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Statistics Tutoring

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Significance Level and Power


If you want help with your undergraduate or graduate statistics course, please contact me (rab@nauticom.net). I'm available to answer your questions about probability and statistics and related subjects such as applied statistics, mathematical statistics, decision analysis, econometrics, economics, biostatistics, reliability, and so forth. Your questions will be answered step-by-step and in detail. Complex problems will be broken down into simpler pieces. See my other web pages for detailed information on my credentials.

For graduate students, I can provide statistics advice for planning the design of your masters thesis or Ph.D. dissertation.

I can also help you with programming in S , R, Minitab, SPSS, SAS, and data analysis using Excel. I use R to do most statistical computations.

Send me your questions by e-mail and I'll respond in a timely manner. Alternatively, if you like we can arrange to work together at the same time. The solutions will be sent to you via e-mail and will include appropriate graphics to help illustrate how the problem is solved. To see an example, click here.

To gain the maximum advantage from tutoring and keep the cost as low as possible, you should try to do as many problems as you can. Then send me the ones that you are finding difficult or impossible to do. The goal is not just to answer the questions but to understand the material. How much you get out of the course will vary directly with the effort you put into the course.

What File Format Do You Want for the Solutions?

I typically type the solutions using typical statistical notation. I can send you the solutions is MS Word .doc format. If you prefer another format, please let me know and I will try to accommodate your request. If you do not have a word processor (or even if you do), I highly recommend OpenOffice. It will do everything you could need, it's free, and you can download it from http://www.openoffice.org/.


If you have a general question in calculus, vector calculus, rings/fields, group theory, discrete math, lie groups, linear algebra, or similar problems, contact Mathematics Consulting Services.


If you are looking for high quality statistical software, you should look at R. You don't even have to download R to use it. You can use R over the web. Check out Rweb. Here is another Rweb server.


Fee Schedule

For course work: $50/hour, time required depending on the problem. If you send me your questions I can give you a time and cost estimate.

For help with statistical analysis for theses and dissertations: $60/hour. I'm available to help you design your study and/or assist you in the analysis of your data.

(Please note that these fees do not apply to business and industrial consulting. Please contact me for a consulting fee schedule.)


Payment Methods: American Express, Visa, Mastercard, Discover, and Money Order

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I accept payment by American Express, Visa, Mastercard, Discover, and PayPal. Credit cards are billed after the work is completed. PayPal requires a payment to rab@nauticom.net before I begin. Using a credit card or PayPal allows us to work together immediately. To use a credit card, please phone your credit card information to me. Please include your card number, the expiration date, your name as it appears on your card, and the three-digit security code on the back of the card. Please phone this information to: 412 922 9749. Do not send the credit card information by e-mail. Please remember that e-mail is not secure.

Payment can also be made by money order sent to:

Richard A. Bilonick
P. O. Box 113564
Pittsburgh, PA 15241


Contact Me

Send e-mail to: rab@nauticom.net

You may also send your questions by fax to 508 445 5821 at any time. (This is an efax account and I can access it using e-mail. Using this fax number also eliminates problems with running out of paper. For security, credit card information should  be sent to 412 922 9749.) Please include your name and e-mail address on the fax.

Mailing Address:

Richard A. Bilonick
P. O. Box 113564
Pittsburgh, PA 15241

IMPORTANT! If you send me a fax, PLEASE also send me e-mail to notify me a fax was sent. Also, many times people contact me by e-mail but their return e-mail address is faulty for one reason or another. If you don't hear from me within a few hours, the chances are I either never received your e-mail or your return e-mail address was faulty. I usually check my e-mail many times a day and will acknowledge receipt of your request for tutoring ordinarily within a few hours (unless I'm out of town, then there might be a slightly longer delay). If you don't hear from me in a timely manner, please try contacting me again, either by fax or phone.


If you are interested in statistical consulting, please click here.

Statistical Consulting


If you would like to find easy-to-read books on statistics, quality control, or design of experiments, please click here.

Rick's Picks - Books for Statistics

Rick's Picks

Recommended Books on Statistics

Here is a list of books I personally recommend for people studying statistics. You can buy these books directly from Amazon.com by clicking on the book's link.

Click here to go to Book Store


Description of the Graph at the Top of This Page

The picture at the top of this page shows a large sample upper-tailed hypothesis test to compare means from two independent groups. The significance level is 5% and is denoted by the area in red under the null sampling distribution. The power for the particular alternative hypothesis (where the true mean difference is +2 standard deviation units) is denoted by the area in blue under the alternative sampling distribution. The vertical line that demarcates the critical region is x = 1.96 (just below the alternative mean difference of 2.00). Thus it is easy to see that the power for this alternative must be greater than 50%. As the significance level decreases (reducing the risk of a Type I error), the vertical line demarcating the critical region must move to the right and thus the power for detecting this alternative must also decrease.

This graph was drawn on a Silicon Graphics Inc. O2 Irix workstation using Maple V . GIMP was used to add the coloring and titles.


In the above graph, the black curve is the probability density function f(x) = 4x exp(-2x) for x > 0. The corresponding random variable has a mean of 1 and variance of 1/2. The portion of the normal pdf > 0 with the same mean and variance is drawn in red for comparison. The graph was drawn with Maple V.


This page was last modified on February 28, 2004.


Copyright © 2004 Richard A. Bilonick (rab@nauticom.net)