Stat 2000: Tips for Web Assign HW 04
Published: Mon, 02/07/11
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Tips for Web Assign and JMP in General
When working with Web Assign, always enter the answer to one specific box and then click "Submit Answer" to confirm that is correct before you move on to another box. Do not enter several answers all at once in several boxes before you click "Submit Answer". You risk being marked wrong due to some typo or something.
For some strange reason, JMP 8 occasionally computes wrong answers even if you have copied and pasted your data correctly. I suggest that, if it is feasible, type the given data into your calculator (in Stat mode as shown in Appendix D of my book), and have your calculator compute the sample mean. Compare that answer with JMP's answer for the sample mean. If they are the same, everything is fine. If they are not the same, close JMP 8 and restart it, recopy and paste the data, and check again. Sometimes you have to do this 2 or 3 times before JMP finally works. If it is not feasible to use your calculator to compute the sample mean, have JMP do the question 2 or 3 times, being sure to restart JMP and recopy the data each time, and confirm that JMP gives you the same answer each time before risking entering the results into Web Assign.
If you are taking the course by distance/online (Section D01) click here to see your tips for HW 04.
Study Lesson 5 in my study book to prepare for this assignment.
For Question 1, note that ni simply means they want you to tell them the values of n1, n2, etc.. The response variable is the variable you are measuring in the problem (what will you be computing mean values for?).
For Question 2, you should do the rest of the problem by hand using the formulas for SSG, SSE, MSG, MSE, and F. Make sure you have memorized those formulas (and the formula for the overall mean or grand mean). There is almost certainly going to be a question or two on the exam that will check to see if you know these formulas (although it is rare to see an exam question that makes you do an entire ANOVA by hand). It is common that an exam will make you compute MSG or MSE by hand having been given the sample means and standard deviations. It is impossible for you to give an exact value for the P-value since you do not have the original data to type into JMP. Just put bounds on it using Table E. (You can google F distributions if you like to find a program in cyberspace that will give you the exact P-value for a given F test statistic, but why bother?)
Note that Question 3 insists you use a pooled t test, so don't bother using your rule of thumb. Put your calculator in Stat mode and enter in the Medication 1 data to get the mean and standard deviation. Reset the mode to delete that data and now enter the Medication 2 data to get their mean and standard deviation. Otherwise this is a rehash of the method taught in Lesson 4 of my book and then they make you repeat it using ANOVA by hand like you would have done in Question 2 above.
Of course, you could just feed the data into JMP and get most of the answers from JMP but, be careful, if you do that. JMP has an annoying habit of doing the t test the opposite way round. By which, I mean it may go "Medication 2 -- Medication 1" when you would rather subtract the other way round. If it does that, it would have the correct test statistic, but the sign would be wrong. In addition, if you are doing a one-tailed test, JMP's upper-tailed P-value would be your lower-tailed P-value and vice-versa. Just check the "Difference" part of the t test on the printout and see what way JMP subtracted the means. Maybe you are just better off doing the question by hand.
When they ask how do the two procedures compare, they are wanting you to discuss the relationship between F and t which I show you in Lesson 5.
Here is how to do the JMP part of Question 4:
It is done the same way you did the JMP in the previous assignment. Open a New Data Table and type the data in manually in this manner (don't bother pasting and stacking, it is not worth the effort): Name your first column "Bone Density" or something like that, and type all the bone density scores down that column. Which is to say, type in the numbers from the Control group down the column, then continue to type all the numbers from the Low jump group, and finally continue to type all the numbers for the High jump group. Double-click at the top to the right of the "Bone Density" column heading to create a new column and name it something like "Jump Height". Down that column type "Control" repeatedly down that column in all the rows that have the data for the Control group. Then type "Low" repeatedly down the column in the rows that have data for the Low jump group. Finally, type "High" for the rest of the column. You may want to type the phrase once and then copy and paste it down the rest of the relevant rows to ensure there are no typos. Once you have done that, double-click the "Jump Height" column heading and confirm that the Data Type is Character and the Modeling Type is Nominal and click OK.
Select Analyze, then Fit Y By X. Highlight the numeric column "Bone Density" and click the Y, Response button. Highlight the character column "Jump Height" and click the X, Factor button. Click OK.
You should now see a graph with three vertical arrays of dots showing the bone density for the three different groups separately. Click the red triangle and select "Means and Std Dev" to get a summary of the means and standard deviations of the three samples. Click the red triangle again and select "Means/Anova/Pooled t" to get the output you need.
Study Lesson 4 in my study book to prepare for this assignment.
Be sure to use your Rule of Thumb (Lesson 4) for all of the questions in this assignment to determine if your are using the pooled method or the generalized method. Note, if you are using an older edition of my study book, you must use that insanely complicated degrees of freedom formula for any question that requires the generalized method. Refer to #1 on the formula sheet included in your course outline to see that formula if you can't find it in my book (it is in most of the recent editions of my book, but it depends how old your book is). Also, be sure to skim through the entire question to see if they ever specify which order they want you to subtract your means, and, if so, be sure to do as they say right from the start.
For Question 1, note that you have been given the Standard Errors of x-bar (the SE values), so you will have to do some algebra to determine the standard deviations. I give you the formula for SE of x-bar back in Lesson 1 of my book and also again in Lesson 4 when I first start talking about standard errors.
Here is how to do the JMP part of Question 3:
Open a New Data Table and type the data in manually in this manner: Name your first column "Price" or something like that, and type all the prices down that column. Which is to say, type in the four-bedroom selling prices down the column and then continue to type all the three-bedroom selling prices below that. Double click at the top to the right of the "Price" column heading to create a new column and name it something like "Type of Home". Down that column type something like "four-bedroom" repeatedly down that column in all the rows that have the prices for four bedroom homes. Then type something like "three-bedroom" repeatedly down the column in the rows that have three bedroom prices. You may want to type the phrase once and then copy and paste it down the rest of the relevant rows to ensure there are no typos. Once you have done that, double-click the "Type of Home" column heading and confirm that the Data Type is Character and the Modeling Type is Nominal and click OK.
Select Analyze, then Fit Y By X. Highlight the numeric column "Price" and click the Y, Response button. Highlight the character column "Type of Home" and click the X, Factor button. Click OK.
You should now see a graph with two vertical arrays of dots showing the prices of three and four bedroom homes separately. Click the red triangle above the graph and select "Display Options" and select Box Plots to see side-by-side boxplots. That will enable you to get a feel for the symmetry or skewness of the distributions to help you decide if use of t is acceptable. Even if use of t is not acceptable, you are going to use it anyway. Click the red triangle again and select "Means and Std Dev" to get a summary of the means and standard deviations of the two samples. Click the red triangle again and select "t-Test" to get the output for a hypothesis test and confidence interval assuming unequal variances. Click the red triangle again and select "Means/Anova/Pooled t" to get the output that includes a hypothesis test and confidence interval assuming equal variances. Click the red triangle again and select "Set α level" to have the outputs change the confidence intervals to your desired level of confidence. For example, if you want 98% confidence intervals you would set alpha to be .02, or, if you want 90% confidence intervals, you would set alpha to be .10. In other words, α = 1 - C.
By the way, I have no idea what they are getting at in part (e), so your guess is as good as mine. I think they mean they are not simple random samples (SRS) since the data is strictly from one place instead of all over the country. There are all sorts of reasons you could give as to why you should not use t in this case, I have no idea how you could justify using t if the samples are not random. You can take it from there.
When you are using JMP to do a two-sample hypothesis test or confidence interval, watch which way it is subtracting. It may not do it the way you expected. For example, you may have called "A" sample 1 and "B" sample 2, so you would expect to do A - B, but JMP may do B - A. It is difficult to get JMP to subtract a specific way, so it is better to let JMP do what it wants to, and you adjust to it. Look at the two sample means JMP computes for A and B, then check if the "difference" in its t test has computed A - B or B - A. If it has done B - A, then define your means accordingly. Which is to say, let μ1 = mean of B and μ2 = mean of A, then state your hypotheses accordingly.
If you do not do this, your signs will be all wrong. For example, the signs in your lower and upper limits for your confidence interval for the difference between the means would be the opposite of what they should be.
Tip: When you want to do a one-sided test, if JMP has a positive test statistic, you must be doing an upper-tailed test; if JMP has a negative test statistic, you must be doing a lower-tailed test. But, again, watch the way JMP has subtracted the two means to identify who is who.
Do the JMP in Question 4 just like I showed you what to do in Question 3 above. Your first column should have all the SSHA scores and your second column will be a character column where you type in women and men in the appropriate rows. Always make the numeric column Y and the character column X when you select Fit Y By X.