1. Psych 231: Research Methods in Psychology
Statistics (cont.)
Psych 231: Research Methods in Psychology

2. Announcements Quiz 10 is due on Friday at midnight
Class experiment final drafts due in labs this week
Please remember to include your commented first draft
Announcements

3. Inferential Statistics
Two approaches
Hypothesis Testing
“There is a statistically significant difference between the two groups”
Confidence Intervals
“The mean difference between the two groups is between 10 ± 4”
Population
Sample A
Treatment
X = 45
Sample B
No Treatment
X = 35
Inferential statistics used to generalize back
Dep Var
Error bars are 95% CIs
Inferential Statistics

4. Two group design: HT & CI
2 separate experimental conditions
Formulae:
Observed difference
t =
X X2
Diff by chance
Dep Var
Error bars are 95% CIs
Based on sampling error: Estimate of the Standard Error
CI: μ=(X1-X2)±(tcrit)(Diff by chance)
Two group design: HT & CI

5. Two group design: HT & CI
2 separate experimental conditions
Formulae:
T =
X X2
Diff by chance
Dep Var
Error bars are 95% CIs
Margin of error
(with a level of confidence)
CI: μ=(X1-X2)±(tcrit)(Diff by chance)
Two group design: HT & CI

6. Interpreting Confidence intervals
CI: μ = (X) ± (tcrit) (diff by chance)
What DOES “confident” mean?
“90% confidence” means that 90% of the interval estimates of this sample size will include the actual population mean
9 out of 10 intervals contain μ
Actual population mean μ
Interpreting Confidence intervals
R-Psychologist: Interpreting Confidence Intervals
Tan & Tan (2010). The correct interpretation of confidence intervals. Procedings of Signapore Healthcare, 19. Retrieved

7. Using Confidence intervals
CI: μ = (X) ± (tcrit) (diff by chance)
Note: How you compute your standard error will depend on your design
Using Confidence intervals

8. Using Confidence intervals
CI: μ = (X) ± (tcrit) (diff by chance)
Distribution of the test statistic
Confidence interval uses the tcrit values that identify the top and bottom tails. Depends on:
α-level
df (degrees of freedom)
The upper and lower 2.5%
2.5%
2.5%
A 95% CI is like using a “two-tailed” t-test with with α = 0.05
95% of the sample means
Using Confidence intervals

9. CI’s in SPSS output for t-tests

10. Error Bars: Reporting CIs
Important point!
In text (APA style) example:
M = 30.5 ms, 95% CI [18.0, 42.0]
In graphs as error bars
In tables (see more examples in APA manual)
Error Bars: Reporting CIs

11. Error Bars: Reporting CIs
Note: Make sure that you label your graphs, let the reader know what your error bars are
Important point!
In graphs as error bars
Two types typically
Standard Error (SE)
diff by chance
Confidence Intervals (CI)
A range of plausible estimates of the population mean
CI: μ = (X) ± (tcrit) (diff by chance)
Error Bars: Reporting CIs

12. Estimation: Why? Because C.I.s are often recommended or required:
“estimates of appropriate effect sizes and confidence intervals are the minimum expectations” (APA, 2009, p. 34)
Loftus (1993) – took over as editor or Memory & Cognition
“Data analysis: a picture is worth a thousand p-values” (pg. 3)
an editorial in Neuropsychology stated that “effect sizes should always be reported along with confidence intervals” (Rao et al., 2008, p. 1)
In 2005, the Journal of Consulting and Clinical Psychology (JCCP) became the first American Psychological Association (APA) journal to require statistical measures of clinical significance, plus effect sizes (ESs) and associated confidence intervals (CIs), for primary outcomes (La Greca, 2005)
For journals in fields like medicine, physics, chemistry, CIs are the standard
Estimation: Why?

13. Hypothesis testing & p-values
Some argue that CIs are more informative than p-values
Hypothesis testing & p-values
Dichotomous thinking
Yes/No reject H0
(remember H0 is “no effect”)
Neyman-Pearson approach
Strength of evidence
Fisher approach
Confidence Intervals
Gives plausible estimates of the pop parameter (values outside are implausible)
Provide information about both level and variability
Wide intervals can indicate low power
Good for emphasizing comparisons across studies (e.g., meta-analytic thinking)
Can also be used for Yes/No reject H0
Brief wiki description of these two approaches
Estimation: Why?
Geoff Cumming:
Introduction to Estimation:

14. Hypothesis testing with CIs
If we had instead done a hypothesis test on 2 independent samples with an α = 0.05, what would you expect our conclusion to be?
H0: “there is no difference between the groups”
MD = 2.23, t(34) = 1.25, p = 0.22
- Fail to reject the H0
-1.4
5.9
MD = 2.23, 95% CI [-1.4, 5.9]
Hypothesis testing with CIs

15. Hypothesis testing with CIs
If we had instead done a hypothesis test on 2 independent samples with an α = 0.05, what would you expect our conclusion to be?
H0: “there is no difference between the groups”
MD = 2.23, t(34) = 1.25, p = 0.22
- Fail to reject the H0
-1.4
5.9
MD = 2.23, 95% CI [-1.4, 5.9]
MD = 3.61, 95% CI [0.6, 6.6]
0.6
6.6
- reject the H0
MD = 3.61, t(42) = 2.43, p = 0.02
Hypothesis testing with CIs

16. CI’s in SPSS output for t-tests
Doesn’t include 0 in interval, so reject H0
P < 0.05, so reject H0
Doesn’t include 0 in interval, so reject H0
P < 0.05, so reject H0
Does include 0 in interval, so fail to reject H0
P > 0.05, so fail to reject H0
CI’s in SPSS output for t-tests

17. Understanding CI: https://www.youtube.com/watch?v=tFWsuO9f74o
Calculating CI:
Kahn Academy:
CI and sample size:
CI and t-test:
CI for Ind Samp: (pt 2)
CI and margin of error:
HT and CI:
HT vs. CI rap:
CIs by Geoff Cumming:
Introduction to:
Workshop (6 part series)
From my PSY 138 course: Estimation Lab | Lecture
The Minitab Blog: Understanding Hypothesis Tests: Confidence Intervals and Confidence Levels
Wang et al. (2009). A practical guide for understanding confidence intervals and P values. Otolaryngology-Head and Neck Surgery. Retrieved from
Additional resources