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Please upload demonstrate in one file in Assignments for Week 10 Use the print screen or snipping tool to show your output.

USING THE

AFC CASE AND DATA SET

RECREATE THE INDEPENDENT SAMPLES T-TEST FOR THE FOLLOWING RESEARCH QUESTIONS.

RQ: Are men or women more likely to recommend the center?

H0 = There is no difference between men and women in their likelihood to recommend the center
H1 = There is a difference between men and women in their likelihood to recommend the center

RQ: Do men or women go to the AFC more?

H0 = There is no difference between men and women in their visits to the center
H1 = There is a difference between men and women in their visits to the center

USING THE AFC CASE AND DATA SET RECREATE THE ONE-WAY ANOVA FOR THE FOLLOWING RESEARCH QUESTIONS.

What is the impact of consumer income on how much members spend at the club?

Ho There is no relationships between member income and how much they spend at AFC.
HA There is a relationship between member income and how much they spend at AFC.

USING THE

WEB DESIGN CASE AND DATA SET

RECREATE THE ONE-WAY ANOVA AND POST HOC FOR THE FOLLOWING RESEARCH QUESTIONS.

Colleen is the marketing manager for Virtually Viral, an entertainment company that collects viral videos from around the Internet and aggregates them on their website. Whether it’s videos of cats or unusual marriage proposals, Virtually Viral collects them all. Almost all of Virtually Viral’s revenue comes from clicks on advertisements surrounding the videos. To maximize profits, Colleen tries to match ad content to video content. For example, for the ‘Wacky Weddings’ section of the website, most advertisements link to wedding planners and invitation/paper product suppliers.
As part of this effort, Colleen contracted a web design firm to put together a new look for the website, with the goal of improving the amount of time visitors spend on the website. They produced four different versions, each arranging the videos and advertisements differently. Colleen is unsure which of these designs would result in the greatest amount of time spent on the site.
To solve this problem, Colleen designs an experiment. She sets up a system to randomly assign visitors to the website to experience one of the four designs, recording the number of seconds that they spend on the site. She wants to compare the groups with each other and see if the different designs result in different lengths of time viewing the website. Whichever results in the longest visits will become the new design for the site in general.
She knows from her market research class that she has a research question and that this calls for some type of hypothesis testing. She learned that treating groups differently and comparing them means that she has independent data. But the independent-samples t-test only compares two groups with each other and she has four. How can she determine which she should run — multiple independent-samples t-tests? Or is there a better way?

Decision Problem: What web design should Colleen choose for her company?

Research Question: Which web design performs best?

Ho There is no difference in web design performance.
HA There is a difference in web design performance.

PART 2: NIKE CASE

In a pretest, data on Nike were obtained from 45 respondents. These data are given in the SPSS file on the course site, which gives the usage, sex, awareness, attitude, preference, intention, and loyalty toward Nike of a sample of Nike users. Usage has been coded as 1, 2, or 3, representing light, medium, or heavy users. The sex has been coded as 1 for females and 2 for males. Awareness, attitude, preference, intention, and loyalty are measured on 7-point Likert-type scales (1 = very unfavorable, 7 = very favorable). Note that five respondents have missing values that are denoted by 9.

The Nike SPSS data file is posted—nike.sav

Using the appropriate hypothesis test utilizing SPSS for the statistical procedure, answer the research questions. 1st state the null hypothesis and the alternative. Calculate the appropriate statistic. State whether you can reject or accept the null hypothesis and why. Interpret the result.Research Questions

1. Is there a difference by gender in awareness, attitude, preference, intention, and loyalty toward Nike among a sample of Nike users?

2. Is there is a difference in awareness, attitude, preference, intention, and loyalty among a sample of Nike users by Nike usage levels (heavy, medium and light)

outputViewer0000000000.xml
输出 Log

FREQUENCIES VARIABLES=rrecom
/PIECHART PERCENT
/ORDER=ANALYSIS.

00000000011_lightNotesData.bin

00000000012_lightTableData.bin

00000000013_lightTableData.bin

00000000014__chartData.bin

00000000014__chart.xml

loyalty

outputViewer0000000001_heading.xml
输出 Frequencies Title

Frequencies Notes 00000000011_lightNotesData.bin Statistics 00000000012_lightTableData.bin loyalty 00000000013_lightTableData.bin Pie Chart 00000000014__chartData.bin 00000000014__chart.xml

outputViewer0000000002.xml
输出 Log

CROSSTABS
  /TABLES=weight classes circuit station pool BY doctor
  /FORMAT=AVALUE TABLES
  /STATISTICS=PHI
  /CELLS=COUNT COLUMN
  /COUNT ROUND CELL.

00000000031_lightNotesData.bin

00000000032_lightTableData.bin

000000000331_lightTableData.bin

000000000332_lightTableData.bin

000000000341_lightTableData.bin

000000000342_lightTableData.bin

000000000351_lightTableData.bin

000000000352_lightTableData.bin

000000000361_lightTableData.bin

000000000362_lightTableData.bin

000000000371_lightTableData.bin

000000000372_lightTableData.bin

outputViewer0000000003_heading.xml
输出 Crosstabs Title

Crosstabs Notes 00000000031_lightNotesData.bin Case Processing Summary 00000000032_lightTableData.bin Utilized weight training? * Doctor recommendation? Title

Utilized weight training? * Doctor recommendation? Crosstab 000000000331_lightTableData.bin Symmetric Measures 000000000332_lightTableData.bin Utilized classes? * Doctor recommendation? Title

Utilized classes? * Doctor recommendation? Crosstab 000000000341_lightTableData.bin Symmetric Measures 000000000342_lightTableData.bin Utilized exercise circuit? * Doctor recommendation? Title

Utilized exercise circuit? * Doctor recommendation? Crosstab 000000000351_lightTableData.bin Symmetric Measures 000000000352_lightTableData.bin Utilized circulation station? * Doctor recommendation? Title

Utilized circulation station? * Doctor recommendation? Crosstab 000000000361_lightTableData.bin Symmetric Measures 000000000362_lightTableData.bin Utilized therapy pool? * Doctor recommendation? Title

Utilized therapy pool? * Doctor recommendation? Crosstab 000000000371_lightTableData.bin Symmetric Measures 000000000372_lightTableData.bin

outputViewer0000000004.xml
输出 Log

GET
FILE=’C:\Users\amuns\OneDrive\Spring 2021\NYU\Nike(1)(1).sav’.
DATASET NAME DataSet11 WINDOW=FRONT.
DATASET ACTIVATE DataSet1.
DATASET CLOSE DataSet11.

outputViewer0000000005.xml
输出 Log

FREQUENCIES VARIABLES=rrecom
/PIECHART PERCENT
/ORDER=ANALYSIS.

00000000061_lightNotesData.bin

00000000063_lightTableData.bin

00000000064_lightTableData.bin

00000000065__chartData.bin

00000000065__chart.xml

loyalty

outputViewer0000000006_heading.xml
输出 Frequencies Title

Frequencies Notes 00000000061_lightNotesData.bin Active Dataset

[DataSet1] Statistics 00000000063_lightTableData.bin loyalty 00000000064_lightTableData.bin Pie Chart 00000000065__chartData.bin 00000000065__chart.xml

META-INF/MANIFEST.MF
allowPivoting=true

Review of Demonstrate Material from Week 9

Please view the output file for SPSS. This is the .spv files (open with SPSS) to see the solution for each Demonstrate activity. You can find these in the Week 6 folder.

Select TRANSFORM.
Click on RECODE and select INTO DIFFERENT VARIABLES…
Click on recom and move it to NUMERIC VARIABLE OUTPUT VARIABLE box.
Type “rrecom” in OUTPUT VARIABLE NAME box.
Type “loyalty” in OUTPUT VARIABLE LABEL box.
Click OLD AND NEW VAULES box.
Under OLD VALUES on the left, click RANGE. Type 0 and 6 in the range boxes. Under NEW VALUES on the right, click VALUE and type 1 in the value box. Click ADD.
Video Recoding Variables with SPSS

Recode the Likelihood To Recommend variable in the Avery Fitness Data Set. Create a pie chart of the distribution of the recoded variable showing the percent loyal and not loyal. Use the snipping tool or print screen to show the image on a Word Document. Recode one other quantitative variable in the data set of your choice to a dichotomous variable (two categories). Create a pie charts showing the distribution of the newly recoded variable.
Please upload demonstrate in one file in Assignments for Week 9. Use the print screen or snipping tool to show your output.
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SPSS: Recoding Likelihood To Recommend
Under OLD VALUES on the left, click RANGE. Type 7 and 10 in the range boxes. Under NEW VALUES on the right, click VALUE and type 2 in the value box. Click ADD.
Click CONTINUE.
Click CHANGE.
Click OK.
Depending on the SPSS version, you must then go to the data view to create value labels for the recoded variable.
For the new variable rrecom code 1 can be labeled “not loyal” and code 2 can be labeled “loyal” as your recoding put lower ratings 0-6 in code 1 and higher ratings 7-10 in code 2. To understand how to edit your data file to create a data labels for this newly created variable see this video. The likelihood to recommend variable in research is a variable to understand customer loyalty.
Creating Data Labels with SPSS

Please upload demonstrate in one file in Assignments for Week 9. Use the print screen or snipping tool to show your output.
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Please watch the video on the course site to learn how to calculate Descriptive Statistics using Excel. The video is posted below as well. The spreadsheet with data is on the course site. Using the video as a guide, add the formulas and calculate the descriptive statistics using EXCEL. Recreate the spreadsheet as described in the video and show a print screen or use the snipping tool to show your work.
Descriptive Statistics with Excel

http://link.brightcove.com/services/player/bcpid790261335001?bckey=AQ~~,AAAAPmbRRLk~,C5G7jhYNtifB7aWTdZf87KOT82XYugjP&bctid=2277365305001

Please upload demonstrate in one file in Assignments for Week 9. Use the print screen or snipping tool to show your output.

Please upload demonstrate in one file in Assignments for Week 9. Use the print screen or snipping tool to show your output.
Ho: There is no difference in use of services based on a doctor’s recommendation
H1: There is a difference in use of services based on a doctor’s recommendation
The null hypothesis can be rejected for therapy pool use and classes. Significantly more members use those services if they came to the center upon a doctor’s recommendation. See the output file .spv for details. The results are strong.
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Research Question:
Is there a difference is usage of any other services at the Avery Fitness Center based on doctor’s recommendation?
State the null hypothesis Ho and the alternative hypothesis Ha.
Is there any area where the null hypothesis can be rejected?
Null Hypothesis: e.g. no effect, no difference between groups. Hope to reject the null: Ho
Alternative Hypothesis: e.g. there is a difference between groups. Hope to accept the alternative: HA

Analysis & Interpretation:Multivariate Analysis/ Inferential Statistics
Independent Samples T-Test and Analysis of Variance

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Relationship Among the Stages in
the Research Process
Formulate Problem
Design Data Collection
Method and Forms
Determine Research Design
Design Sample and Collect Data
Analyze and Interpret the Data
Prepare the Research Report

Why Conduct Multivariate Analysis?
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Multivariate analyses allow researchers a closer look at their data than is possible with univariate analyses
Univariate analyses provide insights about the data while multivariate analyses can often provide further illumination of those insights

Descriptive versus Multivariate/Inferential Statistics
Inferential Statistics. Here we are trying to reach conclusions that extend beyond the immediate data alone. For instance, we use inferential statistics to try to infer from the sample data what the population might think.
Or, we use inferential statistics to make judgments of the probability that an observed difference between variables or a relationship between variables is a dependable one or one that might have happened by chance in this study.
Thus, we use inferential statistics to make inferences from our data to more general conditions; we use descriptive statistics simply to describe what’s going on in our data.

Choosing a Statistical Test
Number of
Variables
Univariate
Analysis/Descriptive Stats
Multivariate
Analysis/Inferential
Stats
One
Two
or More
Example: Frequencies, Measures of Central Tendency and Variability

Key Concepts
Null Hypothesis: e.g. no effect, no difference between groups. Hope to reject the null: Ho
Alternative Hypothesis: e.g. there is a difference between groups. Hope to accept the alternative: HA
Type I Error: wrongly reject the null hypothesis: Saying there is a difference when there is not.
Type II Error: wrongly do not reject the null: Saying there is no difference when there is.
Hypothesis Testing
Watch this video to better understand the concept of hypothesis testing

There are various multivariate/inferential statistics to use for the hypothesis testing. This week we will analyze data with the Independent Samples T-Test and One-Way ANOVA. We will discuss the N-Way ANOVA as hypothesis tests as well. First, the Independent Samples T-Test.

Analysis & Interpretation:Multivariate Analysis/ Inferential Statistics
Independent Samples T-Test

The are many hypothesis tests to evaluate significant differences associated with your research questions. To select the correct question, your data must have the assumptions needed for the test. Let’s define the Independent Samples T-Test and why it is appropriate for the hypothesis test associated with the research question do visits to the AFC differ by gender. Do recommendations for the AFC differ by gender?

Independent Samples T-Test
One of the most used tools in statistical testing in Marketing Research
What is it?
A tool to explain the confidence one has about a result
Explains the likelihood that the result is not due to chance
Tells us whether we have a numerical difference or a statistical difference

p-values are compared to α to determine significance
When the p-value is equal to or less than α, we conclude that there is a significant difference
Low probability of rejected a null hypothesis that is true—saying there is significance when there is not.
When the p-value is greater than α, we conclude that there is not a significant difference
*

Independent Samples T-Test
One of the most used tools in statistical testing in Marketing Research
Application?
Comparing the results from independent samples.

Research Questions?
Is GPA different between athletes and non atheletes in the university?
Are sales higher in the test market versus the control market?
Is there a difference in purchase intent for the brand by gender?
Video Tutorial:

Independent Sample T Test

Types of Hypothesis Tests
What is the research question?
State:
Null Hypothesis Ho—No difference, no effect, no relationship
Alternative Hypothesis Ha—There is a difference, there is an effect
there is a relationship
Test are evaluated by the p value. If the p is low the Null must go
Test DV Scale of Measurement IV Scale of Measurement
Independent Sample t-test Interval or ratio Nominal or ordinal (binary)

The independent samples t-test is used where the dependent variables are quantitative and the independent variables are qualitative and binary—have two groups or two independent samples.
The test statistic as with all hypothesis tests are evaluated by their probability value—p value.
Video Tutorial on the Independent Samples T-Test

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Probability
Probability: the likelihood that a particular event will occur, expressed as a proportion, ranging from .00 (impossible to occur) to 1.00 (will definitely occur)
Example: When flipping a fair coin, the probability of heads of .5

As with all hypothesis tests, the result will be evaluated by the p-value. A probability value.
To identify why data typically appears in the various shapes it appears in, we first need to explore the concept of probability. Probability, broadly, refers to how likely a specific event is to occur. It is typically expressed as a proportion and ranges from .00 (a specific event will never occur) to 1.00 (a specific event will always occur). One of the major purposes of statistics is to accurately assess probabilities associated with data.
In some cases, probability is very easy to compute. For example, consider a coin – one side is heads; the other is tails. Any time you toss the coin in the air and let it fall, it will land either heads-up or tails-up. If there’s nothing strange about the coin, it will fall heads-up about half of the time and tails-up the other half of the time. Thus, the probability of heads is .50. The probability of tails is also .50.
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Probability
Chance: variation that occurs at random, i.e. luck

As we add more possible outcomes, the probabilities become more complex. Next consider a ten-sided die with the numbers 0, 1, 2, 3, 4, 5, 6, 7, 8 and 9 on each side. The probability that any particular number will land facing up when rolling that die is 1/10, which we can express as a probability as .10. Thus, the probability of a 0 is .10, 1 is .10, 2 is .10, 3 is .10, 4 is .10, 5 is .10, 6 is .10, 7 is .10, 8 is .10 and 9 is .10. All together, these numbers add up to 1.00, since with any given roll of the die, one of these numbers will appear 100% of the time.
In organizational research, probability becomes even more complicated, because we typically don’t know the total number of possibilities. In our case study, how likely is it that an employee will sell ten cars in any particular month? What about 6 or 30? Should we consider 100? Although some values may be unrealistic, there are theoretically no boundaries for what this value could be. Even if we did come up with boundaries, there’s no way for us to know beforehand how probable any particular value is.
Without a list of every possibility, we cannot compute a specific, precise probability that any of these events will occur. Fortunately, data typically take one of several common shapes, and we can compute the probability of data occurring within any of these shapes. The next sections will explore what these shapes look like and the relative probabilities of the data they contain.
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Conducting a Statistical Test
p-value: the probability that the given sample was drawn from the population described by a given null hypothesis
Range from .00 – 1.00
p-values are compared to α (this is the risk level generally set to .05) to determine significance
When the p-value is less than or equal to α (.05 typically), we conclude that there is a significant difference
When the p-value is greater than α (.05), we conclude that there is not a significant difference
The risk level is set depending on the problem definition of the study. How much risk is permissible for the action standard for the decision to be made? Generally, in market research if the p-value is less than or equal to α (.05), where we are 95% confident, we have a significant result. In other words, we conclude that there is a significant difference or relationship depending on our research question.

As such, each hypothesis test is evaluated for significance with its associated p value. This week we will focus on the Independent Samples T-Test and the Analysis of Variance—One Way and discuss N-Way Analysis of Variance
*

Conducting a Statistical Test
-p-value: the probability that the given sample was drawn from the population described by a given null hypothesis. What is the probability of rejecting a null hypothesis that is true?
Range from .00 – 1.00
p-values are compared to α to determine significance
When the p-value is equal to or less than α, we conclude that there is a significant difference
When the p-value is greater than α, we conclude that there is not a significant difference

The p value that will be .05 for the 95% confidence level is typical for marketing research.
If a research wants to be 99% confident that would be a p value of .01. For most issues, this amount of conservatism is not needed but again this will be driven by the problem definition.

Region of Rejection

Research questions can require a two tailed statistical test.

Research questions can require a one tailed statistical test
Examples on one-tailed and two-tailed research questions are the slide that follows.
*

One tailed—the researcher is looking in one direction.
Two-tailed the researcher is looking for differences/relationships in either directions.
This depends on your problem definition to include your research questions.
More detailed on one tailed versus two tailed tests can be explored in the link below:
https://stats.idre.ucla.edu/other/mult-pkg/faq/general/faq-what-are-the-differences-between-one-tailed-and-two-tailed-tests/

Based on your research question—to conduct your hypothesis test, state the null hypothesis Ho and the alternative hypothesis Ha.

Avery Fitness Center Project
This is an example of a descriptive study that we will use throughout the semester. The case, the survey and the associated SPSS file are on the course site. The decision problem for the case is how to grow membership at the center. The research problem to determine who their current customers are and what are their attitudes and behavior around fitness center activity. The survey and data collection effort support the problem as defined. Read the case, review the survey and associated data file after watching the video overviews of SPSS.
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Avery Overview
Avery Questionnaire and Code book
Click the files in normal mode to open, they are also on the course site with the SPSS file

We will use the Avery Fitness Center Case, Survey and Data Set to illustrate statistical concepts. The case, survey and SPSS data set are on the course site. We will use the Avery Fitness Center Data Set to review these concepts.
There is a SPSS manual on the course site for your use as well.

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AVERY FITNESS CENTER SURVEY

Thank you for taking time to provide important feedback about Avery Fitness Center (AFC). Please answer the following questions. Your candid
responses will help us provide better services in the future. No one at AFC will see your specific responses, so please be honest.

(I) Which of the following AFC services have you utilized at least once in the last 30 days? (Please check all that apply)

o Weight Training 0 Exercise Circuit 0 Therapy Pool
o Classes 0 Circulation Station

(2) Within the past 30 days, approximately how many times have you visited AFC to exercise?

___ Times in the last 30 days

(3) During what part ofthe day have you normally visited AFC? (Please check only ene)
o morning 0 afternoon 0 evening

(4) How did you learn about AFC? (Please check all that apply)

o Recommendation from Doctor 0 Drove by location
o Recommendation from Friend or Acquaintance 0Article in Paper
o Advertising (including Yellow Pages) 0 Other
o Heard AFC director speak

(5) How important to you personally is each of the following reasons for participating in AFC
programs? (Circle a number on each scale)

not at all
important

very
important

General Health and Fitness 2 3 4 5

Social Aspects 2 3 4 5

Physical Enjoyment 2 3 4 5

Specific Medical Concerns 2 3 4 5

(6) How likely is it that you would recommend AFC to a friend or colleague?
not at all extremely

likely neutral likely

o 1’- 6 7 8 9 103 4 ‘ 5

(7) What was the original event that caused you to begin using services from AFC?

(8) Current Age _

(9) Gender o Male o Female
(10) Highest Level of Education Achieved:

o Less than High School 0 Some College
o High School Degree, 0 Associates Degree

o Four-year College Degree
o Advanced Degree

(II) What is your approximate annual household income from all sources, before taxes?
. (Please check the appropriate category & employment status)

0$0-15,000 0 $6Q,001-75,000

0$15,001-30,000 0 $75,001-90,000
0$30,001-45,000 0 $90,001-105,000
o $45,001-60,000 0 $105,001-120,000o more than $120,000

r———-I

:0 Employed :
10 Retired I~———~

THANKYOUI
© 2012 (engage Learning

Variable Name

WEIGHT

CLASSES

CIRCUIT

STATION

POOL

VISITS

DAYPART

DOCTOR

WOM

ADVERT

SPEAKER

LOCATION

ARTICLE

OTHER

FITNESS

SOCIAL

ENJOY

MEDICAL

RECOM

EVENT

AGE

GENDER

EDUCAT

INCOME

STATUS

REVENUE

102012 (engage Learning

Description Response Options

143

Questionnaire identification number

Utilized weight training in previous 30 days?

Utilized classes in previous 30 days?

Utilized exercise circuit in previous 30 days?

Utilized circulation station in previous 30 days?

Utilized therapy pool in previous 30 days?

Number of visits to AFC in previous 30 days?

Normal time to visit AFC?

O=nol=yes

0= no I = yes

(record number)

I == morning
2 = afternoon

3 = evening

How learned about AFC? Doctor Rec. O=nol=yes

0= no I = yes

O=nol=yes

0= no I = yes

(1-5, “not at all important – very important”)

How learned aboutAFC? Friend Rec.

How learned about AFC? Advertising

How learned aboutAFC?Heard director speak

How learned aboutAFC? Drove by location

How learned about AFC? Article in newspaper

How learned about AFC? Other

Importance for participation: General Health and Fitness

Social Aspects

Physical Enjoyment

Specific Medical Concerns

How likely to recommend?

What original event caused you to begin
AFC? (open ended)

SAME

SAME _.

(1-10, “not at aillikely-extremely likely”)

I = general health / exercise
2 = pool/facilities
3 = rehab / specific medical needs
4 = social considerations
5 = transfer from another center
6 = other

(record number)

I = male
2 = female

I = less than high school
2 = high school degree
3 = some college
4 = associates degree
5 = four-year college degree
6 = advanced degree

Current Age

Gender

Highest level of education achieved?

Annual household income before taxes I = $0 – 15,000
2 = $15,00 I – 30,000
3 = $30,00 I – 45,000
4 = $45,00 I – 60,000
5 = $60,00 I – 75,000
6 = $75,00 I – 90,000
7 = $90,00 I – 105,000
8 = $105,00 I – 120,000
9 = more than $120,000

I = employed 2 = retired

($$$ from secondary records)

Work Status

One-year Revenue from Respondent

MISSING = BLANK

CHAPTER 11: DATA PREPARATION FOR ANALYSIS

The Avery Fitness Center Project

The Avery Fitness Center is located in a mid-size city in the southeastern United States; the company offers a variety of exercise programs to its member under the supervision of personal trainers. The company was founded 10 years ago and operates from a single location in an old shopping center near a large university. AFC primarily targets older men and women. Some of the members are struggling with health issues. Many customers are attracted to the large indoor therapy pool that allows exercise using water resistance, which is much easier on bones and joints than traditional exercise options. Individuals become members of the fitness center by paying a monthly fee; they pay additional fees for special classes, use of personal trainers, etc. Although business had been steady, AFC managers believe that the company could grow substantially without adding additional facilities. As a result, AFC managers are interested in better understanding the kinds of individuals that are attracted to AFC an how best to recruit more of these kinds of people. More specifically, the AFC researchers are addressing two research problems (1) Determine member demographics and usage patterns and (2) investigate how members learn about AFC.
To address these research problems, researchers decided to conduct an online survey of AFCs customer base. Customer was defined as any individual in the company’s member database who had visited AFC at least once in the previous 12 months. Surveys were sent to 400 members drawn using a simple random sample; respondents completed and returned 231 usable surveys for a response rate of 58%. Survey respondents were then matched with total fees paid over the next 12 months. After editing, coding and cleaning the data, the researchers were ready to begin data analysis.

Hypothesis Testing Using an Independent-Samples t-test: Avery Fitness Center Project
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For the research question here, an independent samples T-Test is the statistical technique to use to answer the questions. Why is this a job for the independent samples t-test to be able to reject the Null Hypothesis?
It meets the assumptions for the test where the dependent variables are quantitative, and the independent variables are qualitative and binary—have two groups or two independent samples. Specifically, in this example the independent variable is on a nominal scale and binary in this data set…gender (males versus female); the dependent variable is on an interval scale. (likelihood to recommend and # of times visiting the center in the past 30 days, importance ratings)
Video tutorial: https://www.youtube.com/watch?v=8alv3kZt8Ug
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Independent Samples T-Test: Drawing Conclusions
For an Independent Samples T-Test your conclusions should include:
A formal statement about retaining the null or rejecting the null and accepting the alternative.
A formal statement about the statistical significance of the finding.
A sentence interpreting the results in terms of the research question.
Interpretation of any supplemental analyses.

SPSS Sequence:
Analyze> COMPARE MEANS and the Independent Samples T-Test move “quantitative variable” to the Dependent List Box. Move “ binary qualitative variable” to the Grouping Variable, input coding for the two groups of the independent variable>Click OK.

Independent Samples T-Test Tutorial: https://www.youtube.com/watch?v=8alv3kZt8Ug
*

SPSS
Analyze>Compare Means>Independent T Test, Input Grouping Variable based on coding of gender in this case

Independent Sample T-Test
Avery Fitness Center
Likelihood to Recommend by Gender
Analyze>Compare Means>Independent T Test, Input Grouping Variable based on coding of gender in this case
SPSS Menu Sequence
There is a gender difference in the likelihood to recommend the center: p value of .051
is significant at the 95% confidence interval.

Recreate this analysis in Demonstrate:
Analyze> COMPARE MEANS and the Independent Samples T-Test move “quantitative variable” to the Dependent List Box. Move “ binary qualitative variable” to the Grouping Variable, input coding for the two groups of the independent variable>Click OK.
Independent Samples T-Test Tutorial: https://www.youtube.com/watch?v=8alv3kZt8Ug
The group statistics box shows that females are more likely to recommend the center versus males. The test provides a p value of .05 (.051 does not round the p value to .06). We can reject the null hypothesis. In other words, there is a significant difference in the likelihood to recommend the AFC to a friend or family member.

P value is .051 which rounds to the 95% level of confidence on the T Stat (the F Stat yields same information)…the confidence interval provides the range on the upper and lower . There is a difference between gender and the likelihood to recommend the center.
Potential Marketing Implication: AFC management may want to provide incentives to recommend the center to friends. There is evidence as indicated by the test that efforts to increase male member recommendations could be helpful to AFC decision problem to increase membership at the center.

Independent Sample T-Test
Avery Fitness Center
Visits by Gender
Analyze>Compare Means>Independent T Test, Input Grouping Variable based on coding of gender in this case, male = 1 and female = 2
SPSS Menu Sequence
There is no difference between gender and number of visits: p value of .520 is not significant at the 95% confidence interval

Recreate this analysis in Demonstrate:

Analyze> COMPARE MEANS and the Independent Samples T-Test move “quantitative variable” to the Dependent List Box. Move “ binary qualitative variable” to the Grouping Variable, input coding for the two groups of the independent variable>Click OK.
Independent Samples T-Test Tutorial: https://www.youtube.com/watch?v=8alv3kZt8Ug
The group statistics box shows that females are slightly more likely to visit the center versus males. The test provides a p value of .520. (only a 49.8% confidence 1-.502).
We accept the null hypothesis. In other words, there is no significant difference between men and women in terms of visits to the center.
In other words, there is no difference in likelihood to visit by gender, we cannot reject the null hypothesis.
Marketing implication: No need to create actions to increase visits to the AFC by gender.

Analysis & Interpretation: Hypothesis Testing
Multivariate Analysis
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One Way ANOVA

One-Way Analysis of Variance
Analysis of variance (ANOVA) is used as a test of means for two or more populations. The null hypothesis, typically, is that all means are equal. ANOVA compares the means on the dependent variable.
Analysis of variance must have a dependent variable that is metric (measured using an interval or ratio scale).
There must also be one or more independent variables that are all categorical (nonmetric). Categorical independent variables are also called factors.

One-Way Analysis of Variance
A particular combination of factor levels, or categories, is called a treatment.
One-way analysis of variance involves only one categorical variable, or a single factor. In one-way analysis of variance, a treatment is the same as a factor level.

One-Way Analysis of Variance
Marketing researchers are often interested in examining the differences in the mean values of the dependent variable for several categories of a single independent variable or factor. For example:
Do the various segments differ in terms of their volume of product consumption?
Do the brand evaluations of groups exposed to different commercials vary?
What is the effect of consumers’ familiarity with the store (measured as high, medium, and low) on preference for the store?

One Way Anova

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The are many hypothesis tests to evaluate significant differences associated with your research questions. To select the correct question, your data must have the assumptions needed for the test. Let’s define One Way ANOVA and why it is appropriate for the hypothesis test associated with the research question does spending at the AFC (revenue variable) differ by member income. As with all hypothesis tests, we will reject or accept the null hypothesis based on the p value associated with the test.

Conducting a Statistical Test
There are many possible statistical tests that can be used, depending on your question, your data, and other factors.
To explore differences of spending at the AFC (revenue) by income level, we
will use the One-Way Analysis of Variance

Types of Hypothesis Tests
What is the research question?
State:
Null Hypothesis Ho—No difference, no effect, no relationship
Alternative Hypothesis Ha—There is a difference, there is an effect
there is a relationship
Test are evaluated by the p value. If the p is low the Null must go
Test DV Scale of Measurement IV Scale of Measurement
One Way Anova Interval or ratio Nominal or ordinal (factorial)

Factorial—more than 2 levels of the independent variable.
One Way Anova

MR/Brown & Suter
*

Relationship Amongst Commonly Used Stat Tests: T-Test and Analysis of Variance

One Independent

Metric Dependent Variable

Independent Samples
T-Test
Categorical
Binary (e.g. gender 1
male 2 female)
Independent Variable

One-Way Analysis
of Variance

One Factor

N-Way Analysis
of Variance

More than
One Factor

Analysis of
Variance

Categorical:
Factorial

Analysis of
Covariance

Categorical
and Interval

Correlation

As the diagram illustrates, the Independent Samples T-Test compares 2 groups whereas the One-Way ANOVA compares more than 2 groups (this is called a factorial variable)
One Way Anova

Now let’s look at the application of the One Way Analysis of Variance with the AFC case.

SPSS
Analyze> COMPARE MEANS and the One-Way ANOVA move Revenue to the Dependent List Box. Move Income to the FACTOR box>Click OPTIONS>Click DESCRIPTIVE>Click CONTINUE>Click OK.

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One-Way ANOVA
Avery Fitness Center
Analyze> COMPARE MEANS and the One-Way ANOVA move Revenue to the Dependent List Box. Move Income to the FACTOR box>Click OPTIONS>Click DESCRIPTIVE>Click CONTINUE>Click OK. We maintain the null!
SPSS Menu Sequence
Ho There is no relationships between member income and how much they spend at AFC.
HA There is a relationship between member income and how much they spend at AFC.

Recreate this analysis in Demonstrate:
This is a demonstration of one way ANOVA based on the AFC case.
In this example we accept the null hypothesis (Ho) because the p-value is .958 much larger than a significant p value of .05 or less. No need for any alternate pricing strategies at the AFC. Let’s now look at an example where we have a significant result. The case follows on the next slide and the associated data set is on the course site.

WHICH OF THESE WEBSITES IS THE BEST CHOICE?

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One-Way ANOVA
Web Design
Analyze> COMPARE MEANS and the One-Way ANOVA move Revenue to the Dependent List Box. Move Income to the FACTOR box>Click OPTIONS>Click DESCRIPTIVE>Click CONTINUE>Click OK. We maintain the null!
SPSS Menu Sequence
Ho There is no difference in web design performance.
HA There is a difference in web design performance.

There is a difference in web design performance. We reject the null hypothesis with a p value of .000. When a significant result is presented in a One Way ANOVA, a post hoc test must be completed. The Scheffé is a popular choice. See the next slide for a definition.

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Post Hoc Tests

Once you have a significant result—go back to your One Way ANOVA procedure and select Post Hoc and Scheffe.

SPSS
Analyze> COMPARE MEANS and the One-Way ANOVA move Revenue to the Dependent List Box. Move Income to the FACTOR box>Click OPTIONS>Click DESCRIPTIVE>Click CONTINUE>CLICK POST HOC>CLICK SCHEFFE>CLICK CONTINUE>Click OK.

Since Design B had the highest mean we can check that Design B is significantly different from the other web design options. As we compare the p values of web design B to other web designs (A, C and D), we see that web design B is significantly different (and higher) than all others.
Marketing Implication: Colleen should move forward with Web Design B for her business.

One-way ANOVA: Drawing Conclusions
For the one-way ANOVA, your conclusions should include:
A formal statement about retaining the null or rejecting the null and accepting the alternative.
A formal statement about the statistical significance of the finding.
A sentence interpreting the results in terms of the research question.
Interpretation of any supplemental analyses.

SPSS Sequence:
Analyze> COMPARE MEANS and the One-Way ANOVA move “variable” to the Dependent List Box. Move “variable” to the FACTOR box>Click OPTIONS>Click DESCRIPTIVE>Click CONTINUE>Click OK.

Relationship Amongst Commonly Used Stat Tests: T-Test and Analysis of Variance

One Independent

Metric Dependent Variable

Independent Samples
T-Test
Categorical
Binary (e.g. gender 1
male 2 female)
Independent Variable

One-Way Analysis
of Variance

One Factor

N-Way Analysis
of Variance

More than
One Factor

Analysis of
Variance

Categorical:
Factorial

Analysis of
Covariance

Categorical
and Interval

Correlation

One Way Anova

As the diagram illustrates, the Independent Samples T-Test compares 2 groups whereas the One-Way ANOVA compares more than 2 groups (this is called a factorial variable).
In experimental design in particular, if there is more than one factorial independent variable, a N-Way Analysis of Variance can be used. The slide on the next page diagrams the procedure in comparison to the Independent Samples T-Test and the One Way ANOVA. An example of its use is presented and a video tutorial is presented where you have the opportunity to further EXPLORE this technique in the content for this week.

Relationship Amongst Commonly Used Stat Tests: T-Test and Analysis of Variance

One Independent

Metric Dependent Variable

Independent Samples
T-Test
Categorical
Binary (e.g. gender 1
male 2 female
Independent Variable

One-Way Analysis
of Variance

One Factor

N-Way Analysis
of Variance

More than
One Factor

Analysis of
Variance

Categorical:
Factorial

Analysis of
Covariance

Categorical
and Interval

Correlation

If two or more factors are involved, the analysis is termed n-way analysis of variance.
In marketing research, one is often concerned with the effect of more than one factor simultaneously. For example:
How do advertising levels (high, medium, and low) interact with price levels (high, medium, and low) to influence a brand’s sale?
Do educational levels (less than high school, high school
graduate, some college, and college graduate) and age (less than 35, 35-55, more than 55) affect consumption of a brand?
What is the effect of consumers’ familiarity with a department store (high, medium, and low) and store image (positive, neutral, and negative) on preference for the store?
What is the null hypothesis, Ho what is the alternative hypothesis Ha
Can you reject or accept the null hypothesis?
N Way Analysis of Variance

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Formulas

MR/Brown & Suter
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Chi-Squared Tests: Conducting the Statistical Test
Calculate the chi-squared tests using the following formula:

MR/Brown & Suter
*

Chi-Squared Tests: Conducting Supplemental Analyses
Calculate an effect size using the formula:

MR/Brown & Suter
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Independent-Samples t-test: Conducting the Statistical Test
Calculate an independent-samples t-test using the formula:

MR/Brown & Suter
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Independent-Samples t-test: Conducting the Statistical Test
Calculate the pooled variance using the formula:

MR/Brown & Suter
*

One-way ANOVA Terms
F: the ratio of between-group variability to within-group variability used in ANOVA
k: the number of groups being compared in ANOVA
dfB: between-groups degrees of freedom, calculated as k – 1
dfW: within-groups degrees of freedom, calculated as N – k
SS: sum of squares; shorthand for “sum of the squared deviations”

MR/Brown & Suter
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One-way ANOVA: Conducting the Statistical Test
Calculate the one-way ANOVA using the following formulas:

MR/Brown & Suter
*

One-way ANOVA: Conducting Supplemental Analyses
If we found statistical significance, compute an effect size and a post-hoc test.
If we did not find statistical significance, no further analyses needed.

MR/Brown & Suter
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Region of Rejection
Two-tailed test: a hypothesis test in which the region of rejection falls in both tails
Represented with a ≠ in the alternative hypothesis and = in the null hypothesis

MR/Brown & Suter
*

Region of Rejection
One-tailed test: a hypothesis test in which the region of rejection falls in either the upper or lower tail
Represented with a < or > in the alternative hypothesis and ≤ or ≥ in the null hypothesis

MR/Brown & Suter
*

Chi-Squared Tests: Conducting the Statistical Test
Calculate the chi-squared tests using the following formula:

MR/Brown & Suter
*

Chi-Squared Tests: Conducting Supplemental Analyses
Calculate an effect size using the formula:

MR/Brown & Suter
*

Chi-Squared Test of Independence: Critical Values and Decision Rules
The critical value for the chi-squared test of independence depends on alpha and the degrees of freedom for the test
Example: If α = .05, k1 = 4, and k2 = 3, χ2crit(6) = 12.592

Independent Samples Tests: Critical Values and Decision Rules
The critical value for any t-test depends on alpha, the degrees of freedom for the test, and whether the test is one-tailed or two tailed
Example: For a two-tailed t-test where α = .05 and n = 23, tcrit(21) = 2.080

MR/Brown & Suter
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One-way ANOVA: Critical Values and Decision Rules
The critical value for the one-way ANOVA depends on alpha and the degrees of freedom for the test
Example: If α = .05, k = 3, and N = 21, Fcrit(2, 18) = 3.16

MR/Brown & Suter
*

Independent Samples Tests: Critical Values and Decision Rules
The critical value for any t-test depends on alpha, the degrees of freedom for the test, and whether the test is one-tailed or two tailed
Example: For a one-tailed t-test where α = .05 and n = 23, tcrit(21) = 1.721

MR/Brown & Suter
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Significance Level
Significance level: the probability set as acceptable by the researcher that the null hypothesis is rejected when it is in fact true
Represented by α (alpha)
Example: If α = .05 or less, there is less than a 5% probability that we have rejected a true null hypothesis. In most research situations, this is a permissible amount of risk.

All Hypothesis Tests are evaluated by their p value—the probability value indicating whether or not a significant result exists in the context of your research question.
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