Download Hey People—It`s Not Math—It`s STATISTICS!

Hey People!—It’s Not
Math—It’s STATISTICS!
How I Teach Statistics Using as Little
Mathematics as is Possible
Who Am I?—I Am…
• Alan S. Chesen, Faculty Member
• Department of Information Systems and Supply Chain Management
• Raj Soin College of Business
• Wright State University
• Dayton, Ohio 45435
• [email protected]
Before I Start…A Question for my Audience
• The question is--Why is Wright State University in the national
news/going to be in the national news in 2016?
• Hint: September 26, 2016
• The answer is…
Why Do I Choose to Do What I Do in the Way
I Do It?
• In the workplace, my students will not “do” (will perform very few) statistical techniques.
• Students will, in their employment environments, utilize in some way, shape or form some sort of
statistical software.
• More than likely, what they will do most often is to utilize the results of statistical studies that
have been accomplished by others. To do this they will obviously need to know how to
understand and interpret these types of studies in order to apply the stated results for the benefit
of their specific organizations.
• In my classes, students must interpret statistical software outputs on the in-class tests they
complete as a part of the evaluation process.
• Also, students have to utilize the statistical software correctly as a part of the out-of-class projects
that are an additional part of the evaluation process.
• I can cover more material this way. I have time to utilize techniques other than traditional
lectures in my courses.
• I am cognizant that I must not sacrifice understanding of the material and of the underlying
statistical concepts because I have the ability to utilize the technology and non-mathematical
instructional techniques as a substitute for traditional lecture methods.
Software
• I choose to use PHStat, an enhancement to Microsoft Excel as my software
of choice.
• It is believed by many faculty in my department and college that constant
and repeated exposure to Microsoft Excel in a variety of ways is paramount
in colleges and schools of business.
• While I admit that PHStat may not be the “best” package one can use, it
serves my purposes.
• My goal is not to make my students software experts; rather it is to use a
relatively powerful yet easy to use mechanism designed to effectively teach
the discipline of statistics to them.
• I would not be averse to utilizing a more sophisticated statistical package
such as Minitab or SAS to do what I do.
Specific Examples of How I Test Students
Using Statistical Software Printouts
• Topics
• Statistical estimation (interval estimation) using confidence intervals
• Statistical decision making using hypothesis testing
Confidence Intervals
• An example problem:
• The mean time it takes for a population of office workers to complete a
certain task is to be estimated with 95% confidence. A random sample of 21
workers is selected. Their mean time is found to equal 26.7 minutes with a
standard deviation of 3.4 minutes. Find the required 95% confidence interval.
Explain its meaning in the context of the problem. Assume that the times it
takes to complete the task on the part of this population are normally
distributed.
Full Solution Using PHStat
Confidence Interval (t interval)
Data
Sample Standard Deviation
Sample Mean
Sample Size
Confidence Level
3.4
26.7
21
95%
Intermediate Calculations
Standard Error of the Mean 0.741940827
Degrees of Freedom
20
t Value
2.0860
Interval Half Width
1.5477
Confidence Interval
Interval Lower Limit
Interval Upper Limit
25.15
28.25
Solution as it is Presented to Students on a
Test
Confidence Interval (t interval)
Data
Sample Standard Deviation
Sample Mean
Sample Size
Confidence Level
3.4
26.7
21
95%
Intermediate Calculations
Standard Error of the Mean 0.741940827
Degrees of Freedom
20
t Value
2.0860
Interval Half Width
1.5477
Confidence Interval
One Sample Hypothesis Testing
• An example problem:
• A compensation analyst wishes to decide if the mean salary in a certain
profession for persons with at least 10 years of experience working in a
certain market is greater than $100,000. She selects a random sample of 17
employees. It is found that their mean salary is $107,255 with a standard
deviation of $13,415. At the 10% level of significance, is the mean salary for
this population of employees greater than $100,000? Assume that the
salaries for this population of employees are normally distributed. As a part
of your work, you must state both the null and alternative hypotheses for this
situation, state the calculated value of the test statistic for the problem, make
the proper statistical decision based upon the use of an appropriate criterion,
state that criterion, and provide an explanation of the meaning of your
decision in the context of the problem.
Full Solution Using PHStat
One Sample Hypothesis Test (t-test)
Data
Null Hypothesis
μ=
Level of Significance
Sample Size
Sample Mean
Sample Standard Deviation
100000
0.1
17
107255
13415
Intermediate Calculations
Standard Error of the Mean
3253.6154
Degrees of Freedom
16
t Test Statistic
2.2298
Upper-Tail Test
Upper Critical Value
p-Value
Reject the null hypothesis
1.3368
0.0202
Solution as it Might be Presented to Students
on a Test
One Sample Hypothesis Test (t-test)
Data
Null Hypothesis
μ=
Level of Significance
Sample Size
Sample Mean
Sample Standard Deviation
100000
0.1
17
107255
13415
Intermediate Calculations
Standard Error of the Mean
3253.6154
Degrees of Freedom
16
t Test Statistic
2.2298
Upper-Tail Test
Upper Critical Value
p-Value
0.0202
Another Possible Solution that Might be
Presented to Students on a Test
One Sample Hypothesis Test (t-test)
Data
Null Hypothesis
μ=
Level of Significance
Sample Size
Sample Mean
Sample Standard Deviation
100000
0.1
17
107255
13415
Intermediate Calculations
Standard Error of the Mean
3253.6154
Degrees of Freedom
16
t Test Statistic
2.2298
Upper-Tail Test
Upper Critical Value
p-Value
1.3368
Two Sample Hypothesis Testing
• A political analyst is interested in comparing the proportions of Republicans
and Democrats concerning their feeling about whether their party’s
candidate “won” a particular presidential debate. A random sample of 340
Republicans is chosen. A random sample of 285 Democrats is chosen. 283
Republicans believe that the Republican candidate won the debate. 205
Democrats feel that the Democratic candidate won the debate. At the 1%
level of significance, is there a difference in the proportions of Republicans
and Democrats concerning their feelings about whether their party’s
candidate “won” the debate? Also, find a 99% confidence interval for the
difference in the proportions of the party members concerning whether
their party’s candidate “won” the debate. Explain its meaning in the
context of the problem.
Full Solution Using PHStat
Two Proportion Z test
Data
Hypothesized Difference
Level of Significance
Group 1
Number of Items of Interest
Sample Size
Group 2
Number of Items of Interest
Sample Size
0
0.01
Data
283
340
205
285
Intermediate Calculations
Group 1 Proportion
0.832352941
Group 2 Proportion
0.719298246
Difference in Two Proportions
0.113054696
Average Proportion
0.7808
Z Test Statistic
3.4027
Two-Tail Test
Lower Critical Value
Upper Critical Value
p-Value
Reject the null hypothesis
Confidence Interval Estimate
of the Difference Between Two Proportions
-2.5758
2.5758
0.0007
Confidence Level
99%
Intermediate Calculations
Z Value
Std. Error of the Diff. between two
Proportions
Interval Half Width
-2.5758
0.0334
0.0862
Confidence Interval
Interval Lower Limit
Interval Upper Limit
0.0269
0.1992
Additional Information
• Again, for this and other hypothesis tests, the statement of the
statistical decision will not be shown, so that the students have to
determine the decisions using the supplied information.
• Also for this and all hypothesis testing, either the critical value(s) or
the p-value may not be shown, so that the student is forced to use
what is given to make the decisions, not calculate in order to use
what is not given.
• For the confidence intervals, the confidence limits may be eliminated,
making it necessary that students know how confidence intervals are
constructed using point estimates and margins of error.
Implications for Teaching Professionals—Food
for Thought
• For university professors:
• Decide if this method would work for you and whether or not it is a better method for you to
use than that which you use now. Or decide if parts of what I do are applicable to what you
do.
• Perhaps your decision (and mine) is based upon the kind of student you (and I) teach—the
quality of the students, the department or college in which your courses are housed, the
philosophy of your department and college, and/or the desire for consistency among those
teaching the course among other reasons as well as on your personal philosophy.
• For high school AP teachers:
• Perhaps you are limited by the AP program as to what you can do in this regard. But that’s
ok!
• Would you consider incorporating procedures such as these if you have the time after the
administration of the AP exam? Or, if you have other additional times, would you consider,
after having taught your students how to accomplish the statistical procedures you teach
them in a more mathematical way or with the use of a statistical calculator, using a statistical
software package in the manner that I do?
Thanks for Listening!
• That’s all folks!