MKT 335 Test 2
Range of correlation coefficient r
-1 < r < 1
Range of beta (slope)
0 < B < 1
Key Hypothesis Testing Steps
1. State Hypothesis 2. Choose appropriate test statistic 3. Decision rule 4. Calculate value of test statistic 5. Start conclusion
If the means of two groups being compared are statistically significantly different, we can: A) Accept the null hypothesis B) Accept the alternative hypothesis C) Reject the alternative hypothesis D) None of the above
B) Accept the alternative hypothesis
The R2 statistic ranges from -1 to 1. A) True B) False
B) False
When conducting an ANOVA, it is necessary to always follow up the analysis with a pairwise comparison. A) True B) False
B) False
Least Squares
LS minimizes the Sum of Squared differences (errors) (SSE), or e2 Beta () = slope Steeper slope, larger value
Tabulation that shows the examination of the response to one question relative to one or more other questions (can be applied to ordinal <=5 different responses)
cross tabulations (two-way, three-way)
scales that have characteristics of ordinal scales, plus equal intervals between points (can tell order and distance between)
interval data
data you can compute the mean for
interval, ratio
Measures of Central Tendency- Descriptive Testing
mean, median, mode
Tabulation that shows the number of respondents who gave each possible answer to each question (can be applied to ordinal < 10 different responses)
one-way tabulation/frequency table
scales that have characteristics of interval, plus a meaningful zero point
ratio data
regression coefficient, beta
slope (change in Y (DV) over change in X (IV))
Spearman
test of relation (correlation analysis)- At least one variable is ordinal
Pearson
test of relation (correlation analysis)- both are ratio or interval variables
coefficient of determination, R2
% of total variation in DV (Y) explained (accounted for) by IVs (Xs) Value between 0-1 (always positive) and is the square of the Pearson Correlation aka r between the 2 variables R2 = (total variance - explained variance) / total variance
True or False In the age of big data, where datasets are "tall," many tests are "statistically" significant
True
Which of the following measurement scales can the mode be calculated? A) Nominal B) Ordinal C) Interval D) All of the above
D) All of the above
Effect Size
A quantitative measure of magnitude of (experimental) effect; larger effect size, stronger the relationship between 2 variables
Using the SFO customer survey data, you run a regression to test the effect of education level and income on whether or not the customer purchases food ("yes" or "no" response). The fact that education level and income, you should be cautious interpreting: A) Regression coefficient B) Correlation coefficient C) P value of the model D) Coefficient of determination
A) Regression coefficient
A researcher wanted to compare the salaries of two groups - business graduates of Miami University versus University of Cincinnati- to determine if the mean salary was statistically higher for one of two groups, she would use which of the following? A) Independent samples t-test B) ANOVA C) Chi-square test of independence D) Paired sample t-test
A) Independent samples t-test
Why is the null hypothesis called the hypothesis of the status quo: A) It is the hypothesis that will not be rejected, unless the data provide convincing evidence that it is false, thus maintaining the status quo B) because it is not the research claim being tested C) because it is the hypothesis that recommends the method of analysis D) because the alternative hypothesis is operational only in the event of a Type II error
A) It is the hypothesis that will not be rejected, unless the data provide convincing evidence that it is false, thus maintaining the status quo
In a customer survey, customers are asked to state "no" or "yes" to whether or not they have purchased the product. The number "0" is assigned to "no" and the number "1" is assigned to "yes". Choose the appropriate scale of measurement: A) Nominal B) Ordinal C) Interval D) Ratio
A) Nominal
Which of the following measurement scales can the median NOT be calculated? A) Nominal B) Ordinal C) Interval D) Ratio
A) Nominal
A correlation of -1.00 has a perfect correlation. A) True B) False
A) True
All inferential statistical tests (e.g., t test, ANOVA, regression) produce p value(s). A) True B) False
A) True
The larger the number of observations (datapoints) in a dataset, the greater the likelihood a statistical inferential test (e.g., t-test, ANOVA, regression) will be able to detect small differences (or weak relationships). A) True B) False
A) True
A grocery store owner is interested in testing whether the genre of music—specifically, classical, pop, and rock—affects how many items customer's ultimately bring to the checkout aisle. After collecting the data, which test should be conducted to assess which of the three genres of music yield the highest number of checkout items? A) Independent samples t-test B) ANOVA C) Chi-square test of independence D) Paired sample t-test
B) ANOVA
This analytical procedure shows the responses to one question relative to the responses of another question: A) One-way frequencies B) Cross tabulation C) T-test D) Z-test
B) Cross Tabulation
A perfect correlation indicates that two variables are causally related. A) True B) False
B) False
You are working for an analytics company trying to predict the results of the Ohio governor election. You and your team conduct a random sampling survey of 500 people living in Ohio. You find that in your data, 43% of survey participants support Candidate A and 45% support Candidate B. To test whether the proportions are statistically different, you conduct which statistical test? A) Independent samples t-test B) Non-parametric chi square test C) ANOVA D) Paired samples t-test
B) Non-parametric chi square test
Miami University wants to know which dormitories the students prefer. The administration counts the number of applications for each dorm. Administrators assign a rank to each dorm based on the number of applications received. Choose the appropriate scale of measurement: A) Nominal B) Ordinal C) Interval D) Ratio
B) Ordinal
In a survey, a researcher collects information on the following two items: Q1: Education Level: (1) no high school (2) high school (3) college (4) masters (5) doctoral Q2: Annual Income: $_________ (USD) The researcher wants to analyze the relationship between the two items. Which statistical test would you recommend? A) Chi-square test of independence B) Spearman correlation C) Pearson correlation D) T-test
B) Spearman correlation
If the coefficient of determination is equal to 1, then the correlation coefficient A) must also be equal to 1 B) can be either -1 or +1 C) can be any value between -1 to +1 D) must be -1
B) can be either -1 or +1
The data analytics team at Kroger wants to assess whether households in zip codes in and around Cincinnati differ in terms of weekly grocery spending. Which statistical test would you recommend to be conducted? A) Independent Samples T-test B) Spearman Correlation C) ANOVA D) Chi-Square Test of Independence
C) ANOVA
Which of the following measurement scales can the mean be calculated? A) Interval B) Ratio C) Both (A) and (B) D) Neither (A) nor (B)
C) Both (A) and (B)
Which of the following measurement scales can you add and subtract values? A) Interval B) Ratio C) Both (A) and (B) D) Neither (A) nor (B)
C) Both (A) and (B)
You intend to apply for graduate school. As an application requirement, you must take the Graduate Record Examination (GRE). This is a standardized test. Scores range from 200 to 800 with a population mean of 500 and a population standard deviation of 100. Choose the most appropriate scale of measurement for GRE scores: A) Nominal B) Ordinal C) Interval D) Ratio
C) Interval
This measure of central tendency can be computed only from interval or ratio data. A) Mode B) Median C) Mean D) All of the above must be computed from interval or ratio data
C) Mean
Using the SFO customer survey data, you run a regression to test the effect of education level and income on whether or not the customer purchases food ("yes" or "no" response). The fact that education level and income are correlated is known as: A) Regression coefficient B) Correlation matrix C) Multicollinearity D) Coefficient of determination
C) Multicollinearity
A marketing manager wants to assess how effective the firm's advertising expenditures have been. As a starting point, the manager asks you, the analyst, to access the firm's data and statistically test the relationship between monthly advertising expenses and monthly sales over the past five years. Once you compile the data, what statistical test would you conduct? A) Chi-square test of independence B) Spearman correlation C) Pearson correlation D) T-test
C) Pearson correlation
Using the SFO customer survey data, you run a bivariate regression to test whether age predicts customer satisfaction (1-10 scale). You find that age has a regression coefficient of -0.51 with a p value of .02. What do you conclude? A) There is no statistical effect of age on customer satisfaction. B) There is a statistically positive effect of age on customer satisfaction. C) There is a statistically negative effect of age on customer satisfaction. D) There is a statistical effect of age on customer satisfaction, but the direction is not known.
C) There is a statistically negative effect of age on customer satisfaction.
In a beer consumption study, a researcher makes an assumption that males will consume more beer per week than females; this can be stated in a: A) research objective B) given level of significance C) hypothesis D) theory
C) hypothesis
Regression modeling is a statistical framework for developing a mathematical equation that describes how A) one explanatory and one or more response variables are related B) several explanatory and several response variables response are related C) one response and one or more explanatory variables are related D) All of these are correct
C) one response and one or more explanatory variables are related
A correlation analysis between sales and sales training scores results in R = +.98. Which of the following best interprets the relationship between sales and sales training? A) 98% of the salespeople taking the test have higher sales B) the correlation between sales and sales training is very weak and insignificant C) the correlation between sales and sales training is strong and positive, indicating that higher sales training scores are closely associated with higher sales and vice-versa D) 98% of the variation in sales is explained by variations in sales training scores
C) the correlation between sales and sales training is strong and positive, indicating that higher sales training scores are closely associated with higher sales and vice-versa
Bivariate regression can NOT demonstrate: A) when the two variables are linear B) when the two variables are strongly inversely related C) when the two variables are causally related D) none of the above
C) when the two variables are causally related
Tests of Relation- Inferential Testing
Chi-square test Correlation Regression
difference between a correlation coefficient, r, and a regression coefficient, beta
Correlation coefficient indicates the extent to which two variables move together. Regression indicates the impact of a change of unit on the estimated variable ( y) in the known variable (x)
Correlation vs Regression Analysis
Correlation measures how much a variable is associated with another but regression is when you are presuming cause and effect
Professor P samples 100 Miami University students and asks whether or not they are leaving Oxford, OH, for the fall break weekend (response is either "yes" or "no"). Professor P wants to assess the relationship between class year (freshman, sophomore, junior, senior) and whether or not students leave Oxford for fall break. After collecting the data, what statistical test should Professor P conduct? A) Independent Samples T-test B) Spearman Correlation C) ANOVA D) Chi-Square Test of Independence
D) Chi-Square Test of Independence
Suppose in our sample results we find that males averages drinking five soft drinks per week, compared with six soft drinks per week for females. In the absence of additional analysis, what type of difference has been illustrated? A) Statistical difference B) Managerially important difference C) A difference of dispersion D) Mathematical difference
D) Mathematical difference
Using the SFO customer survey data, you run a regression to test the effect of education level and income on whether or not the customer purchases food ("yes" or "no" response). What type of regression should you conduct? A) Bivariate linear regression B) Bivariate logistic regression C) Multivariate linear regression D) Multivariate logistic regression
D) Multivariate logistic regression
A marketing researcher first shows advertisement A to a group of participants and then measures their purchase intentions for the related product. Soon after, the researcher shows advertisement B to the same group of participants and measures their purchase intentions. In comparing how purchase intentions differ between the two advertisements, which test should the researcher conduct based on this context? A) Independent samples t-test B) ANOVA C) Chi-square test of independence D) Paired sample t-test
D) Paired sample t-test
In regression analysis, if the independent variable is measured in kilograms, the dependent variable A) must also be in kilograms B) must be in some unit of weight C) cannot be in kilograms D) can be any units
D) can be any units
The relationship between number of beers consumed (x) and blood alcohol content (y) was studied in 16 male college students by using least squares regression. The following regression equation was obtained from this study: y= -0.0127 + 0.0180x The above equation implies that: A) each beer consumed increases blood alcohol by 1.27%when the two variables are strongly inversely related B) on average it takes 1.8 beers to increase blood alcohol content by 1% C) each beer consumed increases blood alcohol by an average of amount of 1.8% D) each beer consumed increases blood alcohol by exactly 0.018
D) each beer consumed increases blood alcohol by exactly 0.018
What level of measurement would the following question produce?Please indicate your approximate age by checking the appropriate age category.__(1) 0 to 18 __(2) 19 to 35 __(3) 35 and over A) nominal B) ratio C) interval D) ordinal
D) ordinal
Tests to summarize the characteristics of a dataset with one-way and two-way tabulations
Descriptive Testing
Hypothesis Testing Step 3: Decision Rule
Determining whether difference or deviation between actual value of sample mean and its expected value based on hypothesis could have occurred by chance aka whether to reject or fail to reject null hypothesis
why conduct follow-up pairwise comparison for ANOVA?
Follow-up pairwise comparison when p < .05 because you must explore differences in the multiple group means (always 3+)
an assumption (derived from theory) made about some characteristics of the population
Hypothesis
multicollinearity
IVs in a regression equation are assumed to be uncorrelated If IVs are correlated, results in multicollinearity - Can result in erroneous estimation of the - May not give valid results about any individual predictor or which ones are redundant to others
Hypothesis testing and statistical significance: generalize from sample results to population characteristics primarily used to determine whether 2+ means (%) differ to greater extent than would be expected by random error
Inferential Testing
3 concepts of differences
Mathematical Statistically significant Managerially important (substantive) differences ($, effect size)
Two types of P-values in Multiple Regression Analysis
P-value of F statistic and p-value of coefficient In regression analysis → p-value of F statistic P-value <=.05, reject H0, accept HA P-value > .05, fail to reject H0 Individual IVs → p-value of coefficient P-value <=.05, reject H0, accept HA P-value > .05, fail to reject H0
2 types of correlation analysis
Pearson and Spearman
Examples of Effect Size
Pearson correlation R cohen's d cohen's f2
Tests of Differences- Inferential Testing
T-tests (independent and paired) ANOVA
Independent samples t-test
Test of difference- Difference between 2 groups on one variable - numeric DV
Paired samples t-test
Test of difference- Difference between 2 variables (across the same group) - numeric DV
Chi-Square of Independence
Tests to determine if 2 nominal variables are related to output variables: x2 and p-value **both are categorical Ho: independent (unrelated) HA: dependent (related)
Role of decision rule
The decision rule rules out the effect of random/occurrence by chance and is significant in value to determine how much randomness could be in effect
rejection of null when it's true Probability of occurring = alpha (α)
Type I Error
failure to reject null when it's false Probability of occurring = beta (β)
Type II Error
linear bivariate regression
Used to describe the relationship when one variable is considered independent and one is dependent Does NOT prove cause and effect relationship, but done when one is expecting to predict the other
logistic regression
When DV is binary, logistic regression is used (related to two things) the DV is a dummy variable (nominal data)
difference between a chi-square test of independence and a non-parametric chi-square test of difference between proportions
chi-square test of independence tests whether nominal or categorical variables are associated and non-parametric chi-square tests proportions (likely 2+ proportions)
A graphical user interface which often provides at-a-glance views of key performance indicators (KPIs) relevant to a particular business objective (great way to display descriptive stats)
dashboard (visual progress report)
Process of gathering, selecting & transforming data to help answer an analytical question (from raw data to analyses)
data wrangling (aka data cleaning or data munging)
p-value
exact probability of getting a computed test statistic due to chance Probability the null hypothesis is true Smaller the p-value, smaller probability the observed result occurred by chance
medium effect size
f2 = .15
large effect size
f2 = .35
small effect size
f2= .02
correlation coefficient, r
from Pearson's Correlation Analysis ranges from -1 to 1 When r = |1|, there is perfect correlation When r = 0, there is no correlation Positive 0-1 indicates that if one variable goes up, the other also tends to go up Negative 1-0 indicated that if one variable goes up, the other tends to go down
linear bivariate regression line
line of best fit: y = a + bx IV (x): affects value of dependent variable; cause DV(y): explained/predicted by IV; effect
Dangers of relying on the measures of central tendencies
mean suggests markets are the same, SD indicates they are different
Correlation Analysis
measures the degree to which changes in one variable are associated with changes in another; neither variable is a nominal variable Ho (null): unrelated HA (alternative): related
.3 < R < .7 (+/-)
moderate relationship
4 different types of data
nominal (categorical), ordinal, interval, ratio
scales that partition data into mutually exclusive and collectively exhaustive categories
nominal data (classification type)
data you can compute the mode for
nominal,ordinal,interval, ratio
Null Hypothesis for Multiple Regression Analysis
null hypothesis (H0): B1 = B2 = B3... = Bn = 0 (no relationship between IVs and DV) alternative hypothesis (HA): at least one Bn= 0 (yes relationship)
dummy variable
numeric variable that represents nominal (categorical) data aka indicator/binary variables (takes on the values of 0 and 1)
scales that maintain labeling characteristics of nominal scales and have the ability to store data (can tell order but not the distance between)
ordinal data
data you can compute the median for
ordinal, interval, ratio
ANOVA (analysis of variance) test
test of difference- Difference among 3 + groups on one variable - numeric DV
Non-parametric chi-square test
test of difference- Difference between proportions - DV is a count or proportion (difference) (similar to independent samples t-test)
Measures of Dispersion- Descriptive Testing
standard deviation, variance, range
R > .7 (+/-)
strong relationship
Decision Rule: If we test hypothesis @ α = .05
we reject the null hypothesis if test indicates the probability of observed result is occurring by chance < 5 %
R < .3 (+/-)
weak relationship
Least Squares Line
y = a+bx + e Y = DV a = estimated Y-intercept b = estimated slope (regression coefficient) X = IV E = error (diff. Btw actual and predicted value)
