MKTG 460 Winter 2019 Solutions #1

Transcription

1 MKTG 460 Winter 2019 Solutions #1 Short Answer: Data Analysis 1. What is a data table and how are the data values organized? A data table stores the data values for variables across different observations, such as people, companies, etc. The values in a column are for a specific variable and the values in a row are for a specific observation. The first row usually contains the variable names. 2. What is a csv file? What are its properties, its primary advantage and its primary disadvantage? A csv file is a standard text file, that is, just text characters, the letters of the alphabet, digits, punctuation and a few control codes such as line return. It is a specific type of text file in which adjacent values on the same line are separated by comas. 3. What is the distinction between categorical and continuous variables? Provide an example variable of each along with some sample values. Nominal data are unordered categories, such as the numerals of football player jerseys. Ordinal data are ordered categories. Still not numeric, but Severe Injury indicates a greater amount of injury than Minor Injury. 4. Why do bar charts but not histograms have gaps between the bars? Bar charts for categorical variables. The gaps between the bars on a bar chart reflect the non-numeric lack of continuity. Histograms are for continuous variables. The bars on a histogram are joined to indicate the underlying continuity. 5. Identify and describe two properties of histogram bins that lead to arbitrariness in the histogram display. Bin width: vary the width of the bins and the shape of the histogram changes Bin shift: vary the starting point of the first bin and the shape of the histogram changes 6. What is the histogram artifact of undersmoothing and how does it relate to sample size? Describe a histogram that is undersmoothed? How can the problem be fixed? Undersmoothing occurs when the bin width is too narrow for the given sample size. The result is a histogram that has lots of jaggedness with too many ups and downs that reflect sampling error more than the actual shape of the distribution. Fix the problem by increasing 1

2 2 bin width. 7. What is the histogram artifact of oversmoothing and how does it relate to sample size? Describe a histogram that is oversmoothed? How can the problem be fixed? Oversmoothing occurs when the bin width is too wide for the given sample size. The result is a histogram that does not display as much detail as is available. Too much information is discarded. Fix the problem by decreasing bin width. 8. Compare the mean to the median Both values represent the middle of a distribution, but in two different ways. The mean is the balance point of deviations scores. A deviation score is mean subtracted from a data value. The mean is best for more or less symmetric distributions. The median is the middle of the sorted data values. As such it is less affected by outliers or a skewed distribution. If the last value of a distribution of income is $10000 or $ , the mean is greatly increased while the median is the unchanged. 9. What is an outlier and how does it affect data analysis? An outlier is a data value that is far from most of the other data values. This extreme data value may represent a data value from a different distribution, in which case it should not be included in the analysis with the remaining data values. Short Answer: General Marketing Research 1. How does marketing research relate to management decisions? Managers need to understand their environmentcustomers, market, suppliersand marketing research is used to turn gathered data into useful information regarding their environment 2. What is a market segmentation study? A Market Segmentation Study divides customers into groups according to relevant characteristics such as gender, location, and education level. Different groups of potential customers have different wants, needs and income, so marketers should understand the characteristic of the potential customers. 3. What is a market share and market size study? Market share and market size studies determine the products purchased, the volume purchased, and the actual size of sales being realized by each competitor. In other words, who

3 3 else is selling to our target market and how successful are they? 4. Longer question: List and briefly describe the nine steps in a market research study. a. Define the Management Problem Define the problem clearly for all team members to agree as to the nature of the problem b. State Research Purpose Gathering data can be expensive so clarify role of the research c. State the Research Objectives Specify the questions the research should answer d. Develop Research Design Plan how to obtain the answers your team is searching for, how the hypothesis is to be tested e. Select Data-Collection Methodology The methods, i.e., the protocol, used to gather the data f. Determine Measurement and Data-Analysis Methods Methods for analyzing the data g. Design Data-Collection Forms The forms that are to be filled in. The responses are the data values that measure the variables h. Define Sampling Methods Define the population or universe of the study to specify who can be selected for participation in the study according to the sample procedure i. Collect, Analyze and Interpret the Data, and Present the Results Interpret the results such that the analysis helps guide the team or client to make an informed decision

4 4 Worked Problems 1. Data Entry. Consider the data in Figure 1, randomly selected from a data file of the body measurements of thousands of motorcyclists. Figure 1: Gender, Height and Weight of eight motorcyclists. a. List each of the each variable names in Figure 1 and classify each as continuous or categorical. Gender: Categorical, M and F Height: Continuous Weight: Continuous b. Manually enter each data value from Figure 1 into a worksheet (such as Excel). Copy and paste the data table from your R output into your homework document. See Figure 1. c. Every data table, whether in R or Excel, has a name. What is the name of the worksheet (located on a tab toward the bottom left corner)? What is that name? Note the distinction between the name of the data table and the names of the variable. This is the same distinction in Excel or in R. By default, Excel names the first worksheet of an Excel file Sheet1. Though not necessary, for clarity, this default name could be changed to indicate actual name of the data table, such as HtWt or d. d. Read these data directly from the Excel file you created on your computer system into an R data table named d. You can enter the full path name as an argument to the Read function, but easier to browse for the data file, indicated by an empty character string "". Copy to your homework document the listing from the lessr Read function you used to read the data that displays the variable names, variable types, and first and last data values. The data table will also have a name when stored within R. Use the data table name d.

5 5 > d <- Read("") e. Verify that the data values for the variables in the R data table appear in the intended format. From the output of Read what is the type of each of these three variables that R assigned? What type does R assign to a non-numeric, categorical variable? Variable Missing Unique Name Type Values Values Values First and last values Gender character F F M... M F M 2 Height integer Weight integer NA The Read function lists the name of each variable read and the type of variable, here Gender is read as type character and Height and Weight are read as type integer. f. Display the data from within R with the print(d) function call and then copy to your homework document. Note that simply entering the name of the R object, here called d, is an abbreviation to invoke the print function. > d Gender Weight Height 1 F F M M F M F M Or, particularly useful for larger data tables, just to see the variable names and first 6 lines of data, use head(d). > head(d) Gender Weight Height 1 F F M M F M

6 6 g. From the previous answers, compare the data stored in Excel and then compare to the representation of the data stored in R. In particular, what does NA refer to in the R data table? The representations are the same, which is to be expected because the same data table is represented within Excel and within R. Gender is stored as an R character variable, which means as a categorical variable. The primary distinction is that a blank cell in Excel indicates missing data. R, instead, uses the code NA for numerical data and <NA> non-numeric data, each an abbreviation for Not Assigned. 2. Bar Chart (from data). A motorcycle clothing company makes jackets are of three types: Lite, Medium and Thick. The company needs guidance as to how many different jackets of each type to bring to a gathering of motorcyclists of a specific brand, here BMW or Honda motorcycles. The data are recorded from past sales of motorcycle jackets to owners of BMW or Honda motorcyclists. For now, we just analyze the type of jackets sold, and ignore the motorcycle type. Consider the data at a. Verify that there is an actual data file called Jackets.csv at the specified web address (URL) by pointing your browser at that URL. Take a screenshot of the first several lines of the data file and paste into your homework document. b. What is the format of that document? The data table is stored in a file in csv format, comma separated values, a simple text file with adjacent data values in a row of data separated by commas. c. How many variables are in the data file? What are their names? What is the relevant variable for this analysis? There are two variables in this data file, Bike and Jacket. Here we are only concerned with

7 7 Jacket, which indicates the style of Jacket sold. Describe the distribution of Jacket Types with: First read the data in the file BikeJacket.csv directly from the web into the R data table (frame) called d. Then do the requested text and graphic analyses with the lessr BarChart function. > d <- Read(" The output of the Read function summarizes the variables and their data values. Variable Missing Unique Name Type Values Values Values First and last values Bike character BMW Honda Honda... Honda BMW Jacket character Lite Lite Lite... Med Lite d. frequency table > BarChart(Jacket) --- Jacket --- Lite Med Thick Total Frequencies: Proportions: e. bar chart 300 Count of Jacket % 33% 30% Lite Med Thick Jacket f. pie chart

8 8 > PieChart(Jacket) Jacket 36% Lite Med 33% 30% Thick This version of a pie chart is called a doughnut chart or a ring chart. If you want to see the entire pie, set the size of the hole by entering any value from 0 to 1 for the hole parameter. The default value is pc(jacket, hole=0) Jacket 36% Lite Med 33% 30% Thick

9 9 Interpretation: Almost the same amount of Light, Medium and Thick jackets are sold, though there is a slight tendency in the data for the lighter the jacket the more sales. (A future homework will extend this analysis by relating to the second variable in the data set, Motorcycle Type.) 3. Histogram The data for this exercise are included with lessr, obtained when the package was downloaded. To access these built-in data sets, add the format="lessr" option to the Read statement. Here the data set is the Employee data. > d <- Read("Employee", in.lessr=true) a. Obtain the default histogram for Salary. As an option just to illustrate different styles, here change the default color theme to orange and add a black background such as might be appropriate for a slide presentation. > style("orange", sub.theme="black") > Histogram(Salary) 8 6 Count of Salary Salary b. What is the default bin width? Starting point of the first bin? The obtained frequency distribution shows a bin width of $10,000 with the first bin starting at $30,000. Bin Width: Number of Bins: 10 Bin Midpnt Count Prop Cumul.c Cumul.p >

10 > > > > > > > > > c. Interpret the histogram. Most of the salaries occur in the lower range of Salaries, with $40,000 to $60,000 being the most frequently occurring salaries. The distribution is skewed with a tail of less frequently occurring salaries in the upper end. The largest salary is $124, and the smallest is $63, d. Using the bin.width option deliberately over-smooth the histogram (bins too wide). What is wrong with this histogram? As an option only, try the "darkred" style. > style("darkred") > Histogram(Salary, bin.width=40000) Count of Salary Salary The problem is that the oversmoothed histogram wastes information in the sense that the given sample size allows for a smaller bin width and thus more information to be displayed in the histogram. This histogram does not match the data in that it starts high and then just lowers over three bins. In actuality, the distribution begins lower in frequency, achieves a peak around $40,000 to $60,000 and then gradually descends. e. Using the bin.width option deliberately under-smooth the histogram (bins too narrow). What is wrong with this histogram?

11 11 > Histogram(Salary, bin.width=2000) 4 3 Count of Salary Salary The problem with the undersmoothed histogram is that the bin width is too small for the available sample size. The result are sampling fluctuations illustrated by the zigging and zagging of the histogram that only represent random fluctuations, which would not replicate in future samples. 4. Analysis of Survey Data. The downloaded csv file of your responses to the class survey are on the web. The survey itself is also on the web. The survey was constructed and administered with Qualtrics, the survey administration system you will use for your project. If an item has a specific set of possible responses, Qualtrics labels a response to the first alternative as a 1, a 2 for a response to the second alternative, and so forth. a. Point your browser to the data file. Copy the first five or so lines into your homework document. Describe what you see. Learn_1,Learn_2,Learn_3,Learn_4,Feel_1,Feel_2,Feel_3,Feel_4,Past_1,Past_2,Past_3,Past_4,Past2_ 3,5,7,6,6,7,5,7,3,4,3,4,6,2,2,59,78,95,53 4,4,3,6,2,6,6,6,4,4,4,4,6,1,2,30,50,60,50

12 12 3,3,7,3,5,3,4,1,4,2,3,2,7,2,2,,,100, 4,4,5,5,2,6,4,5,2,2,1,2,6,1,2,50,39,70,60 6,6,5,6,3,6,4,3,2,3,4,3,13,2,2,60,100,50,91 b. Read the data into an R data table called d and then display the data from within R. [Just enter the name of the object, such as a data table, to display the contents of that object.] Show both the R instruction to do this, and then the data. Allow enough width to get all the columns of data across the console window by first enlarging the size of the R console window. > d <- Read(" > d Learn_1 Learn_2 Learn_3 Learn_4 Feel_1 Feel_2 Feel_3 Feel_4 Past_1 Past_2 Past_3 Past_4 Past2_1 Gender Class Learn2_1 Learn2_2 Learn2_3 Learn2_ NA NA 100 NA NA NA NA NA c. By direct examination of the data, what specific values are missing? Missing values are wherever an NA is reported. There are several. For example Person #3 has no data value for the last four variables in the data table, beginning with Learn2 1. d. To help locate the missing data, which R represents as NA, turn to the analysis provided by the initial details function. The Observation specifies the name of each row, here just the row number. To protect anonymity, student names were not collected as part of the data table. Missing Data Analysis n.miss Observation

13 Overall, there is not too much missing data in the analysis. The 3rd person did not respond to three of the last 4 items. People # 19, 20, 27 and 29 did not respond to one of the items. From the Read output, the variable with the most missing data is Past2 1, and it is only missing 4 responses. The analysis can proceed without much concern for missing data. e. Focus on the variable Learn2 1, measured on a response scale from 0 to 100. This variable is the first item listed on under the section Learn2 on the survey, which consists of the last four items on the survey. What is the item? I want to learn more of how to apply statistical techniques to marketing research. f. Plot the histogram and gather the summary statistics of Learn2 1. Put the item content for the Learn2 1 on the x-axis of the resulting histogram. [The lessr histogram function Histogram, or hs, provides both the histogram and summary statistics. The xlab option provides the content of the label on the x axis, which by default is the variable name.] But first a little fun. Optionally, change the default lessr color theme. > style("dodgerblue") By default R plots the histogram according to the range of observed values. It does not know the range of possible values according to the possible responses you had on your survey. Usually one wants to plot the histogram across the range of possible values. One way to do that is to specify that the bins start at 0 with the bin.start=0 specification. If needed, specify the ending value with bin.end option. > Histogram(Learn2 1, bin.start=0, xlab="i want to learn more of how to apply statistical techniques to marketing research.") g. Summarize in a few sentences the results of this analysis in terms of student attitudes toward the course regarding this item. The values of Learn2 1 span the complete range of values from 0 to 100. One person clearly has no interest to apply statistics to data analysis, but most of the values are between 40 and 90. The tendency is for the number of responses in a bin to increase as the value becomes larger, up to the value of 80. The bin with the most number of responses is for the largest scores, from 70 to 80.

14 14 12 Count of Learn2_ I want to learn more of how to apply statistical techniques to marketing research. Figure 2: Histogram fro Learn2 1.