1. Psyc 235: Introduction to Statistics
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2. Extra Credit Final
Deadline to complete 84 ALEKS hours (+/- attendance hours):
11:59pm April 30th

Deadline to your TA to sign up for the extra credit final:
11:59pm May 4th

Extra Credit Final:

3. Applying Inferential Stats in Psychology Research
Several Examples today
Note: No Z-tests!
because in reality we almost never know  (standard deviation of population)
Data set: 100 students in an Intro Psych class
Note: fabricated, for purpose of example!

4. Handout: Statistical Tests Decision Tree
Good overview
(will also be posted online)
Also: handouts on reading research articles (~preview of research methods courses)

5. Data Set used for Examples
Subjects/Participants: students in an Intro Psych class
N=100
4 sections (n=25 for each)
Variables:
Section#, Gender, Midterm Score, Final Exam Score, Letter Grade, GPA
(Excel!)

6. Research Questions
Do the current students’ scores differ significantly from historical?
Is there a gender difference in performance on psychology final exam?
Do students improve their test performance over time in the course? (learning!)
Is there any difference in final exam performance due to method of test preparation?
Are GPA and final exam score associated?
To what degree does GPA predict final exam score?
Are letter grades distributed across section as expected by chance?

7. Example 1 (of 7) Background: Research Q: DV: IV: Which Test?...
Historical mean final exam score: 78
Research Q:
Do the current students’ scores differ significantly from historical?
DV:
final exam score. interval.
IV:
Historical vs Current. nominal. 2 levels. 1 sample.
Which Test?...
Single-sample T-Test

8. Example 1 (of 7): Single-sample t-test
Do the current students’ scores differ significantly from historical (=78)?
H0:
μ=78
sample mean (Xbar)=80.55
sample standard deviation (s)=8.68
standard error:
test statistic (t):
p, tcritical, 95% confidence interval...

9. Example 1 (of 7): Single-sample t-test
Decision:
Reject Null Hypothesis
in a research article:
“Students in the current introductory psychology course scored higher on the final exam (M = 80.55, SD = 8.68) than did University of Illinois students in general [t(99) = 2.94, p = .004].”

10. Example 2 (of 7) Background: Question: DV: IV: Which Test?...
Students randomly sampled.
Question:
Is there a gender difference in performance on psychology final exam?
DV:
final exam score. interval.
IV:
male vs. female. nominal. 2 levels. 2 samples.
Which Test?...
Independent-samples T-Test

11. Example 2 (of 7): Independent-samples t-test
Is there a gender difference in performance on psychology final exam?
H0:
μM=μF or μM-μF=0
sample means (Xbar):
male= female=81.75
sample standard deviation (s):
male= female=8.20
standard error:
test statistic (t):
p, tcritical, 95% confidence interval...

12. Example 2 (of 7): Independent-samples t-test
Decision:
Fail to Reject Null Hypothesis
in a research article:
“The independent variable was gender, with two levels: female and male.  The dependent variable was proportion correct on the final exam.”
“To test the hypothesis that women and men, on average, score differently on this type of exam, we conducted an independent-samples t test.  There was no statistically significant effect of gender [t(98)=-1.39, p=0.17].  Performance by women (M=81.75, SD=8.20) and men (M=79.35, SD=9.05) was not reliably different.”

13. Example 3 (of 7) Background: Question: DV: IV: Which Test?...
Comparable questions on midterm and final exam.
Question:
Do students improve their test performance over time in the course? (learning!)
DV:
test score. interval.
IV:
Which test (midterm vs. final). ordinal/nominal. 2 levels. 2 samples.
Which Test?...
Paired-samples T-Test

14. Example 3 (of 7): Paired-samples t-test
Do students improve their test performance over time in the course?
H0:
μFinal-μMidterm≤ or μDifference=0
Note: we calculate a difference score for each student: (final score - midterm score)
mean difference of score (Xbar): 11.38
sample standard deviation of difference score (s): 10.35
standard error:
test statistic (t):
p, tcritical, 95% confidence interval...

15. Example 3 (of 7): Paired-samples t-test
Decision:
Reject Null Hypothesis
in a research article:
“A paired-samples t test revealed a statistically significant difference between midterm and final exam performance [t(99)=10.99, p<0.05]. Performance was higher on the final (M=80.55, SD=8.68) than on the midterm (M=69.17, SD=12.71). ”

16. Example 4 (of 7) Background: Question: DV: IV: Which Test?...
Students were randomly assigned to one of the 4 Sections.
Each section did something different to prepare for the final exam: control, practice test, explain material to partner, highlight key points in the reading.
Question:
Is there any difference in final exam performance due to method of test preparation?
DV:
final exam score. interval.
IV:
Which Section (control, practice test, explain, highlight). nominal. 4 groups/levels. between-subjects/group design.
Which Test?...
One-way between-groups ANOVA

17. Example 4 (of 7): One-way between-groups ANOVA
Is there any difference in final exam performance due to method of test preparation?
H0:
μ1=μ2=μ3=μ4
Test statistic (F): MSB/MSW
degrees freedom (dfb, dfw)
p, Fcritical...

18. Example 4 (of 7): One-way between-groups ANOVA
Decision:
Reject Null Hypothesis
in a research article:
“A one-way ANOVA revealed an overall effect of test preparation method [F(3,96)=2.745, p<.05].”

19. Example 5 (of 7) Background: Question: DV/IV: Which Test?...
GPA doesn’t include the intro psych course
Question:
Is there an association between GPA and final exam score?
DV/IV:
final exam score. interval.
GPA. interval
Which Test?...
Pearson correlation coefficient

20. Example 5 (of 7): Pearson Correlation Coefficient

21. Example 5 (of 7): Pearson Correlation Coefficient
Is there an association between GPA and final exam score?
H0: rho=0 r:
test statistic (t):
tcritical, p....

22. Example 5 (of 7): Pearson Correlation Coefficient
Decision:
Reject Null Hypothesis
in a research article:
“The correlation between GPA and final exam score was .70 [t(98)=977, p<.05].”

23. Example 6 (of 7) IV Background: Question: DV Which Test?...
now let’s see if we can predict final exam score from GPA
Question:
To what degree does GPA predict final exam score? DV
final exam score. interval. IV
GPA. interval.
Which Test?...
Simple Linear Regression

24. Example 6 (of 7): Simple Linear Regression
To what degree does GPA predict final exam score?
Least squares regression line
Y=b1X+b0

25. Example 6 (of 7): Simple Linear Regression

26. Example 6 (of 7): Simple Linear Regression
To what degree does GPA predict final exam score?
Least squares regression line
Y=b1X+b0
H0: beta1=0
Can also predict new values
ex: student #101 has GPA of

27. Example 6 (of 7): Simple Linear Regression
Decision:
Reject Null Hypothesis
in a research article:
“Final exam score significantly predicted GPA [b=7.81, t(98)=24.57, p<.05].”

28. Example 7 (of 7) Background: Question: DVs Which Test?...
Letter Grade in course based on final and midterm.
Question:
Are letter grades distributed across section as expected by chance?
DVs
letter grade. nominal. 5 levels (A,B,C,D,F).
Which Section (control, practice test, explain, highlight). nominal. 4 groups/levels. between-subjects/group design.
Which Test?...
Chi-Square Test for Independence

29. Example 7 (of 7): Chi-Square Test for Independence
Are letter grades distributed across section as expected by chance?
Observed Frequencies:
Expected Frequencies (under H0):

30. Example 7 (of 7): Chi-Square Test for Independence
df, critical value, p...

31. Example 7 (of 7): Chi-Square Test for Independence
Decision:
Fail to reject Null Hypothesis
in a research article:
“A chi-square test of independence was performed to examine the relation between section and course letter grade. The relation between these variables was not statistically significant [X2 (12, N = 100) = 14.97, p =.245].”

32. Statistics: final words
Way of making sense out of data
Fundamental tool for all scientific inquiry
“Statistics cannot do the scientist’s basic job—looking and wondering and looking again.”
William L. Hays (Statistics, 5th Ed.)
Also: don’t stop the rock.

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