Thoughts, Tips and Suggestions for Teaching Statistics f - PowerPoint Presentation

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 Thoughts, Tips and Suggestions for Teaching Statistics for Today's Students

David M. Levine, Baruch College

(

CUNY)

davidlevine@davidlevinestatistics.comSlide2

The First Day of ClassFirst impressions are critically important in everything you do in life.This is the most important class of the semester.

You need to set the tone to create a new impression that the course will be important to their business education.

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The Typical IntroductoryBusiness Statistics CourseOverview/orientation

Tables and Charts/Descriptive Statistics

Probability and Probability Distributions

Confidence Intervals and Hypothesis Testing

Regression

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Additions?Statistics as a way of thinking and problem-solving. Use a problem-solving framework such as DCOVA (see References 1 - 4):

D

efine

your business objective and the variables for which you want to reach conclusions

C

ollect

the data from appropriate sources

O

rganize the data collectedVisualize the data by constructing chartsAnalyze the data to reach conclusions and present those results

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Additions? continuedDescriptive AnalyticsDrilling downMultidimensional contingency tables

Slicers

Big data

Predictive Analytics

Increased emphasis on

p

-values

Regression

Logistic regression and

classification and regression trees(not possible in one-semester course)DSI Seattle WA 2015Slide6

Reductions?Reduce Probability: no more than 30 minutes to define termsReduce Probability distributions: cover only the normal distribution

Reduce Hypothesis testing: cover only basic concepts, difference between means, difference between proportions (needed in A-B testing common in online presentation systems)

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Tell A StoryEach example should tell a story Focus on an application from a functional area of business – accounting, eco/finance, management, marketing, information systems

For every story, use the DCOVA steps of Define, Collect, Organize, Visualize, and Analyze

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Tables and Charts/Descriptive StatisticsOrganizing and Visualizing Categorical DataSummary tables

Bar charts

Pie charts

Pareto diagrams

Two-way contingency tables

Multiway

contingency tables

Drilling down/Excel slicers

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Tables and Charts/Descriptive StatisticsOrganizing and Visualizing Categorical DataSummary tables

Bar charts

Pie charts

Pareto diagrams

Two-way contingency tables

Multiway

contingency tables

Drilling down/Excel slicers

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Experiment 1Web designers tested a new call to action button on its webpage. Every visitor to the webpage was randomly shown either the original call to action button (the control) or the new variation. The metric used to measure success was the download rate: the number of people who downloaded the file divided by the number of people who saw that particular call to action button. Results of the experiment yielded the following:

Variations

Downloads

Visitors

Original

Call to Action Button 351

3,642

New Call to Action Button

485 3,556

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ResultsApproximately 9.6% of the web site visitors who were shown the original call to action button downloaded the file as compared to approximately 13.6% of the web site visitors who were shown the new call to action button.

The

results were highly statistically significant showing that the download rate was higher for the new call to action button. There was 95% confidence that the actual difference in the download rate between the original and new call to action buttons was between approximately 2.5% and 5.5%.

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Experiment 2Web designers tested a new web design on its webpage. Every visitor to the webpage was randomly shown either the original web design (the control) or the new variation. The metric used to measure success was the download rate: the number of people who downloaded the file divided by the number of people who saw that particular web design. Results of the experiment yielded the following:

Variations

Downloads

Visitors

Original

web design

305

3,427New web design 353 3,751DSI Seattle WA 2015Slide13

ResultsApproximately 8.9% of the web site visitors who were shown the original web design downloaded the file as compared to approximately 9.4% of the web site visitors who were shown the new web design.

The

results showed that there was

insufficient statistical evidence

that the

download

rate was higher for the new web design.

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Experiment 3Web designers now tested two factors simultaneously – the call to action button and the new web design. Every visitor to the webpage was randomly shown one of the following:Old call to action button with old web design

New call to action button with old web design

Old call to action button with new web design

New call to action button with new web design

Again

, the metric used to measure success was the download rate: the number of people who downloaded the file divided by the number of people who saw that particular call to action button and web design. Results of the experiment yielded the following:

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Old call to action button with old web design: 8.3% downloaded the fileNew call to action button with old web design: 13.7

% downloaded the file

Old call to action button with new web

design: 9.5

% downloaded the file

New call to action button with new web

design: 17.0%

downloaded the

file

Downloads

Call to Action

Button

Web Design

Yes

No

Total

Old

Old

83

917

1,000

New

Old

137

863

1,000

Old

New

95

905

1,000NewNew170 8301,000Total 485 3,5154,000

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ResultsNotice that the results for the first three combinations of call to action button and web design were similar to the first two experiments. However, when the new call to action button was combined with the new web design, there was a multiplicative or synergistic

effect in which having both of these together resulted in an effect that was more than each effect separately. This effect

could only be discovered by simultaneously varying the two effects

and was not seen in the first two experiments when only one effect was varied at a time.

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Pedagogical PointYour analytical process worked as you added variables and determined whether unforeseen relationships were uncovered.

Drilling down with the additional factor enabled you to find uncover an unforeseen relationship on the likelihood of downloading the file that was not apparent when only one of the factor was studied.

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Excel SlicersA panel of clickable buttons that appears superimposed over a worksheet.

Each

slicer panel corresponds to one of the variables that is under

study.

Each

button in a variable’s slicer panel represents a unique value of the variable that is found in the data under study.

You

can create a slicer for any variable that has been

associated

with a PivotTable and not just the variables that you have physically inserted into a PivotTable. This allows you to work with more than three or four variables at same time in a way that avoids creating an overly complex multidimensional contingency table that would be hard to read.DSI Seattle WA 2015Slide19

Excel Slicers (continued)By clicking buttons in slicer panels you can ask questions of the data you have collected, one of the basic methods of business analytics. This contrasts to the methods of organizing data which allow you to observe data relationships but not ask about the presence or absence of specific relationships.

Because a set of slicers can give you a “heads-up” about the data you have collected, using a set of slicers mimics the function of a business analytics dashboard.

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An Excel Slicer

Count of Category

Column Labels

Row Labels

Four

Grand Total

Growth

1

1

Mid-Cap

1

1

Grand Total

1

1

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Descriptive StatisticsMeasures of Central Tendency – mean, median, modeMeasures of variation – range, variance, standard deviation, coefficient of variation,

Z

scores

Shape:

skewness

and kurtosis

Exploring data – quartiles, interquartile range, five-number summary, boxplot

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Probability and Probability DistributionsProbability – no more than 30 – 60 minutesDo an example without formulas

Define terms

Make sure students know that the smallest value is 0 and the largest value is 1

Probability distributions – cover only the normal distribution

No need to explicitly cover the binomial distribution

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Sampling Distributions and Confidence IntervalsFocus on the concept of the sampling distribution and the Central limit theorem. Show chart of what happens as sample size is increased for different populations

Develop concept of confidence interval possibly with different samples taken from a population

Cover confidence intervals and sample size determination only for mean and for proportion

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Hypothesis TestingDon’t try to cover too many different tests. The more tests you try to cover, the less that students will understand.Fundamental concepts using one sample test for the mean or the proportion to be able to develop concept of the

p

-value.

Test for difference between means

Test for difference between proportions (Z or chi-square)

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RegressionOnly simple linear regression in a one semester undergraduate courseUse software; don’t compute regression coefficients

Focus on interpretation

Residual analysis

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Logistic RegressionPredicting a categorical dependent variableCannot use least squares regression

Odds ratio

Logistic regression model

Predicting probability of an event of interest

Deviance statistic

Wald statisticSlide27

ExamplePredicting the likelihood of upgrading to a premium credit card based on the monthly purchase amount and whether the account has multiple cardsSlide28

Classification and Regression TreesDecision trees that split data into groups based on the values of independent or explanatory (X

) variables.

Not affected by the distribution of the variables

Splitting determines which values of a specific independent variable are useful in predicting the dependent (

Y

) variable present

Using a

categorical

dependent

Y variable results in a classification tree Using a numerical

dependent

Y

variable results in a

regression tree

Rules for splitting the tree

Pruning back a tree

If possible, divide data into training sample and validation sampleSlide29

ExamplePredicting the likelihood of upgrading to a premium credit card based on the monthly purchase amount and whether the account has multiple cards” (same example used

in

logistic regression)Slide30

ExamplePredicting sales of energy bars based on price and promotion expenses” (could use same example as in multiple regression)Slide31

ReferencesBerenson, M. L., D. M. Levine, and K. A.

Szabat

,

Basic Business Statistics 13

th

Ed., (Boston, MA.: Pearson Education, 2015)

Levine

, D. M. and D. F. Stephan, “Teaching Introductory Business Statistics Using the DCOVA Framework”,

Decision Sciences Journal of Innovative Education, Vol. 9, September 2011, pp. 393-397Levine, D. M., D. F. Stephan, and K.A. Szabat,

Statistics for Managers Using Microsoft Excel

, 8

th

Ed., (Boston, MA.: Pearson Education, 2017)

Levine

, D. M.,

K. A.

Szabat

, and D

. F.

Stephan,

Business

Statistics: A First Course

,

7

th

Ed.,

(Boston, MA.: Pearson Education, 2016)

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