| Sample questions |
| You work for a pharmaceutical company that is currently testing a new antihypertensive (drug to reduce blood pressure). Your manager has recently asked you to do a quick preliminary analysis looking at the effectiveness of this drug. You have a sample of 104 patients who all had, prior to this test, a systolic blood pressure of approximately 175. These patients were given varying dosages of your drug, including some receiving a placebo. The quantity they were given is measured in mg/kg/day and is found in the column titled "dosage." After a two month treatment period, each patient had their systolic blood pressure retested; the difference between their initial blood pressure and their new blood pressure can be found in the colum "pressure." Lower (i.e. "more" negative) numbers in this column indicate a greater reduction in systolic blood pressure, and higher numbers imply that their systolic blood pressure actually increased. You also have data on patient blood type (A, B, AB, and O) in the column titled "blood type." Use this data to answer the following questions. Problem 4.1 comes from week 9 material, 4.2 comes from week 10 material, and 4.3 relates to week 11 material. Because this is due before week 11, question 4.3 is extra credit. Should you encounter any difficulties with these problems, the optional problems below are very similar to the questions in this problem set, and the answers to the optional questions can be found in the back of the textbook. You can also request that the tutor work extensively with you on the optional problems. |
| Research Question #1 |
| The first issue your boss has asked you to address is whether or not there are differences in the effectiveness of the drug between the four different blood types. Use the 0.05 level of significance to:
a) Perform a one-way ANOVA to look for differences in changes in blood pressure between blood types. (Use your book to solve this)
b) Briefly summarize (in plain English) your procedures and the results of (a)
Excel Tips: When using the Data Analysis ToolPak, Excel requires that your data be formatted differently for ANOVA than for regression. The data as downloaded is formatted correctly for regression analysis, so you will have to transform your data prior to estimating the ANOVA.
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| Research Question #2 |
| In addition to looking at differences between blood types, your manager also wants to know the relationship between dosage and change in systolic blood pressure. Thus, the dosage is your independent variable and the change in blood pressure is your dependent variable.
a)Construct a scatter plot of the two variables (note: the scatter plot should look non-linear. Still, do these questions and we'll address the non-linearity in 4.3)
b)Estimate a simple linear regression between these two variables.
c)Interpret the meaning of β0 and β1.
d)Predict the mean blood pressure change associated with dosages of 0, 2.5, 5, 7.5, 10, and 12.5 Are these appropriate predictions?
e)Comment briefly on the predictive power/statistical significance of your estimates. |
| Use The differents techniques that we used in that class to come up with some usefull way to abanlyze this data |
| Suggestion #1 |
| Use the data to determine the following:
(a) Which of the variables are categorical and which are numerical?
(b) Which of the categorical variables are nominal and which are ordinal?
(c) Which of the numerical variables are ratio and which are interval?
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| Suggestion #2 |
| Use the salesperson data to do the following:
(a) Create a summary table and an ordered summary table of the departments the salespeople work in.
(b) Construct a bar chart, a pie chart, and a Pareto diagram.
(c) Which graphical method do you think is best to portray these data?
(d) Based on this data, what conclusions can you make about the departments your salespeople work in?
Excel tips:
The easiest way to create the frequency summary table is with the COUNTIF command. The command works like this: =COUNTIF(x,y), where x is the set of cells you want to look in for a particular value, and y is the value you are looking for. For example, =COUNTIF(E:E, "Female") would look in the E column for all instances of the term "Female", count them up, and give you the number.
Excel doesn't have a "canned" option to create a Pareto Diagram, so this is what you need to do: First, construct a column chart with data for both percentage and cumulative percentage. Then, click on one of the columns that represents data from one of the cumulative percentages, choose "change series chart type," and set it to line. |
| Suggestion #3 |
| Use the data to do the following:
(a) Construct a frequency distribution and a percentage distribution of the years of experience of your sales force.
(b) Construct a histogram and a percentage polygon.
(c) Plot a cumulative percentage polygon.
Excel tips:
As a general rule of thumb, the fewer times you type out a formula, the better. If you can accomplish a task by writing one formula and then filling it down with the fill bar, do it that way so you can minimize your chances of making mistakes. One feature that is very useful for accomplishing this task is making use of relative and absolute cell references. Say, for example, in cell C1 you have the expression =A1+B1. If you fill C1 down to C2, C2 will have the equation =A2+B2...when filling down, Excel viewed your cell references as relative, as if you said in C1 to make C1 equal to the sum of the two cells to the left of it. When you fill down to C2, Excel said that C2 should equal the sum of the two cells to the left of it, in this case A2 and B2. In some cases this is exactly what you want Excel to do, but in others you do not want relative cell references. For example, cell D1 may have total nationwide sales for your company, A1:A51 may have the names of the 50 states (plus DC!), and B1:B51 may have total sales within each state. In column C you want to have the percentage of total sales within that state. If in C1 you type =B1/D1, you will get the correct result, but then if you fill D1 down to D51, you will get error messages (or wrong answers) everywhere else. The easiest fix is to use an absolute reference in your equation, which you accomplish with the dollar sign ($). The $ is essentially a way of "locking" in either a row or column in a cell reference. If you type in C1 =B1/D$1, and then fill down, Excel will "lock in" the first row in the reference, so all of your formulae will compute correctly! With knowledge and appropriate application of relative and absolute references, it is possible to create the table in part (a) by typing exactly 4 equations (and filling them down) and nothing else! |
| Suggestion #4 |
| :
(a) Compute the mean, median, first quartile, and third quartile for the sales variable.
(b) Compute the variance, standard deviation, range, interquartile range, coefficient of variation, skewness, and Z scores for the sales variable.
(c) Are the data skewed? If so, how?
(d) Based on the results of (a) through (c), what conclusions can you reach concerning sales?
(e) Calculate the proportion of patient incomes that are +/- 1, +/- 2, and +/- 3 standard deviations of the mean.
(f) Compare and contrast your findings with what would be expected on the basis of the empirical rule.
Excel Tips:
Excel has built-in functions to calculate the mean (AVERAGE), median (MEDIAN), quartiles (QUARTILE), variance (VAR for samples, VARP for populations), and standard deviation (STDEV for samples, STDEVP for populations). You might also think to use the MIN and MAX commands in calculating range. Search the Excel helpfile for the appropriate syntax of these commands. You should note that the method Excel uses to calculate quartiles differs slightly from the method outlined in the book.
I mentioned the COUNTIF command above, and you may have thought to use COUNTIF to accomplish part (e). However, a single COUNTIF command cannot handle more than one condition, so if you want to use COUNTIF you should absolutely (hint hint) think outside the box a bit. Or, if you are using Excel 2007 or later, there is a COUNTIFS command that handles multiple conditions. |
angelina_2
group_3project.xlsx
