1. Introduction to Statistics for the Social Sciences SBS200 - Lecture Section 001, Fall 2016 Room 150 Harvill Building 10: :50 Mondays, Wednesdays & Fridays.
Welcome

3. Homework Assignments Homework Assignment #20 Hypothesis testing
Comparing Two means
(Two samples)
Due Monday November 7th

4. Before next exam (November 18th)
Please read chapters in OpenStax textbook
Please read Chapters 2, 3, and 4 in Plous
Chapter 2: Cognitive Dissonance
Chapter 3: Memory and Hindsight Bias
Chapter 4: Context Dependence

5. Lab sessions Everyone will want to be enrolled
in one of the lab sessions
Labs continue
Next week
Project 3 due &
Start Project 4

7. This lab builds on the work we did in our very first lab
This lab builds on the work we did in our very first lab. But now we are using the correlation for prediction. This is called regression analysis

9. Five steps to hypothesis testing
Step 1: Identify the research problem (hypothesis)
Describe the null and alternative hypotheses
Step 2: Decision rule
Alpha level? (α = .05 or .01)?
Critical statistic (e.g. z or t) value?
Step 3: Calculations
Step 4: Make decision whether or not to reject null hypothesis
If observed z (or t) is bigger then critical z (or t) then
reject null
Step 5: Conclusion - tie findings back in to research problem

10. Hypothesis testing with t-tests
The result is “statistically significant” if:
the observed statistic is larger than the critical statistic
observed stat > critical stat If we want to reject the null, we want our t (or z or r or F or x2) to be big!!
the p value is less than 0.05 (which is our alpha)
p < If we want to reject the null, we want our “p” to be small!!
we reject the null hypothesis
then we have support for our alternative hypothesis

11. Independent samples t-test
Are the two means significantly different from each other, or is the difference just due to chance?
Independent samples t-test
Donald is a consultant and leads training sessions. As part of his training sessions, he provides the students with breakfast. He has noticed that when he provides a full breakfast people seem to learn better than when he provides just a small meal (donuts and muffins). So, he put his hunch to the test. He had two classes, both with three people enrolled. The one group was given a big meal and the other group was given only a small meal. He then compared their test performance at the end of the day. Please test with an alpha = .05
Big Meal 22 25
Small meal 19 23 21
Mean= 21
Mean= 24
x1 – x2
t =
24 – 21
variability
t =
Got to figure this part out: We want to average the variance from 2 samples - Call it “pooled”
variability 11

12. α = .05 Independent samples t-test
Step 1: Identify the research problem
Did the size of the meal affect the learning / test scores?
Step 2: Describe the null and alternative hypotheses
Step 3: Decision rule
α = .05
Two tailed test
n1 = 3; n2 = 3
Degrees of freedom total (df total) = (n1 - 1) + (n2 – 1)
Critical t(4)
= 2.776
= (3 - 1) + (3 – 1) = 4 12

13. α = .05 Independent samples t-test
Step 1: Identify the research problem
Did the size of the meal affect the learning / test scores?
Step 2: Describe the null and alternative hypotheses
Step 3: Decision rule
α = .05
Two tailed test
n1 = 3; n2 = 3
Degrees of freedom total (df total) = (n1 - 1) + (n2 – 1)
Critical t(4)
= 2.776
= (3 - 1) + (3 – 1) = 4
Step 4: Calculate observed t score 13

14. Notice: Simple Average = 3.5
Mean= 21
Mean= 24
Big Meal
Deviation
From mean -2 1
Small Meal
Deviation
From mean -2 2
Squared
deviation 4 1
Squared Deviation 4
Big Meal 22 25
Small meal 19 23 21
Σ = 6
Σ = 8 6 3
Notice: s2 = 3.0 1 2 1
Notice: Simple Average = 3.5 8 4
Notice: s2 = 4.0 2 2 2
S2pooled =
(n1 – 1) s12 + (n2 – 1) s22
n1 + n2 - 2
S2pooled =
(3 – 1) (3) + (3 – 1) (4)
= 3.5 14

15. S2p = 3.5
Mean= 21
Mean= 24
Big Meal
Deviation
From mean -2 1
Small Meal
Deviation
From mean -2 2
Squared
deviation 4 1
Squared Deviation 4
Participant 1 2 3
Big Meal 22 25
Small meal 19 23 21
Σ = 6
Σ = 8 =
24 – 21
1.5275
= 1.964
3.5
3.5 3 3
Observed t
Observed t =
Critical t = 2.776
1.964 is not larger than so, we do not reject the null hypothesis
t(4) = 1.964; n.s.
Conclusion: There appears to be no difference between the groups 15

16. Type of test with degrees of freedom Value of observed statistic
We compared test scores for large and small meals. The mean test
scores for the big meal was 24, and was 21 for the small meal.
A t-test was calculated and there appears to be no significant
difference in test scores between the two types of meals,
t(4) = 1.964; n.s.
Type of test with degrees of freedom
n.s. = “not significant”
p<0.05 = “significant”
Value of observed statistic
Start summary with two means (based on DV) for two levels of the IV
Finish with statistical summary t(4) = 1.96; ns
Describe type of test (t-test versus anova) with brief overview of results
Or if it *were* significant:
t(9) = 3.93; p < 0.05 16

17. Homework Assignment
Using Excel ?

18. Homework Assignment
Using Excel

19. Complete a t-test Mean= 21 Mean= 24 Participant 1 2 3 Big Meal 22 25
Small meal 19 23 21 19

20. Complete a t-test Mean= 21 Mean= 24 Participant 1 2 3 Big Meal 22 25
Small meal 19 23 21 20

21. Complete a t-test Mean= 21 Mean= 24 Participant 1 2 3 Big Meal 22 25
Small meal 19 23 21
If checked you’ll want to include the labels in your variable range
If checked, you’ll want to include the labels in your variable range
If checked you’ll want to include the labels in your variable range 21

22. Complete a t-test
Finding Means
Finding Means 22

23. Complete a t-test This is variance for each sample
(Remember, variance is just standard deviation squared)
Please note:
“Pooled variance” is just like the average of the two sample variances, so notice that the average of 3 and 4 is 3.5 23

24. Complete a t-test This is “n” for each sample
(Remember, “n” is just number of observations for each sample)
This is “n” for each sample
(Remember, “n” is just number of observations for each sample)
Remember, “degrees of freedom” is just (n-1) for each sample.
So for sample 1: n-1 =3-1 = 2
And for sample 2: n-1=2-1 = 2
Then, df = 2+2=4
df = “degrees of freedom” 24

25. Finding degrees of freedom
Complete a t-test
Finding degrees of freedom 25

26. Complete a t-test
Finding Observed t 26

27. Complete a t-test
Finding Critical t 27

28. Finding Critical t 28

29. Finding p value (Is it less than .05?)
Complete a t-test
Finding p value (Is it less than .05?) 29

30. Step 4: Make decision whether or not to reject null hypothesis
Complete a t-test
Step 4: Make decision whether or not to reject null hypothesis
Reject when:
observed stat > critical stat
is not bigger than 2.776
“p” is less than 0.05 (or whatever alpha is)
p = is not less than 0.05
Step 5: Conclusion - tie findings back in to research problem
There was no significant difference, there is no
evidence that size of meal affected test scores 30

31. Type of test with degrees of freedom Value of observed statistic
We compared test scores for large and small meals. The mean test
scores for the big meal was 24, and was 21 for the small meal.
A t-test was calculated and there appears to be no significant
difference in test scores between the two types of meals,
t(4) = 1.964; n.s.
Type of test with degrees of freedom
n.s. = “not significant”
p<0.05 = “significant”
Value of observed statistic
Start summary with two means (based on DV) for two levels of the IV
Finish with statistical summary t(4) = 1.96; ns
Describe type of test (t-test versus Anova) with brief overview of results
Or if it *were* significant:
t(9) = 3.93; p < 0.05 31

32. Graphing your
t-test results 32

33. Graphing your
t-test results 33

34. Graphing your
t-test results
Chart Layout 34

35. Fill out titles 35

36. Thank you!
See you next time!!