Assignment #3: ANOVA with SPSS
Due March 3, 2016
In this assignment, we will elaborate on some of the examples we went through in class with larger datasets and will conduct each of the two types of ANOVA using SPSS. Remember that I have posted the “ANOVA SPSS Syntax Sheet” which is useful to have beside you. This sheet also describes what all the output represents.
In this assignment, we will elaborate on some of the examples we went through in class with larger datasets and will conduct each of the two types of ANOVA using SPSS. Remember that I have posted the “ANOVA SPSS Syntax Sheet” which is useful to have beside you. This sheet also describes what all the output represents.
TASK #1: JURY DECISION MAKING
Download the data file from https://www.dropbox.com/s/01xcrv4d5o04o51/Jury_Duty.txt?dl=0www.dropbox.com/s/01xcrv4d5o04o51/Jury_Duty.txt?dl=0
This file contains data from an experiment on decision making. Each participant was randomly assigned to one of three different scenarios, in which the participant learns details of a crime. In the first scenario, the defendant provides testimony and argues he is not guilty. The second scenario is similar but also includes a statement that a witness saw the defendant commit the crime. In the third and final scenario, an attorney indicates that the witness was not wearing his glasses, thus his testimony may have been false. Loftus (1979) found that participants, acting in the role of juror would be more likely to convict someone on the basis of eyewitness testimony, even if that testimony was questioned.
Participants are in one of three treatment conditions (a) discredited eyewitness, (b) no eyewitness, and (c) unrefuted eyewitness. Participants in this study rate their belief about the defendant's guilt. The rating scale ranges from a 1 (definitely not guilty) to a 7 (definitely guilty)
The data file contains two variables: Condition (1 = discredited eyewitness, 2 = no eyewitness, 3 = unrefuted eyewitness) and rating (1 to 7) in that order. Read the data into SPSS using the data list command in the syntax editor. Then, run a Oneway ANOVA:
ONEWAY rating BY condition /STATS DESC.
The output gives two tables. The first table is a list of descriptive statistics by level of the factor (those are the instructions after the / in syntax). The second is an ANOVA source table exactly as we have seen in class.
1) State the null and alternate hypotheses for Loftus’ study
2) What was the mean rating for each information condition?
3) Write a conclusion for her study using the F(df_B,df_W) = convention in research reports.
Now, let’s determine what the pattern of significant differences between means is that was leading to the omnibus ANOVA yielding significance. We will do two liberal tests, the Student-Newman-Keuls, and the Tukey honestly significant difference (HSD) test that we did by hand in class (b/c they illustrate the two types of post-hoc output tables):
ONEWAY rating BY condition
/POSTHOC=SNK TUKEY.
The first table in the output is your omnibus ANOVA table. The second table shows each pairwise comparison compared to an HSD. Mean differences that are “honestly significantly different” will surpass this distance and are significant (indicated by the star and sig test). The third table illustrates “homogeneous subsets” under both Tukey’s HSD and SNK tests. Your jury conditions are the rows, and the columns are the inferred populations they come from under the post-hoc test. If the means for two conditions are listed under the same subset, then their means do not differ significantly from one another (i.e., we believe they come from the same population). This is a nice way to quickly visualize the significant differences between means.
4) Write a results paragraph for the Loftus study as if you were writing it for publication. In it, include the omnibus ANOVA first, with our F(df_b, df_w) = ...reporting convention. Then, report on which conditions differed significantly from one another using either post-hoc test, and draw a conclusion about what these results mean for jury decision making.
Download the data file from https://www.dropbox.com/s/01xcrv4d5o04o51/Jury_Duty.txt?dl=0www.dropbox.com/s/01xcrv4d5o04o51/Jury_Duty.txt?dl=0
This file contains data from an experiment on decision making. Each participant was randomly assigned to one of three different scenarios, in which the participant learns details of a crime. In the first scenario, the defendant provides testimony and argues he is not guilty. The second scenario is similar but also includes a statement that a witness saw the defendant commit the crime. In the third and final scenario, an attorney indicates that the witness was not wearing his glasses, thus his testimony may have been false. Loftus (1979) found that participants, acting in the role of juror would be more likely to convict someone on the basis of eyewitness testimony, even if that testimony was questioned.
Participants are in one of three treatment conditions (a) discredited eyewitness, (b) no eyewitness, and (c) unrefuted eyewitness. Participants in this study rate their belief about the defendant's guilt. The rating scale ranges from a 1 (definitely not guilty) to a 7 (definitely guilty)
The data file contains two variables: Condition (1 = discredited eyewitness, 2 = no eyewitness, 3 = unrefuted eyewitness) and rating (1 to 7) in that order. Read the data into SPSS using the data list command in the syntax editor. Then, run a Oneway ANOVA:
ONEWAY rating BY condition /STATS DESC.
The output gives two tables. The first table is a list of descriptive statistics by level of the factor (those are the instructions after the / in syntax). The second is an ANOVA source table exactly as we have seen in class.
1) State the null and alternate hypotheses for Loftus’ study
2) What was the mean rating for each information condition?
3) Write a conclusion for her study using the F(df_B,df_W) = convention in research reports.
Now, let’s determine what the pattern of significant differences between means is that was leading to the omnibus ANOVA yielding significance. We will do two liberal tests, the Student-Newman-Keuls, and the Tukey honestly significant difference (HSD) test that we did by hand in class (b/c they illustrate the two types of post-hoc output tables):
ONEWAY rating BY condition
/POSTHOC=SNK TUKEY.
The first table in the output is your omnibus ANOVA table. The second table shows each pairwise comparison compared to an HSD. Mean differences that are “honestly significantly different” will surpass this distance and are significant (indicated by the star and sig test). The third table illustrates “homogeneous subsets” under both Tukey’s HSD and SNK tests. Your jury conditions are the rows, and the columns are the inferred populations they come from under the post-hoc test. If the means for two conditions are listed under the same subset, then their means do not differ significantly from one another (i.e., we believe they come from the same population). This is a nice way to quickly visualize the significant differences between means.
4) Write a results paragraph for the Loftus study as if you were writing it for publication. In it, include the omnibus ANOVA first, with our F(df_b, df_w) = ...reporting convention. Then, report on which conditions differed significantly from one another using either post-hoc test, and draw a conclusion about what these results mean for jury decision making.
TASK 2: MENTAL ROTATION
Download the data file from https://www.dropbox.com/s/4ramzy8ccdwrvl7/Mental_Rotation.txt?dl=0www.dropbox.com/s/4ramzy8ccdwrvl7/Mental_Rotation.txt?dl=0
This file contains data from a mental rotation experiment modeled after Shepard and Metzler (1971). On each trial, participants were to make speeded judgments whether two shapes were the same or different. For same trials, the two versions of the shape could be the same orientation, or one could be a rotated version of the other, and the variable of interest is how long it takes you to "mentally rotate" the stimuli to determine whether they match or not. The data file contains only reaction times (seconds) for same responses (and latencies for correct responses only). There are three columns for each participant: 0-degrees rotation, 90-degrees rotation, and 180-degrees rotation, so this is a repeated-measures design.
Download the data file from https://www.dropbox.com/s/4ramzy8ccdwrvl7/Mental_Rotation.txt?dl=0www.dropbox.com/s/4ramzy8ccdwrvl7/Mental_Rotation.txt?dl=0
This file contains data from a mental rotation experiment modeled after Shepard and Metzler (1971). On each trial, participants were to make speeded judgments whether two shapes were the same or different. For same trials, the two versions of the shape could be the same orientation, or one could be a rotated version of the other, and the variable of interest is how long it takes you to "mentally rotate" the stimuli to determine whether they match or not. The data file contains only reaction times (seconds) for same responses (and latencies for correct responses only). There are three columns for each participant: 0-degrees rotation, 90-degrees rotation, and 180-degrees rotation, so this is a repeated-measures design.
Read in the data file using the data list command. Because variable names cannot begin with a digit, use names like deg_0, deg_90, and deg_180 for the three columns. As with our paired-samples t-test, remember that the actual factor (here “rotation level”) is not explicitly named, but the three levels of the factor are each their own variable/column in SPSS since each case (person) must have a score on each of the levels of the factor.
Next, conduct a repeated-measures ANOVA. In your syntax editor, type:
GLM deg_0 deg_90 deg_180
/WSFACTOR=rotation 3
/PLOT=PROFILE(rotation)
/PRINT=DESCRIPTIVE.
The first line specifies that we will use the General Linear Model (GLM) to analyze the data from the three variables (really, three levels of an implicit variable). The next line names the within-subjects factor to which these are levels (here, I have just called it “rotation,” which has 3 levels). The third line asks for a line graph showing the pattern of means, and the final line just asks for descriptive statistics on each level. If the null hypothesis is correct, we expect a flat line across levels (and roughly equal means).
Unfortunately, the output from GLM is huge (b/c so many types of analyses can be done with it), and there is no way to suppress the output that we don’t care about. So we’ll just have to ignore most of it for now.
The first two tables just show the variables used in the analysis and their descriptive statistics. Notice that the null is looking like it might not be true. You can ignore the multivaritate tests and Mauchly’s Spericity Tests because we are not dealing with multivariate data. Your omnibus ANOVA is presented in the Test of Within-Subjects Effects under “Sphericity assumed.” The test of contrasts is the next table, followed by a table of between-subject effects, which you can ignore b/c we have none. The final piece of output is the line plot which shows the profile pattern of your mean RT across the levels of rotation.
1. Write the null and alternate hypotheses for this study. Should you reject or retain the null?
2. Write a brief results paragraph for this experiment using our conventions for reporting the results of a statistical test, and draw a conclusion for the experimenter.
Next, conduct a repeated-measures ANOVA. In your syntax editor, type:
GLM deg_0 deg_90 deg_180
/WSFACTOR=rotation 3
/PLOT=PROFILE(rotation)
/PRINT=DESCRIPTIVE.
The first line specifies that we will use the General Linear Model (GLM) to analyze the data from the three variables (really, three levels of an implicit variable). The next line names the within-subjects factor to which these are levels (here, I have just called it “rotation,” which has 3 levels). The third line asks for a line graph showing the pattern of means, and the final line just asks for descriptive statistics on each level. If the null hypothesis is correct, we expect a flat line across levels (and roughly equal means).
Unfortunately, the output from GLM is huge (b/c so many types of analyses can be done with it), and there is no way to suppress the output that we don’t care about. So we’ll just have to ignore most of it for now.
The first two tables just show the variables used in the analysis and their descriptive statistics. Notice that the null is looking like it might not be true. You can ignore the multivaritate tests and Mauchly’s Spericity Tests because we are not dealing with multivariate data. Your omnibus ANOVA is presented in the Test of Within-Subjects Effects under “Sphericity assumed.” The test of contrasts is the next table, followed by a table of between-subject effects, which you can ignore b/c we have none. The final piece of output is the line plot which shows the profile pattern of your mean RT across the levels of rotation.
1. Write the null and alternate hypotheses for this study. Should you reject or retain the null?
2. Write a brief results paragraph for this experiment using our conventions for reporting the results of a statistical test, and draw a conclusion for the experimenter.
TASK #3: RM-ANOVA DETECTIVE
Dr. B. Chen has spent years collecting data for her thesis, but lost the original data, and spilled coffee on parts of her summary table (below). The source table is based on a repeated-measures ANOVA. Please fill in the blanks below and tell Dr. Ruck what her F-ratio was, and if it was a statistically significant finding. Go back to our Repeated-Measures ANOVA Lecture if you are confused.
Dr. B. Chen has spent years collecting data for her thesis, but lost the original data, and spilled coffee on parts of her summary table (below). The source table is based on a repeated-measures ANOVA. Please fill in the blanks below and tell Dr. Ruck what her F-ratio was, and if it was a statistically significant finding. Go back to our Repeated-Measures ANOVA Lecture if you are confused.
Source |
SS |
df |
MS |
F |
Between Within b/w Ss Error Total |
____ ____ 24 8 82 |
____ 16 4 ____ 19 |
____ ____ |
____ |