1. Statistical Significance
If a particular difference is large enough to be unlikely to have occurred because of chance or sampling error, then the difference is statistically significance.

2. Statistical Significance
The basic motive for making statistical inferences is to be able to generalize from sample results to population characteristics.
Three different concepts can be applied to the notion of differences:
Mathematical Differences
Statistical Significance
Managerially Important Differences

3. One last thing
When you are performing tests on the data you might not find the results to be statistically significant. That is okay- you don’t have to keep testing.
What does this tell you? If there is no difference between males and females or freshman, sophomore, junior or seniors.

4. Hypotheses Testing Hypotheses
Assumptions or theories that a researcher or manager makes about some characteristic of the population under study.
In other words, it is an “educated guess!”

5. Hypothesis Testing
Null Hypothesis (Ho). States that there is no difference between groups.
Alternative Hypothesis (Ha). States that there is a difference between groups.
Typically, you will state the alternative hypothesis when you write your hypothesis statement.
Sometimes (but rarely) you might write a null hypothesis if that is what you are looking for:
(Example) H1: There is no difference with perceived exit barriers in regards to customer grudge-holding after a service failure.
But, you ALWAYS test the alternative hypothesis.

6. Steps in Hypothesis Testing
Hypotheses Testing: This is how your results section in the quantitative part of the Project Should Look
Steps in Hypothesis Testing
1. Specify the hypothesis.
2. Select an appropriate statistical technique to test the hypothesis.
3. Specify a decision rule as the basis for determining whether to
reject or fail to reject the null hypothesis.
4. Calculate the value of the test statistic and perform the test.
5. State your conclusion from the perspective of the original
research problem or question.

7. This is important, so let’s repeat it!

8. Other Issues in Hypothesis Testing
Types of errors in hypothesis testing.
Type I error
Type II error
Rejection of a null hypothesis when, in fact, it is true
Acceptance of a null hypothesis when, in fact, it is false

9. Example for project
Hypothesis 1: People are more likely to go to bars if there are drink specials.
Using one sample t-test we found our hypothesis to be true, people are more likely to go to bars if there is a drink special (mean = 5.83, standard deviation =1.609, t = -6.37, degrees of freedom = 76, significance < .001).
We believe this is because most of the people going to bars are of college age and are on a budget.
Hypothesis 6: Age does not have an effect on how important food, music, and drink specials are to a customer.
Using an ANOVA test with alpha = .05 we found no significant difference between age and the importance of food, music and drink specials to customers.
We believe that while ages vary, mostly everyone we surveyed is in college. Therefore, they have the same bar going preferences.

10. The Following Slides are Instructions on Using SPSS To Analyze Data:
They Look at:
One-Sample T-Test
Independent (Two) Samples T-Test
One-Way ANOVA
With a Post-Hoc Tukey Test

11. One-Sample T-Test
Used to test the whole sample in regards to a single construct.
Example: Using a 1-7 scale with 1=strongly disagree and 7=strongly agree, how many people prefer premium ice cream?
Significance is at .05 or less

12. One Sample T-Test

13. One Sample T-Test 4) Click “OK” 1) Choose the construct from here
3) Create the test value (should be the median on your scale items)
2) Click the arrow

14. One Sample T-Test

15. One Sample T-Test
We found that people prefer premium ice Cream (mean=5.2, sd=1.5, t=5.190(df=39), p<.001).

16. Displaying Multiple One-Sample T-Tests (Chart)
Sales Support
Mean
Standard Deviation T P
Calls on me often
9.33
1.24
52.414
<.001
Understands my business
9.30
1.15
57.525
Is knowledgeable about products
9.55
0.88
80.044
Keeps me well supplied
9.36
1.11
60.590

17. Displaying One Sample T-Test (Graph)

18. Independent Samples T-Test
Used to determine if two groups differ on a characteristic or variable that is assessed using a continuous measure.
The continuous measure in question is the construct that you created.
…Or some open ended question that would lead to a continuous measure, such as income or age.
Example, Using a 1-7 scale with 1= strongly disagree and 7=strongly agree, we test if students like premium ice cream more so than non-students?

19. Independent Samples T-Test

20. Independent Samples T-Test

21. Independent Samples T-Test

22. Independent Samples T-Test

23. Independent Samples T-Test
Group Statistics 20
5.7500
.51299
.11471
4.6500
.41770
Are you a student?
yes no
premium ic construct N
Mean
Std. Deviation
Std. Error
Independent Samples Test
74.128
.000
2.539 38
.015
1.1000
.43316
.22310
21.850
.019
.20131
Equal variances
assumed
not assumed
premium ic construct F
Sig.
Levene's Test for
Equality of Variances t df
Sig. (2-tailed)
Mean
Difference
Std. Error
Lower
Upper
95% Confidence
Interval of the
t-test for Equality of Means

24. Independent Samples- T-test
If the significance level in the Levene’s Test for Equality of Variances is significant at .05 or less- use Equal Variances not assumed.
If the significance level in the Levene’s Test for Equality of Variances is NOT significant at .05 or more- use Equal Variances assumed.
Higher-top Lower-bottom

25. Independent Samples T-Test
Using an independent samples t-test with α = .05, we found that students like ice cream more than non-students. The results are found in table 1.
Table 1: mean score to the question, “do you like ice cream?”
Mean
S.D. T
Sig
Student
5.75
0.51
Non-Student
4.65
1.87
2.539
.019

26. Independent Samples T-Test: Graph Example
Difference is significant with t = 2.539, p = .019

27. Analysis of Variance (ANOVA)
Used to test one or more categorical variables (with two or more groups within that variable) with a continuous dependent variable (or construct).
If your categorical variable has only two categories (student / non-student) your ANOVA test statistic (F-statistic) will be the same as squaring your t-statistic from the independent samples t-test (t2).
So the p-value (sig.) will be exactly the same.

28. Analysis of Variance (ANOVA)
One advantage of the ANOVA is that it can test a categorical variable even if that variable has more than two categories.
Example: student status (freshman, sophomore, junior, senior).

29. Analysis of Variance (ANOVA) Running Post Hoc Tests
If the variable you are testing has more than one category, and the ANOVA is significant, this tells you that there is a difference between the groups, but does not tell where that difference is.
So…I will expect you to run a post-hoc test.
In this case you will run the Tukey test.

30. Analysis of Variance (ANOVA) Running Post Hoc Tests
Purpose of the Tukey test:
To look for the differences between the individual groups.
In other words, the ANOVA will show that there is a difference between freshman, sophomores, juniors, and seniors in regards to specialty ice cream. But you won’t know where any differences are.
The Tukey test shows you where those differences are.

31. Analysis of Variance (ANOVA)

32. Analysis of Variance (ANOVA)

33. Analysis of Variance (ANOVA)
Then hit “OK” when you get back to the ANOVA screen.

34. Analysis of Variance (ANOVA)

35. Analysis of Variance (ANOVA)
Notice that the ANOVA test is significant (f=4.871, p=.006). That means there is a difference between years in school and ice cream preference.
The means can give you a good idea where that difference is.
But now you want to run the Tukey test to determine exactly where that difference is.

36. Analysis of Variance (ANOVA)
Go through the same steps previously mentioned to run the ANOVA. This time click “Post Hoc.”

37. Analysis of Variance (ANOVA)

38. Analysis of Variance (ANOVA)
Click “OK” on the next screen

39. Analysis of Variance (ANOVA)
Multiple Comparisons
Dependent Variable: premium ic construct
Tukey HSD
.0000
.68615
1.000
1.8480 *
.59423
.042
-.0425
.61051
.057
.0371
1.6429
.0425
3.2432
.0357
.50499
1.3958
1.6071
-.0371
3.2514
-.0357
1.3244
(J) Year in school
sophomore
junior
senior
freshman
(I) Year in school
Mean
Difference
(I-J)
Std. Error
Sig.
Lower Bound
Upper Bound
95% Confidence Interval
The mean difference is significant at the .05 level. *.

40. Analysis of Variance (ANOVA)
Using ANOVA we found that there is a difference between class standing and whether or not a person prefers premium ice cream.
Class
Mean
S.D. F
Sig
Freshman
4.14
2.14
Sophomore
Junior
5.78
.41
Senior
5.75
.44
4.871
.006

41. Analysis of Variance (ANOVA)
Upon further analysis, using a Tukey test at α =.05, we found that juniors liked premium ice cream more than freshmen and sophomores.
You can stop with the above statement or you can also draw a graph showing the same thing.

42. ANOVA: Graph Example Overall ANOVA F=4.871, P=.006
Tukey Post-Hoc Test for Individual Differences (Significant Differences Shown):
Freshman and Junior p= Sophomore and Junior p=.042