Chapter 2 Assignment (due Thursday, April 19)

Transcription

1 (due Thursday, April 19) Introduction: The purpose of this assignment is to analyze data sets by creating histograms and scatterplots. You will use the STATDISK program for both. Therefore, you should start by downloading the STATDISK Version 13 program. A link to the textbook website is given on the Links and Information page of our class webpage, plus I did a demo in class. To start the program, just double-click on the Statdisk.exe file (or icon), and it should open looking approximately like this: There are datasets preloaded into the program. To open them, just go to Data Sets/Elementary Statistics 13 th Edition, and pick a file. For example, I will open up the Bear Measurements dataset to use as an example throughout this assignment file (Data Set no. 9). You might want to open this file and run through it with the examples as practice. Page 1 of 16

2 You can click and drag the corner of the data box to make the box bigger. Also, if needed, you can scroll over to the rest of the columns using the scroll bar at the bottom of the window (for example, there are 9 columns of data in this file). There are two parts to the assignment: Part A: Frequency Distributions and Histograms Part B: Scatterplot Page 2 of 16

3 Part A Frequency Distributions and Histograms The data that you will be analyzing for this assignment deals with the smoking prevalence of the world s population (persons aged 15 and over), listed by country and gender. This data is from the United Nations Statistics Division, and it is accurate as of The data is given for 149 countries in the world, and it is given as a percentage (%) of the country s male and female population who are smokers. There is one set of data for males in each country, and one set of data for females in each country. You are going to create two different frequency distributions and histograms for this part of the assignment. You will use data in the Excel file smoking_by_gender_un_2009 which is posted on the Assignment page. Source of data: Notice that the units of measurement are in percent (%), representing the % of the country s population (male or female) that are smokers. You need to copy the data from the Excel file into STATDISK. Start STATDISK, so all of the data columns should be empty. In Excel, make sure that you are on the STATDISK data tab, the tabs are labeled at the bottom of the spreadsheet. You can copy both columns of data over at the same time. All you want to copy over are the numbers in columns B and C, you do not want to copy over the country names or the column headers. Therefore, in the Excel file, click on cell B5, which is the first data value (60). Keeping your mouse button down, drag all the way down and over to cell C153, which is the last data value (4). Now when you release the mouse button, the columns of numbers should be highlighted. Page 3 of 16

4 Then just hit Ctrl c (shortcut command for copying). So you hold the Control button down on your keyboard, and hit the letter c at the same time. Now transfer over to STATDISK, click in the very upper left cell (row 1 column 1), and hit Ctrl v (shortcut command for pasting). Both columns of numbers should now be pasted into STATDISK. Scroll down to confirm that you did get all 149 rows of numbers copied over. I would suggest that you go to Data Tools/Edit Column Titles, and add appropriate column headers for the data (Male and Female), just to keep them straight. Making the Frequency Distributions and Histograms In both cases, use the continuous data method to set up your data classes. Use the following starting lower class limits and class widths for the frequency distributions: Dataset Starting Lower Class Width Class Limit Male % Smokers (Column 1) 0 10 Female % Smokers (Column 2) 0 5 Fill in all of the details of the frequency distributions on the Answer Sheet given at the end of the assignment. To set up the class limits, notice that both columns of data are given in integers, so write your class limits accordingly. Use the histogram (instructions below) to find the frequencies for each data class, just by checking the Bar labels button at the bottom of the histogram. Disclaimer: I noticed that sometimes if you change something in the histogram and replot it, the bar labels (frequencies) disappear. Just uncheck and recheck the Bar labels button and they should reappear. Page 4 of 16

5 If you wanted to, you can verify counting up the frequencies by hand (like we did in class), by looking at the sorted data. If you need to sort data (smallest to largest), go to Data Tools/Sort Data. Then select the Sort/One column, pick the column number, leave the order from A to Z and hit the Sort button. You don t need to do this in this case, since your histogram has counted them up for you (plus I already sorted them in Excel, given on separate sorted tabs of the spreadsheet), but it s handy to know how to sort the data in STATDISK, and you may want to use this in the future for quizzes or assignments. Also, you will need to know how to do this process by hand on the test. To create the histograms, go to Data/Histogram. Select the column of data that you want to plot, and then hit the Plot button. STATDISK will auto-fit the plot options for you, and generate a histogram. For example, I am plotting the head length of the bears (column 4). Page 5 of 16

6 In most cases, you will want to define your own plot options, including the Class width and the Class start (starting lower class limit). To do this, click on the User defined button. Enter the correct class width and starting lower class limit (which I specified above for this assignment), and hit Plot. For example, for the bear s head length histogram, I will change the starting lower class limit to 4. Note: anytime you change the input options for the histogram (class width or class start), you need to hit the Plot button at the top again! Finally, for all histograms, you need to add a title and an x-axis label, including any appropriate units of measurement. Use the Title and x Label boxes at the upper right Now you should have a nice histogram with the title and x-axis label displayed. For example (see above): Page 6 of 16

7 Print out each of the histograms. Do NOT use the Print or Copy button at the bottom of the STATDISK histogram box. The problem is that these commands only copy the plot itself (the part with the white background), and not the column on the right showing the input plot options. I want to see these! Instead, you can use an alternative method, especially if you want to print more than one graph per page. This method is described separately in the file Printing Out Applet Output, which is on the Assignment webpage. Wherever it says applet, just think STATDISK instead, it is exactly the same. I will demonstrate this in class also, if I haven t already done so. Finish this portion of the assignment by answering the questions given on the Answer Sheet. Page 7 of 16

8 Part B Scatterplots You are going to create one scatterplot. The purpose of making scatterplots is to investigate whether or not there is a relationship between the two variables. Where applicable, you will confirm a linear relationship (or not) by running a linear correlation and regression analysis. From the bear data, for example, here is a plot of a bear s weight as a function of its chest measurement. From the graph, there appears to be a strong linear relationship between the two variables, since the data points approximately form a line. We can confirm this by running a Correlation and Regression analysis in STATDISK. Go to Analysis/Correlation and Regression, select the correct columns for the x variable and the y variable, and then hit the Evaluate button. Page 8 of 16

9 In this case, the calculated correlation coefficient r = 0.963, which indicates a very strong positive linear correlation. It is much higher than the critical r = 0.268, which confirms the linear correlation. On the other hand, this plot of the bears weight as a function of month of measurement does NOT seem to show a strong linear correlation between the two variables. The data is scattered about in no particular pattern. Which makes sense, because it is the weight plotted as a function of the month in which the measurement was taken. There s no reason for these two variables to be correlated! The correlation and regression analysis confirms that there is no linear correlation, since the calculated correlation coefficient (r = 0.171) is less than (closer to 0 than) the critical r (critical r = 0.268). Also note a scatterplot may reveal that there IS a relationship between the two variables, but that it is clearly NOT a linear relationship. We will specifically look at an example of this in class on the Chapter 2 worksheet (world population). In Page 9 of 16

10 this case, it would NOT be appropriate to run a linear correlation and regression analysis, because a visual inspection of the data has already shown that the data is clearly not linear. Scatterplot: Female % as a Function of Male % Smokers for World Countries You are going to make a scatter plot of the paired data (male % smokers, female % smokers) or (x, y) for each country in the table. In other words, you will plot female % as a function of male %. The point is: each country in the world has a certain percentage of male smokers and a certain percentage of female smokers. Is there a relationship between the two variables? Use the same two columns of data that you already copied over from Excel. To create the scatterplot, go to Data/Scatterplot. Select the two columns of data you want to plot, then hit the Plot button. Note that you want to choose Female (which is in Excel column C and STATDISK column 2) as the Y Value variable, and Male (which is in Excel column B and STATDISK column 1) as the X Value variable (the independent variable). UNCHECK the Visible box shown at the bottom of the plot (see figure on previous page) to get rid of the green line. The program will automatically plot a green regression line whether or not there is a linear correlation, so it can be very deceiving. I noticed that I sometimes had to check and uncheck the box a couple of times to get rid of the line, so just play around with that. Add a title and both an x- and y-axis label every time you make a scatterplot. I noticed that when I typed them in, I had to immediately hit the Enter key on my keyboard, and then it would appear. Make sure that your title correctly reflects which variable is a function of the other variable. Also always make sure that Page 10 of 16

11 you have included the correct units of measurement for both the x and y axes. In this case, the units of measurement for both variables is just percent (%). Print out the scatterplot, using one of the methods described in Printing Out Applet Output. Run a correlation and regression analysis on the two variables, as described above. Snip and save the output for printing. CAUTION! NEVER SORT the data when you are making scatterplots! The scatterplots consist of paired (x, y) data, so if you sort the columns individually, then the pairs will no longer exist, and the data will be meaningless when you plot it. WHAT YOU NEED TO TURN IN: 1. Printout of two histograms. Don t forget to add a title and an x-axis label, including the measurement units where applicable. The units in this case are just percent (%). 2. Printout of the scatterplot. Don t forget to include a title and x- and y-axis labels, including the measurement units. 3. Printout of one correlation and regression analysis. 4. Fully completed Answer Sheet (5 pages total). Note: you do NOT need to turn in all the pages of instructions. Page 11 of 16

12 Name: Answer Sheet Part A Frequency Distributions and Histograms Frequency Distribution for: Male % Smoking Prevalence Note: Write the data classes as: lower class limit upper class limit, to the integer level of accuracy. Given: Starting lower class limit = 0 Class width = 10 Fill in ALL of the boxes: Data Classes (%) Frequency (Count) Relative Frequency* (%) * Note: calculate the relative frequencies (in %) to TWO decimal places. Do NOT just use the values from the STATDISK histogram, because they are rounded off to the nearest integer. Page 12 of 16

13 Name: Frequency Distribution for: Female % Smoking Prevalence Note: Write the data classes as: lower class limit upper class limit, to the integer level of accuracy. Given: Starting lower class limit = 0 Class width = 5 Fill in ALL of the boxes: Data Classes (%) Frequency (Count) Relative Frequency* (%) * Note: calculate the relative frequencies to TWO decimal places. Do NOT just use the values from the STATDISK histogram, because they are rounded off to the nearest integer. Page 13 of 16

14 Name: Part A Questions: Histograms 1. a. Describe the distribution (shape) of the data for the male histogram. b. Describe the distribution (shape) of the data for the female histogram. 2. What are the significant differences in the two histograms, and what does it tell you about the smoking prevalence of males vs. females? Look carefully at the histograms and notice that the scales are different for both the x- and y-axes, so account for that when you are comparing them. 3. WHY do you think the distributions are so different, what could be some possible explanations? Consider the underlying causes, not the mechanics of the histograms. Specifically address the differences between males and females. Page 14 of 16

15 Name: 4. As you can see from the data, some parts of the world have a much higher prevalence of smoking than others. Why is that? Do a little research to investigate specifically why the smoking rates are so high in some parts of the world, and describe your results here. Also, list your source of information below. List your source: (list website link): Page 15 of 16

16 Name: Part B Scatterplot 5. Look at the scatter plot of Female % smokers as a function of Male % smokers. From the graph, does there appear to be a linear relationship between the two variables? (yes or no) If there does appear to be a linear relationship, how STRONG does the relationship appear to be? Does the correlation and regression analysis indicate that there is a linear relationship between the two variables? (yes or no) List: Calculated r = Critical r = Briefly explain why you think this is the case. (Not why you came to the conclusion based on the plot, but what the underlying cause may be for the relationship or lack thereof.) Why is there or is there not a relationship between the percentage of male and female smokers for each country in the world? Page 16 of 16