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2. Screen Stage Social Sciences 100 Lecturer’s desk broken desk
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Projection Booth

3. MGMT 276: Statistical Inference in Management Fall, 2014
Welcome
Green sheets

4. Exam 2 –
Thanks for your patience and cooperation
The grades are posted on D2L

5. Reminder A note on doodling
Talking or whispering to your neighbor can be a problem for us – please consider writing short notes.

7. Schedule of readings Before our next exam (November 6th)
Lind (10 – 12)
Chapter 10: One sample Tests of Hypothesis
Chapter 11: Two sample Tests of Hypothesis
Chapter 12: Analysis of Variance
Plous (2, 3, & 4)
Chapter 2: Cognitive Dissonance
Chapter 3: Memory and Hindsight Bias
Chapter 4: Context Dependence

8. Homework
On class website:
Please print and complete homework worksheets
Assignment 14: Hypothesis Testing using t-tests
Due: Thursday, October 30th
Assignments 15 & 16: Hypothesis Testing using t-tests
Due: Tuesday, November 4th

9. By the end of lecture today 10/28/14
Use this as your
study guide
By the end of lecture today 10/28/14
Logic of hypothesis testing
Steps for hypothesis testing
Levels of significance (Levels of alpha)
what does p < 0.05 mean?
what does p < 0.01 mean?
t-tests

10. Who is taller men or women?
Type I or type II error? .
Independent
Variable?
Gender
Dependent Variable?
Height
IV:
Nominal
IV: Nominal Ordinal Interval or Ratio?
Who is taller men or women?
DV: Nominal Ordinal Interval or Ratio?
DV:
Ratio
IV: Continuous or discrete?
IV:
Discrete
What would null hypothesis be?
DV: Continuous or discrete?
DV: Continuous
No difference in the height between men and women
Section 2 only - Section 1
completed this last week

11. Who is taller men or women?.
Type I or type II error?
Two –tailed
One-tailed Or
Two –tailed?
Between
Between
Or within?
Who is taller men or women?
Quasi
Quasi or True?
What would null hypothesis be?
No difference in the height between men and women
Section 2 only - Section 1
completed this last week

12. Who is taller men or women?
Type I or type II error? .
Who is taller men or women?
What would null hypothesis be?
No difference in the height between men and women
Type I
Error
Type I error: Rejecting a true null hypothesis
Saying that there is a difference in height when in fact there is not (false alarm)
Type II error: Not rejecting a false null hypothesis
Type II
Error
Saying there is no difference in height when
in fact there is a difference (miss)
This is an example of a _____.
a. correlation
b. t-test
c. one-way ANOVA
d. two-way ANOVA
t-test
Section 2 only - Section 1
completed this last week

13. Type I or type II error? .
Curly versus straight hair – which is more “dateable”?
What would null hypothesis be?
No difference in the dateability between curly and straight hair
Type I error: Rejecting a true null hypothesis
Saying that there is a difference in dateability when in fact there is not (false alarm)
Type II error: Not rejecting a false null hypothesis
Saying there is no difference in dateability when
in fact there is a difference (miss)
This is an example of a _____.
a. correlation
b. t-test
c. one-way ANOVA
d. two-way ANOVA
t-test
Section 2 only - Section 1
completed this last week

14. Writing Assignment
Please watch this video describing a series of t-tests
What is the independent variable?
How many different dependent variables did they use?
(They would conduct a different t-test
for every dependent variable)
Section 2 only - Section 1
completed this last week

15. Writing Assignment Worksheet
Design two t-tests
Section 2 only - Section 1
completed this last week

16. 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)?
One or two tailed test?
Balance between Type I versus Type II error
Critical statistic (e.g. z or t or F or r) 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

17. We lose one degree of freedom for every parameter we estimate
Degrees of Freedom
Degrees of Freedom (d.f.) is a parameter based on the sample size that is used to determine the value of the t statistic.
Degrees of freedom tell how many observations are used to calculate s, less the number of intermediate estimates used in the calculation.

18. Hypothesis testing: one sample t-test
Let’s jump right in
and do a t-test
Hypothesis testing: one sample t-test
Is the mean of my observed sample consistent with the known population mean or did it come from some other distribution?
We are given the following problem:
800 students took a chemistry exam. Accidentally, 25 students got an additional ten minutes. Did this extra time make a significant difference in the scores? The average number correct by the large class was 74.
The scores for the sample of 25 was
Please note:
In this example we are comparing our sample mean with the population mean
(One-sample t-test)
76, 72, 78, 80, 73
70, 81, 75, 79, 76
77, 79, 81, 74, 62
95, 81, 69, 84, 76
75, 77, 74, 72, 75

19. µ = 74 µ Hypothesis testing
Step 1: Identify the research problem / hypothesis
Did the extra time given to this sample of students affect
their chemistry test scores
Describe the null and alternative hypotheses
One tail or two tail test?
Ho:
µ = 74
= 74
H1:

20. Hypothesis testing n = 25 Step 2: Decision rule = .05
Degrees of freedom (df) = (n - 1)
= (25 - 1) = 24
two tail test

21. two tail test
α= .05
(df) = 24
Critical t(24)
= 2.064

22. µ = 74 Hypothesis testing = = 868.16 = 6.01 24 x (x - x) (x - x)276 72 78 80 73 70 81 75 79 77 74 62 95 69 84
76 – 76.44
72 – 76.44
78 – 76.44
80 – 76.44
73 – 76.44
70 – 76.44
81 – 76.44
75 – 76.44
79 – 76.44
77 – 76.44
74 – 76.44
62 – 76.44
95 – 76.44
69 – 76.44
84 – 76.44
= -0.44 = = = = = = = = = = = = = = =
0.1936
2.4336
2.0736
6.5536
0.3136
5.9536
Step 3: Calculations
µ = 74 Σx = N
1911 25 =
= 76.44
N = 25
= 6.01
868.16 24
Σx = 1911
Σ(x- x) = 0
Σ(x- x)2 =

23. µ = 74 Hypothesis testing = 76.44 - 74 1.20 2.03 .
Step 3: Calculations
µ = 74
= 76.44
N = 25
s = 6.01 =
1.20
2.03
critical t
6.01 25
Observed t(24) = 2.03

24. Hypothesis testing
Step 4: Make decision whether or not to reject null hypothesis
Observed t(24) = 2.03
Critical t(24) = 2.064
2.03 is not farther out on the curve than 2.064,
so, we do not reject the null hypothesis
Step 6: Conclusion: The extra time did not have a significant
effect on the scores

25. Hypothesis testing:
Did the extra time given to these 25 students affect their average test score?
Start summary with two means (based on DV) for two levels of the IV
notice we are comparing a sample mean with a population mean:
single sample t-test
Finish with statistical summary t(24) = 2.03; ns
Describe type of test (t-test versus z-test) with brief overview of results
Or if it had been different results that *were* significant: t(24) = -5.71; p < 0.05
The mean score for those students who where given extra time
was percent correct, while the mean score for the rest of
the class was only 74 percent correct. A t-test was completed
and there appears to be no significant difference in the test scores
for these two groups t(24) = 2.03; n.s.
Type of test with degrees of freedom
n.s. = “not significant”
p<0.05 = “significant”
n.s. = “not significant”
p<0.05 = “significant”
Value of observed statistic 25

26. What if we had chosen a one-tail test?
Step 1: Identify the research problem
Did the extra time given to this sample of students increase
their chemistry test scores
Prediction is uni-directional
Describe the null and alternative hypotheses
One tail or two tail test?
Prediction is uni-directional
Ho:
µ ≤ 74
µ > 74
H1:
Step 2: Decision rule
α= .05
Degrees of freedom (df) = (n - 1)
= (25 - 1) = 24
α is all at one end so “critical t” changes
Critical t (24) =
?????

27. one tail test
α= .05
(df) = 24
Critical t(24)
= 1.711

28. What if we had chosen a one-tail test?
Step 1: Identify the research problem
Did the extra time given to this sample of students increase
their chemistry test scores
Describe the null and alternative hypotheses
One tail or two tail test?
Ho:
µ ≤ 74
µ > 74
H1:
Step 2: Decision rule
= .05
Degrees of freedom (df) = (n - 1)
= (25 - 1) = 24
Critical t (24) =
1.711

29. Calculations (exactly same as two-tail test)
(x - x)
(x - x)2 76 72 78 80 73 70 81 75 79 77 74 62 95 69 84
76 – 76.44
72 – 76.44
78 – 76.44
80 – 76.44
73 – 76.44
70 – 76.44
81 – 76.44
75 – 76.44
79 – 76.44
77 – 76.44
74 – 76.44
62 – 76.44
95 – 76.44
69 – 76.44
84 – 76.44
= -0.44 = = = = = = = = = = = = = = =
0.1936
2.4336
2.0736
6.5536
0.3136
5.9536
Step 3: Calculations
µ = 74 Σx = N
1911 25 =
= 76.44
N = 25
= 6.01
868.16 24
Σx = 1911
Σ(x- x) = 0
One-tailed test
has no effect on calculations stage
Σ(x- x)2 =

30. Calculations (exactly same as two-tail test).
One-tailed test
has no effect on calculations stage
Calculations (exactly same as two-tail test)
Step 3: Calculations
µ = 74
= 76.44
N = 25
s = 6.01 =
1.20
2.03
critical t
6.01 25
Observed t(24) = 2.03

31. µ = 74 Hypothesis testing t(24) = 2.03 Step 3: Calculations N = 25
µ = 74
N = 25
t(24) = 2.03
= 76.44
s = 6.01
Step 4: Make decision whether or not to reject null hypothesis
Observed t(24) = 2.03
Critical t(24) = 1.711
2.0 is farther out on the curve than 1.711,
so, we do reject the null hypothesis
Step 5: Conclusion: The extra time did have a significant
effect on the scores

32. Hypothesis testing:
Did the extra time given to these 25 students affect their average test score?
Start summary with two means (based on DV) for two levels of the IV
notice we are comparing a sample mean with a population mean:
single sample t-test
Finish with statistical summary t(24) = 2.03; ns
Describe type of test (t-test versus z-test) with brief overview of results
Or if it had been different results that *were* significant: t(24) = -5.71; p < 0.05
The mean score for those students who where given extra time
was percent correct, while the mean score for the rest of
the class was only 74 percent correct. A one-tailed t-test was
completed and there appears to be significant difference in the
test scores for these two groups t(24) = 2.03; p < 0.05.
Type of test with degrees of freedom
n.s. = “not significant”
p<0.05 = “significant”
n.s. = “not significant”
p<0.05 = “significant”
Value of observed statistic 32

33. A note on z scores, and t score: . .
A note on z scores, and t score:
Numerator is always distance between means
(how far away the distributions are or “effect size”)
Denominator is always measure of variability
(how wide or much overlap there is between distributions)
Difference between means
Difference between means
Variability of curve(s) (within group variability)
Variability of curve(s)

34. Thank you!
See you next time!!