1. Reasoning in Psychology Using Statistics
2015

2. Quiz 10, due Friday May 1st. You may take it up to 10 times, your top score is what counts. Feel free to take it even after getting a 10/10, as practice for the Final exam.

3. Lab Exam 4: Conclusions from Data
Inferential Statistics: Procedures which allow us to make claims about the population based on sample data
Hypothesis testing
Correlation
Regression
Chi-squared test
Estimation
Point estimates
Confidence intervals
1-sample z test
1-sample t test
Related samples t-test
Independent samples t-test
Testing claims about populations (based on data collected from samples)
Using sample statistics to estimate the population parameters
Lab Exam 4: Conclusions from Data

4. Performing your inferential statistics
Analyze the question/problem.
The design of the research: how many groups, how many scores per person, is the population σ known, etc.
Write out what information is given
Is it asking you to test a difference, test a relationship, or make an estimate?
What is your critical value of your test statistic (z or t from table, you’ll need you’re α-level)
Now you are ready to do some computations
Write out all of the formulas that you’ll need
Then fill in the numbers as you know them
Interpret your final answer
Reject or fail to reject the null hypothesis? What does that mean?
State your confidence interval and what it means
Performing your inferential statistics

5. The design determines the test
Which test do I use?

6. Correlation within hypothesis testingX Y
Suppose that you notice that the more you study for an exam (X= hours of study), the better your exam score typically is (Y = exam score). Test if there is a significant correlation between the two variables (α = 0.05) A B C D E
Correlation
2-tailed Y X 1 2 3 4 5 6
ρ = 0
H0:
14.0
= 15.20
SSX
SP =
= 16.0
SSY
HA:
ρ ≠ 0
df = n - 2
= =3
rcrit = 0.878
Reject H0
There is a significant positive correlation between study time and exam performance
Correlation within hypothesis testing

7. The design determines the test
Which test do I use?

8. The “best fitting line” is the one that minimizes the differences (error or residuals) between the predicted scores (the line) and the actual scores (the points) Y X 1 2 3 4 5 6
Directly compute the equation for the best fitting line
Slope
Intercept
Also need a measure of error:
r2 (r-squared)
Sum of the squared residuals = SSresidual= SSerror
Standard error of estimate
Regression

9. Prediction with Bi-variate regressionX Y
Suppose that you notice that the more you study for an exam (X= hours of study), the better your exam score typically is (Y = exam score). Compute the regression equation predicting exam score with study time. A B C D E
SSY
= 16.0
Bi-variate regression
SSX
= 15.20
SP =
14.0
Hypothesis testing
on each of these Y X 1 2 3 4 5 6
r2 = 0.806
Prediction with Bi-variate regression

10. Hypothesis testing with Regression
Standard error of the estimate r2
Measures of Error
SPSS Regression output gives you a lot of stuff
Unstandardized coefficients
“(Constant)” = intercept
Variable name = slope
These t-tests test hypotheses
H0: Slope = 0
H0: Intercept (constant) = 0
Hypothesis testing with Regression

11. The design determines the test
Which test do I use?

12. Crosstabulation and χ2 When do we use these methods?
When we have categorical variables
Step 1: State the hypotheses and select an alpha level
Step 2: Compute your degrees of freedom df = (#Cols-1)*(#Rows-1) & Go to Chi-square statistic table and find the critical value
Step 3: Obtain row and column totals and calculate the expected frequencies
Step 4: compute the χ2
Step 5: Compare the computed statistic against the critical value and make a decision about your hypotheses
Crosstabulation and χ2

13. Lab Exam 4: Conclusions from Data
Inferential Statistics: Procedures which allow us to make claims about the population based on sample data
Hypothesis testing
Correlation
Regression
Chi-squared test
Estimation
Point estimates
Confidence intervals
1-sample z test
1-sample t test
Related samples t-test
Independent samples t-test
Testing claims about populations (based on data collected from samples)
Using sample statistics to estimate the population parameters
Lab Exam 4: Conclusions from Data

14. Estimation of population parameters
Describe the typical college student
Point estimates
“12 hrs”
hours of studying per week
Interval estimates
“2 to 21 hrs”
Age
“19 yrs”
“17 to 21 yrs”
hours of sleep
per night
pizza consumption
“8 hrs”
“1 per wk”
“4 to 10 hrs”
“0 to 8 per wk”
Estimation of population parameters

15. Estimation Both kinds of estimates use the same basic procedure
Finding the right test statistic (z or t)
Margin of error
You begin by making a reasonable estimation of what the z (or t) value should be for your estimate.
For a point estimation, you want what? z (or t) = 0, right in the middle
For an interval, your values will depend on how confident you want to be in your estimate
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
Estimation

16. Estimation The size of the margin of error related to: Sample size
As n decreases, the margin of error gets wider(changes the standard error)
Level of confidence
As confidence decreases (e.g., 95%-> 90%), the margin of error gets narrower (changes the critical test statistic values)
Estimation

17. Estimates with z-scores
Make an interval estimate with 95% confidence of the population mean given a sample with a X = 85, n = 25, and a population σ = 5.
or 85 ± 1.96
All centered on 85 85 87 83 89 81
86.96
83.04
Make an interval estimate with 90% confidence of the population mean given a sample with a X = 85, n = 25, and a population σ = 5.
or 85 ± 1.65
narrower
86.65
83.35
Make an interval estimate with 90% confidence of the population mean given a sample with a X = 85, n = 4, and a population σ = 5.
or 85 ± 4.13
wider
89.13
80.88
Estimates with z-scores

18. The design determines the formula that you’ll use for the estimation
Which test do I use?

19. The design determines the formula that you’ll use for the estimation
(Estimated) Standard error
One sample, σ known
One sample, σ unknown
Two related samples, σ unknown
Two independent samples, σ unknown
Estimation Summary

20. Estimates with z-scores
Make an interval estimate with 95% confidence of the population mean given a sample with a X = 85, n = 25, and a population σ = 5.
What two z-scores do 95% of the data lie between?
From the table:
So the 95% confidence interval is: to 86.96
z(1.96) =.0250
or 85 ± 1.96
95%
2.5%
Estimates with z-scores

21. 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
2.5%
95%
Estimation in one sample t-design

22. 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

23. 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