Ch 11: Basic Data Analysis for Quantitative Research Flashcards
Market analytics can help __________
better understand the responses
Almost all data needs summary statistics to ___
describe the information it contains
Statistical Analysis
every set of data collected needs a summary developed that describes the number it contains
Three types of statistical analysis
Central Tendency & Dispersion
Relationships of the Sample Data
Hypothesis Testing
Measures of Central Tendency
Mean, Median, Mode
What do the measures of central tendency locate?
the center of the distribution
Likely to recommend X to a friend
7-point scale (Interval Scale) Question
Mean
The arithmetic average of the sample. All values of the distribution are added and divided by the number of responses.
Median
The middle value of a rank-ordered distribution. Exactly half the value is above and half are below the value.
Mode
The most common value in the set of responses in a question. The most given responses to a question.
Mean should only be calculated with _____
interval and radio data.
Median and Mode can be calculated on _____
all types of data.
x24 – Likely to Recommend Restaurant to a Friend – Jose’s Mean (4.07) is higher than Santa Fe Mean (3.61). This means _____________
Jose’s customers are more likely to recommend that restaurant to others than are the customers of Santa Fe.
Mean is the most commonly used measure of central tendency (T/F)
True
Mean is fairly insensitive to data values being added or deleted. (T/F)
True
If extreme values are added to the distribution, the Mean is NOT subject to distortion. (T/F)
False
Compare coffee consumption between two groups: Male and Female.
A=1 cup, B=10 cups, C=5 cups, D=6 cups.
Males (A+B) = 1+10= 11 / 2 = 5.5
Females (C=D) = 5+6=11 / 2 = 5.5
By looking at the mean, you don’t see any differences between the two groups. However, considering _____________ , we must conclude there are some differences. Therefore, the mean is ________ our understanding of coffee consumption patterns of males and females.
Underlying Distribution, Distorting
The Median is ordered in ONLY ascending sequence. (T/F)
False.
If the Median number of coffee cups consumed is 4, that means ___________________
the number of cups of coffee consumed above and below this number would be the same.
If there is an even number of data observations, the median is generally considered to be __________
the average of two middle values
If there is an odd number of data observations, the median is generally considered to be __________
middle value
Ordinal data and skewed data (left or right) are most useful for which measure of central tendency?
Median
Income data is skewed right since there is no upper limit on income. Which measure of central tendency is best for this?
Median
The mode represents the _________ in the distribution’s graph.
highest peak
The mode is especially useful as a measure of data that has been somehow grouped into categories. (T/F)
True
Each measure of central tendency has its own strengths and weaknesses. (T/F)
True
Nominal data best measure is ___
Mode
Ordinal data best measure is ____
Median
Interval or Radio data best measure is ___
Mean, except when there are extreme values/outliers
When outliers are present, the __________ are likely to provide more useful information about the central tendency of the distribution.
median and mode
If you want to report the mean with outliers, you should _______
remove the outliers first
Measures of Dispersion
Range, Standard Deviation, Variance
What do measures of dispersion describe?
How close the mean, or other measures of central tendency, fall
Using measures of dispersion, you can find out if most of the respondents had similar opinions. (T/F)
True
Range and Standard Deviation describe the ________
variability in a distribution of numbers
Range
The distance between the smallest and largest values in a set of responses; the spread of data.
Standard Deviation
The average distance of the distribution values from the mean
Variance
The average squared deviation about the mean of a
distribution of values
Definitely will recommend (7) and Definitely will not recommend (1) for – Variable x24 : Likely to Recommend.
Ranges: Santa Fe: 4, Jose Cafe: 5
What is the maximum possible range?
6.
7-1
If we subtracted each value in a distribution from the mean and added them up, the result would be ________
close to zero
Square the individual deviations before we add them up
How to calculate the estimated standard deviation Formula
If the estimated standard deviation is small…
you know the distribution values are close to the mean
If the estimated standard deviation is large…
the responses in the distribution of numbers do not fall very close to the mean of the distribution.
What does the size of the estimated standard deviation tell you?
something about the level of agreement among respondents when they answered a particular question.
Which descriptive statistics reveal a lot about the distribution of a set of numbers representing the answers to an item on a questionnaire?
Central tendency and measures of dispersion
Preparation of Charts
Charts and other visual communication approaches should be used whenever practical
the preparation of charts helps information users quickly grasp the essence of results developed in data analysis and can be an effective ________ & ________
Visual aid to enhance the communication process,
Add clarity and impact to research reports and presentations
a bar chart shows
tabulated data in the form of bars that may be horizontally or vertically oriented.
Researchers have preliminary ideas
regarding data relationships based on
research objectives (T/F)
True
Hypotheses
Ideas derived by
researchers from previous research,
theory and/or the current business
situation
The hypothesis is developed prior to data collection, As a part of the _______
research plan
Null hypothesis
Based on the notion
that any change from the past is due
entirely to random error
Alternative hypothesis
States the opposite of the null hypothesis
The ___ hypothesis is no difference in the group means, while ____ hypothesis is that there is a difference between the group means.
null, alternative
Methods to test hypotheses
Chi-square analysis, t distribution
Sample statistics
are useful in making inferences regarding the population’s parameter
Population parameter
A variable or some
sort of measured characteristic of the
entire population
sample statistics are measures obtained ____
directly from the sample or calculated from the data in the sample
actual population parameters are unknown due to the cost of the true census and are
prohibitive
A nominal scale is appropriately measured with the central tendency ____, with the measure of dispersion ____, and the appropriate statistic is ______
Mode, None, Chi-Square (non-parametric)
An ordinal scale is appropriately measured with the central tendency ____, with the measure of dispersion ____, and the appropriate statistic is ______
Median, Percentile, Chi-Square
An Interval or Ratio scale is appropriately measured with the central tendency ____, with the measure of dispersion ____, and the appropriate statistic is ______
Mean, Standard Deviation, T-test/ANOVA (parametric)
Considerations influencing the choice of appropriate statistical technique
number of variables, the scale of measurements, parametric versus nonparametric statistics
Univariate Statistical Tests
Used to test hypotheses when
a researcher wishes to test a proposition
about a sample characteristic against
a known or given standard
the major difference between parametric and nonparametric lies within the
underlying assumptions about the data
Example of propositions for Univariate Statistical Test
- the new product or service will be preferred by 80% of our current customers
- more than 50% of current coke zero customers will prefer the new coke zero that includes a lime taste.
Bivariate Statistical Tests
Test hypotheses that compare the
characteristics of two groups or two
variables
Three types of bivariate hypothesis
tests
– Chi-square – nominal
– t-test – compare two means
– Analysis of variance – compare three+ means
Cross-Tabulation
Useful for examining relationships and
reporting the findings for two variables
the purpose of cross-tabulation is to
determine if differences
exist between subgroups of the total
sample
Cross-tabulation is one of the simplest methods for describing sets of relationships. It’s purpose is to
determine if differences exist between subgroups of the total sample
Example questions that can be answered with chi-square analysis with cross-tabulations
Does frequency of dining (very, frequent,somewhat) differ between Santa Fe Grill and Hose’s Cafe?
Is brand awareness (aware/unaware) related to the geographic area in which people live? (NA, Europe,Asia,Africa,etc)
Chi-Square Analysis
Assesses how closely the observed
frequencies fit the pattern of the
expected frequencies
– Referred to as a “goodness-of-fit” test
Independent samples
Two or more groups of responses that are tested as
though they may come from different
populations
Two or more groups of
responses that originated from the
sample population
Related samples
Using the t -Test to
Compare Two Means
t-test: A hypothesis test that utilizes
the t distribution
– Used when the sample size is smaller than
30 and the standard deviation is unknown
Analysis of Variance (ANOVA)
A statistical technique that determines
whether three or more means are
statistically different from one another
Null hypothesis for ANOVA always
states that
there is no difference
between the dependent variable group
Analysis of Variance
(ANOVA)
• F-test:
The test used to statistically
evaluate the differences between the
group means in ANOVA
Follow-up tests:
A test that flags the
means that are statistically different
from each other
follow up tests are performed after an
ANOVA determines
there are differences between means
n-Way ANOVA
A type of ANOVA that can analyze
several independent variables at the
same time
n-Way ANOVA
Multiple independent variables in an
ANOVA can act together to affect
dependent variable group means
Perceptual Mapping
Used to develop maps showing the
perceptions of respondents
Maps are visual representations of
respondents’ perceptions of
a company, product, service, brand, or
any other object in two dimensions
three Approaches used to develop
perceptual maps
- Rankings
– Medians
– Mean ratings
Perceptual Mapping
Applications in Marketing
Research
- New-product development
- Image measurement
- Advertising
- Distribution
independent samples
two or more groups of responses that are tested as though they may come from different populations
related samples
two or more groups of responses that originated from the sample population
interaction effect
multiple independent variables in an ANOVA can act together to affect dependent variable group means
new product development
perceptual mapping can identify gaps in perceptions and thereby help to position new products
image measurement
perceptual mapping can be used to identify the image of the company to help to position one company relative to the competition
advertising
perceptual mapping can assess advertising effectiveness in positioning the brand
distribution
perceptual mapping could be used to assess similarities of brands and channel outlets
