Marketing Research Final Exam Study Guide PDF

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Marketing Research Final Exam Study Guide Ch. 12 Using Descriptive Analysis, Performing Population Estimates, and Testing Hypothesis Types of Statistical Analyses Used in Marketing Research -

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Dataset= an arrangement of numbers in rows and columns o Columns= answers to the various questions on the survey questionnaire o Row= a respondent Data Analysis= the process of describing a dataset by computing a small number of statistics that characterize various aspects of the data. o Distills the dataset while retaining enough info. so the client can mentally envision its salient characteristics. 5 basic types of statistical analyses used to reduce a dataset: o Descriptive Analysis o Inferential Analysis o Differences Analysis o Associative Analysis o Predictive Analysis

Descriptive Analysis (1)

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Descriptive Analysis= used to describe the variables (answers to questions) in a dataset (all respondents’ answers) o Uses mean, median, mode, range, and standard deviation to describe the sample dataset in such a way as to portray the “typical” respondent and to reveal the general pattern of responses. o Describes the typical respondent, describes how similar respondents are to the typical respondent. o Summarizes basic findings for the sample o Typically used early in the analysis process and become foundations for subsequent analysis o Non probability samples

Inference Analysis (2)

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Inference Analysis= using statistical procedures to generalize the results of the sample to the target population it represents. o Allow a researcher to draw conclusions about the population based on info. in the dataset provided by the sample. o Include hypothesis testing and estimating true population values based on sample info. o Estimates population values o Standard error, null hypothesis

Difference Analysis (3)

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Difference Analysis= used to determine the degree to which real and generalizable differences exist in the population to help the manager make an enlightened decision on which advertising theme to use. o Used to compare the mean of the responses of one group to that of another group, such as satisfaction ratings for “heavy” users vs “light” users. o Evaluates the statistical significance of difference in the means of two groups in a sample. o t test for significant differences between groups and analysis of variance. o Look to see how 2 or more groups answered the questions

Association Analysis (4)

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Association Analysis= investigates if and how two variables are related. o When you want to see to see if 2 or more variables are related in a systematic way o May indicate the strength of the association and/or direction of the association between two questions on a questionnaire in a given study. o Deterines if two variables are related in a systematic way o Determines simple relationships o Cross tabulations, correlation

Predictive Analysis (5)

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Predictive Analysis= used to help make forecasts about future events. o Finds complex relationships for variables in the dataset o Allows insights into multiple relationships among variables o Determines how several independent variables influence a dependent variable o Involves forecasting and Multiple regression analysis o Complex data analysis

Understanding Data via Descriptive Analysis -

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Only kind of analysis you can do with a convenience sample is descriptive statistics. The rest don’t apply with a convenience sample. Descriptive Statistics: o Can find the center of the data- Measures of central tendency o Can find the spread of the data- measures of variability o Can find the shape of the data- bell shape curve 2 sets of measures are used extensively to describe the info. obtained in a sample o Measures of central tendency or measures that describe the “typical” respondent or response o Measures of variability or measures that describe how similar (dissimilar) respondents or responses are to (from) “typical” respondents or responses

Measures of Central Tendency: Summarizing the “Typical” Respondent

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Basic goal is to report a single piece of info. that describes the most typical response to a question. Central tendency= any statistical measure used that somehow reflects a typical of frequent response 3 measures used as data analysis devices: o Mean o Median o Mean Mode= that value in a string of numbers that occurs most often. o Relative measure of central tendency, for it doesn’t require that a majority of responses occurred for this value. o Can take on any value as long as it is the most frequently occurring number. o If a tie for the mode occurs, the distribution is considered to be “bimodal” or “trimodal” for a three-way tie. o Works with nominal data o Can be more than 1 mode o Where the lump of data is Median= expresses the value whose occurrence lies in the middle of an ordered set of values. o Tells us the approximate halfway point in a set or string of numbers that are arranged in ascending or descending order while taking into account the frequency of each value. o Supplies more info. than does the mode, for a mode may occur anywhere in the string, but the median must be at the halfway point. o The middle of the data set o Can be used for ordinal data, sometimes better to use if you have outliers Mean= the arithmetic average of a set of numbers. o Differs from median and mode in that a computation is necessary. o All numbers are summed and that total is divided by the number of members in that set.  Resulting number is a measure that indicates the central tendency of those values. o Approximates the typical value in that set of values o More informative than the median and can be plotted for quick interpretations o Problem: can be distorted by outliers, doesn’t work with all types of data. o Will ONLY work for interval or ratio NOT nominal or ordinal

Measures of Variability: Visualizing the Diversity of Respondents -

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Measures of central tendency do not indicate the variability of responses to a particular question or, alternatively, the diversity of respondents on some characteristic measured in our survey. Measures of Variability= reveal the “typical” difference between the values in a set of values. Knowing the variability of the data could greatly influence a marketing decision based on the data because it expresses how similar the respondents are to one another on the topic under examination. 3 measures of variability:

o Frequency distribution o Range o Standard Deviation -

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Frequency Distribution= a tabulation of the number of times that each different value appears in a particular set of values. o Frequencies themselves are raw counts, and normally these frequencies are converted into percentages for ease of comparison. o Quickly communicates all the different values in a set, and it expresses how similar the values are. o Percentage distributions are often used b/c people often easily relate to percentages  distributions are often presented as pie or bar charts. Range= identifies the distance between lowest value (minimum) and the highest value (maximum) in an ordered set of values. o Specifies the difference between the endpoints in a set of values arranged in order. o Doesn’t provide the same info as a freq. dist., but it identifies the interval in which the set of values occurs o Doesn’t tell you how often the minimum and maximum occurred, but it does provide some info. on the dispersion by indicating how far apart the extremes are found. Standard Deviation= indicates the degree of variation or diversity in the values in such a way as to be translatable into a normal or bell-shaped curve distribution. o The std. deviation and variance gives you the avg. distance from all the variables in a data set from the endpoints o Marketing researchers often rely on the standard deviation when performing basic analyses o On a bell curve, exactly 50% of the distribution lies on either side of the midpoint (the apex of the curve).  With a normal curve, the midpoint is also the mean.  Standard deviations are known units of measurement that are located on the horizontal axis. They relate directly to assumptions about the normal curve. o Because the bell-shaped curve is a theoretical or ideal concept, this property never changes. Moreover, the proportion of area under the curve and within plus or minus any number of standard deviations from the mean is perfectly known.  The Standard Deviation embodies the properties of a bell-shaped distribution of values. o Calculating Standard Deviation:  The standard deviation is a measure of the differences of all observations from the mean, expressed as a single number.  The squaring operation in the standard deviation formula is used to avoid the cancellation effect.  Variance= the standard deviation squared  If the standard deviation is small, the distribution is greatly compressed (with a high peak)

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If the standard deviation is large, the distribution is consequently flat because it is stretched out at both ends.

When to Use a Particular Descriptive Measure -

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As a general rule, statistical measures that communicate the most amount if information should be used with scales that contain the most amount if information, and measures that communicate the least amount of information should be used with scales that contain the least amount of information. What Descriptive Statistic to Use When Example Question

Measurement Level

What is your gender?

Nominal Scale

Central Tendency (The most Typical Response) Mode

Variability (How Similar the Responses Are) Frequency and/or Percentage distribution Cumulative percentage distribution

Rank these 5 brands from your 1st choice to your 5th choice. On a scale of 1-5, how does Starbuck’s rate on variety of its coffee drinks? Last week, about how many times did you buy fast food for lunch

Ordinal Scale

Median

Interval Scale

Mean

Standard deviation and/or Range

Ratio Scale

Mean

Standard deviation and/or Range

The Global Motors Survey: Obtaining Descriptive Statistics with SPSS Obtaining a Frequency Distribution and the Mode with SPSS -

With a nominal scale, a frequency distribution and mode are the appropriate measures of central tendency Use the ANALYZE-DESCRIPTIVE STATISTICS-FREQUENCIES procedure to produce descriptive statistics for variables with nominal or ordinal scaling Steps: o 1 Use descriptive statistics frequencies to open the frequencies window o 2 select variables to be analyzed. Click on statistics… o 3 click a check mark for “mode” and click Continue to return to the Frequencies window o 4 After selecting variables and Statistics, click OK to perform analysis

Reporting Descriptive Statistics to Clients -

It’s the researcher’s responsibility to build tables, graphs, or other presentation methods to efficiently and effectively communicate the basic findings to a manager

Reporting Scale Data (Interval and Ratio Scales) -

Scale data is sum

Descriptive Measure Average (mean)

For a Standard Scale Variable table… Absolutely include as averages are the most commonly used central tendency measure for scale data

Median, Mode

Do not Include.

Standard Deviation

Typically include in a table

Minimum, Maximum

Include of the data has several different values.

Comment Place averages in a column very close to the variable descriptions and arrange variables in ascending or descending order of the averages. Managers do not relate to medians or modes of scale data. If most standard deviations are approximately equal, do not include as redundancy would result. Reporting the same value several times is redundant.

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marized with the following descriptive measures: average, median, mode, standard deviation, minimum, and maximum - Recommendations for what to include in a standard scale variable table:

Descriptive Measure Frequencies, Frequency Distribution

For a Standard Categorical Variable Table… Include of the researcher wants the reader to note something about the sample such as a very small sample where percents are greatly affected by a few respondents

Percents, Percent Distribution

Absolutely include as percents are the most commonly used descriptive measure for nominal data.

Mode

Highlight, but if obvious, do not report in the table.

Comment Place frequencies in a column very close to the variable group labels (such as male, female, etc.). If appropriate, arrange the categories in ascending or descending order of the percents. Include a total of frequencies at the bottom. Place percents in a column close to the variable group labels and beside the frequencies, if used. If appropriate, arrange the categories in ascending or descending order of the percents. Include a 100% total at the bottom. The largest percentage group is usually readily apparent in a percent distribution and especially if ascending or descending

Reporting Nominal or Categorical Data -

Nomin al data is

summarized with following descriptive measures: frequencies, frequency distribution, percents, percent distribution, and mode. o Important to note that only one categorical variable is summarized in each table because the categories are unique to each variable.

Statistical Inference: Sample Statistics and Population Parameters -

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Statistics= values that are computed from the info. provided by a sample. Parameters= values that are computed from a complete census, which are considered to be precise and valid measures of the population. Statisticials use GREEK LETTERS when referring to population parameters and ROMAN LETTERS when referring to statistics. o Every sample has a corresponding population parameter. Inference= a form of logic in which you make a general statement (a generalization) about an entire class based on what you have observed about a small set of members of that class. o When you infer, you draw a conclusion from a small amount of evidence such as a sample. Statistical Inference= a set of procedures in which the sample size and sample statistics are used to make an estimate of the corresponding population parameter. o Statistical inference has formal steps for estimating the population parameter based on the evidence of the sample statistic and taking into account the sample error based on sample size. o Statistical inference takes into account that large random samples are more accurate than are small ones. o Statistical inferences is based on sample size and variability, which then determine the amount of sampling error. o With statistical inference for estimates of population parameters such as the percentage or mean, the sample statistic is used as the beginning point, and then a range is computed in which the population parameter is estimated to fall. 2 types of statistical inferences: o Parameter estimates o Hypothesis tests Parameter estimate= used to approximate the population value (parameter) through the use of confidence intervals. Hypothesis testing= used to compare the sample statistic which is believed (hypothesized) to be the population value prior to undertaking the study.

Parameter Estimation: Estimating the Population Percent or Mean -

Parameter estimation= the process of using sample info. to compute an interval that describes the range of a parameter such as the population mean (µ) or the population percentage (π). o Involves the use of 3 values:  Sample statistic (such as the mean or percentage)  Standard error of the statistic  Desired level of confidence (usually 95% or 99%)

Sample Statistic -

In parameter estimation, the sample statistic is usually a mean or a percentage

Standard Error -

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There is usually some degree of variability in the sample. If you theoretically took many, many samples and plotted the mean or percentage as a frequency distribution, it would approximate a bell-shaped curve called the sampling distribution. Standard Error= a measure of variability in the sampling distribution based on what is theoretically believed to occur were we to take a multitude of independent samples from the same population. Standard Error of the mean:

s x´ =

s √n

Sx= standard error of the mean s= standard deviation n= sample size

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Standard Error of the percentage: Sp= standard error of the percentage p= the sample percentage q= (100-p) n= sample size

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s ´p=

√

pxq n

The sample standard error will be smaller with larger samples, and larger with smaller samples. In either equation, the variation is in the numerator, so the greater the variability, the greater the standard error o This, the standard error simultaneously takes into account both the sample size and the amount of variation found in the sample.

Confidence Intervals -

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Because there is always some sampling error when a sample is taken, it is necessary to estimate the population parameter with a range. One factor affecting the size of the range is how confident the researcher wants to be that the range includes the true population percentage (parameter). o The researcher first decides how confident they want to be. o The sample statistic is the beginning of the estimate, but b/c there’s a sample error present, a “plus” amount and an identical “minus” amount are added and subtracted from the sample statistic to det. the max. and min., respectively, of the range. Confidence intervals= the degree of accuracy desired by the researcher and stipulated as a level of confidence in the form of a range with a lower boundary and an upper boundary. 99% confidence= ±2.58 standard errors

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95% confidence= ±1.96 standard errors 90% confidence= ±1.64 standard errors Most commonly used level of confidence in marketing research is the 95% level, corresponding to ±1.96 standard errors. The range of your estimate of the population mean or percentage depends largely on the sample size and the variability found in the sample. Confidence Interval for a mean:

´x ± z ∝ s x´ X bar= sample mean z= z value for a lvl of confidence sx= standard error of the mean

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Confidence Interval for a Percentage:

p± z ∝ s p

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p= sample percentage z= z value for a lvl of confidence sp= standard error of the percentage

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How do these formulas relate to inference? o We are indicating a range into which it is believed that the true population parameter falls. o The size of the range is determined by those pieces of info. we have about the population on hand as a result of our sample. o The final ingredient is our level of confidence or the degree to which we want to be correct in our estimate of the population parameter.

How to Interpret an Estimated Population Mean or Percentage Range -

Statistical inference procedures are the direct linkages b/t the probability sample design and data analysis. Confidence intervals must be used when estimating population parameters, and the size of the random sample used is always reflected in these confidence intervals. Detailed confidence intervals are typically not reported.

Hypothesis Tests -

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Hypothesis= ...