Lab 2 STAT

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Auburn University *

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2010

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Statistics

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Apr 3, 2024

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STAT 3090 S ECTION 2 L AB S PRING 2024 Q UALITATIVE AND Q UANTITATIVE D ATA D ISPLAYS 1 N AME : Matt Schmidt P URPOSE : We have all made various displays of data throughout our lives either by hand or in software. The purpose of this lab is to introduce the statistical software JMP and explore its graphical abilities. O BJECTIVES : Upon successful completion of this lab, you wi ll be able to… • Identify the type of variable(s) in the context of a problem, • Create graphical displays, frequency tables, and relative frequency tables in JMP and by hand for categorical data, • Create histograms, stem and leaf plots, and dot plots for quantitative variables by hand and in JMP, • Make and support decisions on the best way to display data, • Use data displays to answer relevant questions. D IRECTIONS : Answer the following questions and include units whenever it is appropriate. Use complete sentences if you are asked to explain an answer. Please provide any appropriate output and/or screenshots from JMP. Paste your answers and any output into this document. If you would like to handwrite calculations, please insert a picture of your work into the appropriate question. Please delete the JMP instructions from your final document. P ART O NE Q UALITATIVE D ATA : 1. (30 points). Complete in WebAssign the Section 2 assignment. This can be completed anytime prior to the due date of the lab. 2. (20 points) Breakfast Cereal We will use the Cereal Data file built into JMP create a variety of graphical displays. Open the software JMP. Select Help >> Sample Data Folder and choose the data file Cereal . (a) Observe the column named “ Manufacturer ”, then classify the variable “ Manufacturer ” as: 1. categorical or quantitative, 2. nominal, or ordinal, or interval, or ratio. (5 pts) 1. categorical 2. nominal (b) Using only the Manufacturer column in the Cereal data set, create the following graphical displays in JMP. Copy and paste your tables and graphs into the space provided. (10 pts)

STAT 3090 S ECTION 2 L AB S PRING 2024 Q UALITATIVE AND Q UANTITATIVE D ATA D ISPLAYS 2 i. Frequency / Relative Frequency Table Step 1, create a frequency / relative frequency table. Use the following instructions to create a frequency/relative frequency table for the variable “ Manufacturer ”. Frequency table, relative frequency table, and histogram: 1. Look at the toolbar on the top and find Analyze. Click on it. 2. Click on Distribution, the first option. 3. Highlight the column of interest (In this problem it will be Manufacturer -> Click Y, Columns -> Click OK. Alternatively, you can drag the column to Y,Columns. 4. Click on the red arrow next to “Distributions” and select “Stack” to switch the histogram to be horizontal. Step 2, modify titles: Change the column titles of the table to Manufacturer, Frequency, and Relative Frequency instead of Level, Count, and Prob. To change a title, simply double-click the title and enter your own. Step 3, copy/paste your table: Right click on the table, and select Copy Table from the drop-down menu, then paste it here. Don’t close the JMP window. We will use it for bar chart next. Manufacturer frequency relative frequency American Home 1 0.01316 General Mills 25 0.32895 Kelloggs 23 0.30263 Nabisco 5 0.06579 Post 10 0.13158 Quaker Oats 12 0.15789 Total 76 1.00000 ii. Bar Chart Step 1, create a bar chart: We almost have a bar chart in the same JMP window when we created the frequency/relative frequency table. By default, JMP does not separate the bars. Make sure the bar chart is horizontal, otherwise check the JMP Instructions above. Step 2, modify axis/labels: For y-axis, click the red triangle to the left of the column heading (in this case it is Manufacturer). Select Histogram Options >> Count Axis or Prob Axis . This will place either the frequency or relative frequency axis on the bar chart depends on what you want to plot. Once more click the red triangle and select Display Options >> Axes on Left to change the location of y-axis. Change the label of the y-axis to

STAT 3090 S ECTION 2 L AB S PRING 2024 Q UALITATIVE AND Q UANTITATIVE D ATA D ISPLAYS 3 Frequency instead of Count, or Relative Frequency instead of Probability by single clicking on the default label. For x-axis, right click on the manufactures on x-axis and select Add Axis Label , then enter the name “Cereal Manufacturer s ”. Step 3, aesthetics: Click the red triangle again left to “ Manufacturer ” and select Histogram Options >> Separate Bars . If you would like to change the color of the bars, right click in the white space around the bars and select Histogram Color . Step 4, copy/paste your chart: Right click on the white space around the bars and select Edit >> Copy Graph , then paste it here. iii. Pie Chart Create a pie chart of the manufacturer data. Step 1, create a basic pie chart: 1. Click on Graph in the toolbar on top. 2. Click on Graph Builder, the first option. 3. Click Pie Chart picture. 4. Drag the variable of interest into white zone in the middle. Step 2, add counts or percentages: Use the Label dropdown on the bottom left of the Graph Builder window. Choose “Label by Value” or “Label by Percent of Total Values” depend ing on what you want. Step 3, copy/paste your chart: Copy and paste your chart here. To copy the pie chart, right click on the chart, go to Edit >> Copy Graph. This should both copy the graph

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STAT 3090 S ECTION 2 L AB S PRING 2024 Q UALITATIVE AND Q UANTITATIVE D ATA D ISPLAYS 4 and the legend. (c) Do you prefer the bar chart or the pie chart? Explain your choice in a few sentences. (5 pts) I prefer the bar chart. It shows the values relative to each other much better than the pie chart. The pie chart displays its values well, but the differences are much easier to see on a bar graph. 3. (20 points) Dividing Data Let’s separate the cereal manufacturer data based on whether the cereal is a hot cereal or a cold cereal and create a crosstabulation table. (a) Make a crosstabulation table to divide the cereal into whether it is a hot or cold cereal. (5 points) Step 1: In JMP go to Analyze >> Tabulate .

STAT 3090 S ECTION 2 L AB S PRING 2024 Q UALITATIVE AND Q UANTITATIVE D ATA D ISPLAYS 5 Step 2: Drag Manufacturer to “ Drop zone for columns ” first. Then, drag Hot/Cold to the first column, second row of the table that is created. Step 3: Select “Add Aggregate Statistics” .

STAT 3090 S ECTION 2 L AB S PRING 2024 Q UALITATIVE AND Q UANTITATIVE D ATA D ISPLAYS 6 Step 4: Copy and paste your table below. You can use a screenshot. (b) Use the crosstabulation table to find the proportion of all Cold cereals that are manufactured by Quaker Oats . (5 pts) 11/73 (c) Use the Graph Builder feature in JMP to make a side-by-side or stacked bar chart for Manufacturer that separates the cereals by hot and cold. (10 points) Step 1, create a bar chart: Go to Graph >> Graph Builder . Select the bar graph tab at top then place the Manufacturer column on the horizontal axis. Step 2, add in the Hot/Cold information: Place the Hot/Cold column into the box on the right of the graph labeled Overlay . The default graph will be a side-by-side bar chart of the manufacturers with the frequency on the vertical axis. By selecting on the left the drop- down menu for “ Bar Style ” you can switch to the stacked bar chart. (Optional) Step 3, explore other settings: Experiment with the different types of bar charts JMP produces. On the lower left of the Graph Builder window are various options for the graph. Change the Bar Style options and choose the one you like the best. Also experiment with the Summary Statistic options. The default statistic is Mean , which provides you with the frequencies on the vertical axis. Experiment and see what happens when you change the Summary Statistic from Mean to % of Total , or some of the other options. Be careful that you understand how the information is being displayed. Step 4 copy/paste your chart: Right click on the chart, go to Edit >> Copy Graph, paste it here.

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STAT 3090 S ECTION 2 L AB S PRING 2024 Q UALITATIVE AND Q UANTITATIVE D ATA D ISPLAYS 7 P ART T WO Q UANTITATIVE D ATA : 4. (20 points) Candy Bar Calories (a) Open the file candy bars in JMP. Select Help >> Sample Data Folder and choose the data file Candy Bars . Look at the data in the column Calories . Is Calories a nominal, ordinal, interval or ratio? Explain your answer. (2 pts) Ratio. It has both equidistant scales and a true zero, making it a ratio measurement. (b) Using JMP, create a histogram for the Calories data. Use the following basic steps. You may explore additional changes if you wish such as changing the color. (5 pts)

STAT 3090 S ECTION 2 L AB S PRING 2024 Q UALITATIVE AND Q UANTITATIVE D ATA D ISPLAYS 8 Step 1: Select Analyze >> Distribution from the JMP menu bar Step 2: Place the column Calories into the field for Y, Columns, and select OK. Step 3: Select the red triangle next to the word Distributions in your output. From the drop-down menu choose Stack . This places your output into a horizontal format.

STAT 3090 S ECTION 2 L AB S PRING 2024 Q UALITATIVE AND Q UANTITATIVE D ATA D ISPLAYS 9 Step 4: Add a horizontal and vertical axis. To add the horizontal axis label put, put the cursor over this axis until you see it change to a hand symbol. Right click on the horizontal axis and select Add Axis Label . To add a vertical axis: • Select the red triangle next to the word Calories . From the dropdown menu choose Display Options >> Axis on Left. • Select the red triangle next to the word Calories again and select Histogram Options . Add either the Count Axis (frequency) or Prob Axis (relative frequency) Step 5: Copy and paste your histogram here. Right click on the histogram, go to Edit >> Copy Graph, paste it here. (c) JMP has chosen a default bin width for the histogram. What is your default bin width? (1 pts) 50 (d) Change the default bin width to something else. To change the bin width select the red triangle next to the word Calories and choose Histogram Options . In the next dropdown menu select Set Bin Width . You may experiment with different bin

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STAT 3090 S ECTION 2 L AB S PRING 2024 Q UALITATIVE AND Q UANTITATIVE D ATA D ISPLAYS 10 widths and their effect on your histogram. Bin widths are subjective. Select one that you like then copy and paste the resulting histogram here. (3 pts) (e) Have JMP make a stem and leaf diagram. To add the stem and leaf diagram select the red triangle next to the word Calories and choose Stem and Leaf . Pay attention to the key and how JMP creates a stem and leaf diagram for this data. Copy and paste the resulting diagram here. (3 pts) (f) Use JMP to create a dot plot of the Calories Data. (3 pts) Step 1: Go to Graph >> Graph Builder . Place the column Calories on the horizontal axis. At the top of the window, be sure only the scatterplot icon is selected.

STAT 3090 S ECTION 2 L AB S PRING 2024 Q UALITATIVE AND Q UANTITATIVE D ATA D ISPLAYS 11 Step 2: On the bottom left under the heading Points , select Jitter >> Positive Grid. Step 3: Copy and paste your dot plot here. (g) In a sentence or two, describe the shape of the data distribution for Calories (see section 2.3.5 of the lecture guide). You may use any of the graphical displays from this problem to assist you. (3 pts) It looks like a bell curve. 5. (10 points) Candy Bars: Calories and Fat Content Relationship Use the Calories and Total Fat variables from the Candy Bars data set to determine if there is a linear relationship between these two variables.

STAT 3090 S ECTION 2 L AB S PRING 2024 Q UALITATIVE AND Q UANTITATIVE D ATA D ISPLAYS 12 (a) Use JMP to make a scatterplot. (5 pts) Go to Graph >> Graph Builder . Place the column Calories on the horizontal axis and Total Fat on the vertical axis. At the top of the window, be sure only the scatterplot icon is selected. Copy and paste the scatterplot below. (b) Using your scatterplot, write a sentence or two explaining whether there appears to be a positive linear relationship, negative linear relationship, or no linear relationship between the two variables (see section 2.4.2). (5 pts) There is a positive linear relationship between the number of calories in the candy bar and the total grams of fat. If a candy bar has more calories, the amount of fat goes up as well. Less calories also equals less fat.

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Lab 2 STAT

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