessed for their influence on one dependent variable in combination, then a 2-WAY ANOVA is used. Tasks For this assignment you will using SPSS to assess differences and associations between variables, and then interpret the findings. OUTPUTS Save the following outputs for Parts 1-3: copy and paste to MS Word as per usual. Ensure that each section is titled appropriately. Part 1 Differences between two means (T-test) You are interested in assessing whether or not there is a significant difference between males and females (two independent groups) in terms of the number of hours of sleep and income (continuous variables). Procedure 1. On Moodle, access the datafile ‘PSYC_Bodner_Sleep_Income_SP2021.sav’ 2. Under Analyze Compare Means Independent samples T-Test 3. Select the variables ‘SLEEP’ and ‘INCOME’ and add to ‘Test Variables’ 4. Under ‘Grouping Variable’ select the variable ‘SEX’ 5. Under ‘Define Groups’ select ‘0’ for Group 1 (Male) and ‘1’ for Group 2 (Female) 6. Hit ‘OK’ 7. Save this output. Use subtitle ‘Differences in sleep and income by sex’ to describe this output. Part 2 Differences between more than two means (One-Way ANOVA) Say a researcher was interested in whether or not levels of physical activity influenced body mass index (BMI) levels. She draws a sample from a population and allocates them into three groups based on self-reported physical activity (PA): Group 1: low level PA Group 2: moderate level PA Group 3: high level PA She then measures the BMI of each person in each group. BMI is a population measure of obesity and is a continuous variable that ranges from <18 to="">40. The researcher’s hypothesis is that those who engage in high levels of physical activity will have lower levels of BMI compared to the other groups. The researcher will correctly choose a one-way ANOVA to answer her research question. Recall that a one-way ANOVA informs the researcher that a significant difference in BMI exists somewhere between the three levels of physical activity, but it will not tell her WHERE that difference exists. Perhaps the difference exists between high PA and low PA; or maybe between high and moderate and low PA, but no difference between moderate and low PA. So what can the researcher do here? She will run a post-hoc (“after the fact”) test to assess where that difference(s) exists. And SPSS has several options to do this. The choice of option depends on how ‘conservative’ or ‘liberal’ the post-hoc test is in assessing the significant difference. Think of ‘conservative’ as greater scrutiny as to whether or not there is a significant difference, and ‘liberal’ as robust, but not as hard-edged as the conservative test. In reality, these conservative and liberal post-hoc tests have their own characteristics that the researcher considers, depending on the data characteristics. But we must also consider the variances. Just like with t-tests, ANOVA assumes equal variances among independent groups. So one-way ANOVA also presents tests for homogeneity of variance. For our purposes for this assignment choose to use the post-hoc test: Bonferroni if assumptions of variance ARE met and Games-Howell if assumptions are NOT met. PROCEDURE 1. Access Moodle and open the ‘ANOVA_BMI_SP2021’ file 2. Under Analyze Compare Means One-way ANOVA 3. For the Dependent List choose select the variable ‘BMI’ 4. For Factors, choose the variable ‘Level of Physical Activity’ 6. Under the Options button select ‘Descriptives’ ‘Homogeneity of variance test’ and ‘Means plot’ 7. Click ‘OK’ Examine your data output. Is a post-hoc test needed? If so, perform the next steps. If not, the analysis is complete. 8. Under Analyze Compare Means One-way ANOVA 9. Under the Post-hoc button select ‘Bonferonni’ or ‘Games-Howell’ depending on whether or not the assumption of homogeneity has been met (the level of significance should be set at 0.05 (default). 9. If you run a post-hoc test, you will get two outputs (a repeat of the descriptive tables, etc.). Copy and paste into MS Word the SECOND output (Descriptives, test for homogeneity of variance, ANOVA table, Means plot and post-hoc test table). Use sub-title of ‘Physical Activity and BMI’ to describe this output. Part 3 Factorial Two-Way ANOVA) Before you start into Part 3, let’s remember what exactly a 2-Way ANOVA does. A 2-Way ANOVA allows the researcher to assess whether or not a factor (independent variable) on its own influences an outcome (dependent variable). This is similar to One-Way ANOVA, right? Right! But – with 2-Way ANOVA, a researcher can assess two factors (or independent variables) at the same time. It’s a ‘two-fer’! Here is an example: physical activity and nutrition - independent of each other - have an effect on weight gain/loss. Both physical activity and nutrition are the independent factors or variables and weight gain/loss is the dependent variable (a way to remember this is that the dependent variable ‘depends’ on the independent variable to determine whether or not it changes…) But – as we know sometimes these factors can have associations with each other (real world) – and their combined effects (accounting for both independent factors operating on a dependent variable or outcome at the same time) may change the dependent variable. So the researcher can assess the combined effect of both factors on the dependent variable and consider this combined effort another independent factor or variable. So really, a 2-Way ANOVA is a’ three-fer’: it can assess the independent effect of the two factors on their own as well as a third factor (the combined effect of both factors) - all at the same time. Now to the question. You hypothesize that physical activity and hours of studying (independent variables) will influence test scores (dependent variable). Specifically you think that the more one studies the better the score, but also you think that a dose of physical activity (45 minutes) right before an exam will also have a positive effect (i.e., increase) on exam scores. It is also possible that a combined effect of studying plus physical activity may influence exam scores. You recruit a sample of 40 individuals (n=40) and organize them into the following groups: Group 1 1 hour of studying plus low level of physical activity Group 22 hours of studying plus low level of physical activity Group 31 hour of studying plus high level of physical activity Group 42 hours of studying plus high level of physical activity Each group was given a booklet of material to study and were allowed either 1 or 2 hours of study time. Immediately following the study session, each group engaged in 45 minutes of physical activity (combined cardio plus weight training) at either a high intensity or low intensity. Immediately following the exercise session, each group was given an exam. There was a 60 minute time limit on the exam. All participants had enough time to finish. Exam scores were then tabulated. PROCEDURE 1. Access Moodle and open the ‘2-Way ANOVA_PA_Studying_EXAM SP2021’ file 2. Using procedures outlined in the 2-Way ANOVA Practice in Moodle, run a 2-Way ANOVA with this data 3. Copy and paste this output into MS Word. Label this output ‘2-Way Physical Activity and Studying’ *Note – no post-hoc tests are needed with this analysis Hand in: 1. OUTPUTS (4 marks) - please ensure that the outputs have sub-titles to identify each. Part 1 ‘Sleep hours and Sex’; ‘Income and Sex’ SPSS Output (1 mark) Part 2‘Physical Activity and BMI’ ANOVA SPSS Output (1 marks) Part 3‘Factorial 2-Way ANOVA Exam’ SPSS Output (2 marks) 2. QUESTIONS (23 marks) Please answer in full sentences. Marks will be deducted if answers are not in full sentences. Use data from your outputs to buttress your answers (where needed). Please type your answers below the questions in bold font, please. Ensure that your name is on your document. Part 1 Differences between two means Review your data output from your T-tests. 1. If we use t-tests to assess a significant difference between two means, why do we have consider the variance of the two group scores as part of this process? (1 mark) 2. Did you violate assumptions of variance with either t-tests? Explain. (2 marks) 3. What would be the statistical conclusion from the analyses for both sleep and income? Ensure that in your conclusion you express your t-scores from your data (see Powerpoint for how to express t-values for such write-ups) (2 marks) 4. When would you use a one-tailed t-test? Two-tailed? Give examples with your answer (1 mark) 5. Which type