1. Reasoning in Psychology Using Statistics
2019

2. Annoucements Quiz 9, due on Friday Lab exam 4 one week from today
Final projects due May 3 (uploaded to ReggieNet)
On-line course evaluations
Look for an (from Monday morning) with a link to take the on-line course evaluations. Please take 10 mins. or so to provide feedback.
Annoucements

3. Inferential statistics
Hypothesis testing
Testing claims about populations (and the effect of variables) based on data collected from samples
Estimation
Using sample statistics to estimate the population parameters
Inferential statistics used to generalize back
Sampling to make data collection manageable
Population
Sample
Inferential statistics

4. Estimation from last time
Design
Estimation
(Estimated) Standard error
One sample, σ known
Center/point estimate
Test statistic with level of confidence
Standard error (difference expected due to chance)
Estimation from last time

5. Estimation Summary Design Estimation (Estimated) Standard error
One sample, σ known
One sample, σ unknown
Two related samples, σ unknown
Two independent samples, σ unknown
Things to note:
The design drives the formula used
The standard error differs depending on the design (kind of comparison)
Sample size plays a role in SE formula and in df’s of the critical value
Level of confidence comes in with the critical value used
Estimation Summary

6. Estimation in other designs
Two kinds of estimates that use the same basic procedure
Computing the point estimate or the confidence interval:
Step 1: Take your “reasonable” estimate for your test statistic
Step 2: Put it into the formula
Step 3: Solve for the unknown population parameter
Center/point estimate?
How do we find this?
How do we find this?
Depends on the design
(what is being estimated)
Use the t-table & your confidence level
Depends on the design
Estimation in other designs

7. Estimates with t-scores
Confidence intervals always involve + a margin of error
This is similar to a two-tailed test, so in the t-table, always use the “proportion in two tails” heading, and select the α-level corresponding to (1 - Confidence level)
What is the tcrit needed for a 95% confidence interval?
2.5%+2.5% = 5% or α = 0.05, so look here
95%
95% in middle
2.5%
so two tails with 2.5% in each
Estimates with t-scores

8. Estimation in one sample-t
Estimating the difference between the population mean and the sample mean based when the population standard deviation is not known
Confidence interval
Diff. Expected by chance
Estimation in one sample-t

9. Estimation in one sample t-design
Make an interval estimate with 95% confidence of the population mean given a sample with a X = 85, n = 25, and a sample s = 5.
What two critical t-scores do 95% of the data lie between?
So the confidence interval is: to 87.06
From the table:
tcrit =+2.064
or 85 ± 2.064
95%
2.5%
-2.06
2.06
Estimation in one sample t-design

10. Estimation in related samples design
Estimating the difference between two population means based on two related samples
Confidence interval
Diff. Expected by chance
Estimation in related samples design

11. Estimation in related samples design
Dr. S. Beach reported on the effectiveness of cognitive-behavioral therapy as a treatment for anorexia. He examined 12 patients, weighing each of them before and after the treatment. Estimate the average population weight gain for those undergoing the treatment with 90% confidence.
Differences (post treatment - pre treatment weights):
10, 6, 3, 23, 18, 17, 0, 4, 21, 10, -2, 10
Related samples estimation
Confidence level 90%
CI(90%)= 5.72 to 14.28
Estimation in related samples design

12. Estimation in independent samples design
Estimating the difference between two population means based on two independent samples
Confidence interval
Diff. Expected by chance
Estimation in independent samples design

13. Estimation in independent samples design
Dr. Mnemonic develops a new treatment for patients with a memory disorder. He randomly assigns 8 patients to one of two samples. He then gives one sample (A) the new treatment but not the other (B) and then tests both groups with a memory test. Estimate the population difference between the two groups with 95% confidence.
Independent samples t-test situation
Confidence level 95%
CI(95%)= -8.73to 19.73
Estimation in independent samples design

14. Estimation Summary Design Estimation (Estimated) Standard error
One sample, σ known
One sample, σ unknown
Two related samples, σ unknown
Two independent samples, σ unknown
Things to note:
The design drives the formula used
The standard error differs depending on the design (kind of comparison)
Sample size plays a role in SE formula and in df’s of the critical value
Level of confidence comes in with the critical value used
Estimation Summary

15. Estimation in independent samples design
Dr. Mnemonic develops a new treatment for patients with a memory disorder. He randomly assigns 8 patients to one of two samples. He then gives one sample (A) the new treatment but not the other (B) and then tests both groups with a memory test. Estimate the population difference between the two groups with 95% confidence.
If we had instead done a hypothesis test with an α = 0.05, what would you expect our conclusion to be?
- Fail to reject the H0
Independent samples t-test situation
CI(95%)= -8.73to 19.73
Confidence level 95%
-8.73
19.73
Notice that this interval includes zero
So the estimate of the population mean difference includes the possibility of zero (“no difference”)
Estimation in independent samples design

16. 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)
Note: Make sure that you label your graphs, let the reader know what your error bars are
Error bars

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

18. 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
Cummings (2012)
website
Estimation: Why?
Cummings’ introduction to Estimation

19. In labs Practice computing and interpreting confidence intervals
Understanding CI:
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)
In labs

20. 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

21. 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

22. Group Differences: 95%CI Rule of Thumb
Error bars can be informative about group differences, but you have to know what to look for
Rule of thumb for 95% CIs*:
If the overlap is about half of one one-sided error bar, the difference is significant at ~ p < .05
If the error bars just abut, the difference is significant at ~ p< .01
*works if n > 10 and error bars don’t differ by more than a factor of 2
Cumming & Finch, 2005
Error Bars: Reporting CIs