Lesson8Part2 - Let us look at another tool that will help as compare population proportions for more than two populations Chi Square Distribution

Info iconThis preview shows pages 1–5. Sign up to view the full content.

View Full Document Right Arrow Icon
1 Let us look at another tool that will help as compare population proportions for more than two populations. Chi Square Distribution Introduction and Applications Atul N Roy The Chi Square distribution is a probability distribution, where the random variable assumes only non negative real values. It is skewed to the right. Its shape depends on a characteristic called the degrees of freedom. Here are a few examples: 1. Chi Square () 2 also expressed by χ with 2 degrees of freedom 2. 2 χ with 3 degrees of freedom looks like the following 3. 2 χ with 11 degrees of freedom looks like 0 0.1 0.2 0.3 0.4 0.5 24681 0 x 0 0.05 0.1 0.15 0.2 0 x
Background image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
2 4. 2 χ with 31 degrees of freedom looks like Note that the distribution has become quite symmetric with the increase in the degrees of freedom. Fact: If the degrees of freedom of a 2 χ distribution is n, then its mean is n and the standard deviation is 2 n. We shall either use the tables or a computing device to use the probabilities involving the 2 χ distribution. I shall write the description of the computer usage later in this section, first let us look at a table that is typically found in most statistics-text books. 0 0.02 0.04 0.06 0.08 5 1 01 52 02 53 0 x 0 0.01 0.02 0.03 0.04 0.05 10 20 30 40 50 60 x
Background image of page 2
3 The values in the top row are the right tail probabilities and the values in the first column are the degrees of freedom. Following is the way to interpret this table. Note that 005 6 12.591 . means that the area under the graph of the density function to the right of 2 χ =12.591 at 6 degrees of freedom is approximately 0.05 as shown in the following graph. 0.5 0.1 0.05 0.025 0.01 0.005 2 1.386294 4.605176 5.991476 7.377779 9.210351 10.59653 3 2.365973 6.251394 7.814725 9.348404 11.34488 12.83807 4 3.356695 7.779434 9.487728 11.14326 13.2767 14.86017 5 4.351459 9.236349 11.07048 12.83249 15.08632 16.74965 6 5.348119 10.64464 12.59158 14.44935 16.81187 18.54751 7 6.345809 12.01703 14.06713 16.01277 18.47532 20.27774 8 7.34412 13.36156 15.50731 17.53454 20.09016 21.95486 9 8.342832 14.68366 16.91896 19.02278 21.66605 23.58927 10 9.341816 15.98717 18.30703 20.4832 23.20929 25.18805 11 10.341 17.27501 19.67515 21.92002 24.72502 26.75686 12 11.34032 18.54934 21.02606 23.33666 26.21696 28.29966 13 12.33975 19.81193 22.36203 24.73558 27.68818 29.81932 14 13.33927 21.06414 23.68478 26.11893 29.14116 31.31943 15 14.33886 22.30712 24.9958 27.48836 30.57795 32.80149 16 15.3385 23.54182 26.29622 28.84532 31.99986 34.26705 17 16.33818 24.76903 27.5871 30.19098 33.40872 35.71838 18 17.3379 25.98942 28.86932 31.52641 34.80524 37.15639 19 18.33765 27.20356 30.14351 32.85234 36.19077 38.58212 20 19.33743 28.41197 31.41042 34.16958 37.56627 39.99686 21 20.33723 29.61509 32.67056 35.47886 38.93223 41.40094 22 21.33704 30.81329 33.92446 36.78068 40.28945 42.79566 23 22.33688 32.00689 35.17246 38.07561 41.63833 44.18139 24 23.33673 33.19624 36.41503 39.36406 42.97978 45.55836 25 24.33658 34.38158 37.65249 40.6465 44.31401 46.92797 26 25.33646 35.56316 38.88513 41.92314 45.64164 48.28978 27 26.33634 36.74123 40.11327 43.19452 46.96284 49.64504 28 27.33623 37.91591 41.33715 44.46079 48.27817 50.99356 29 28.33613 39.08748 42.55695 45.72228 49.58783 52.3355 30 29.33603 40.25602 43.77295 46.97922 50.89218 53.67187 Area=0.05
Background image of page 3

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
4 This distribution has many uses in statistical analyses, we shall use it for comparing population proportions. Example 1. The following data is based on the information provided by a heartburn medication called Aciphex regarding relief from heartburn symptoms among the patients who took placebo and the patients who took different dosage of Aciphex. The table shows the number that maintained the healing from ulcers verses the number that did not under two treatment groups and the placebo group 52 weeks after the treatment. Maintained Healing YES NO Placebo 49 120 ACIPHEX 10 mg 119 40 ACIPHEX 20 mg 139 21 We call such a table a 3 × 2 table that is a table with 3 rows and 2 columns and having 6 cells overall. Note that the following shows us the proportion of the subjects who maintained healing for these three groups.
Background image of page 4
Image of page 5
This is the end of the preview. Sign up to access the rest of the document.

This note was uploaded on 09/22/2011 for the course STAT 101 taught by Professor Unknown during the Fall '08 term at Alabama State University.

Page1 / 22

Lesson8Part2 - Let us look at another tool that will help as compare population proportions for more than two populations Chi Square Distribution

This preview shows document pages 1 - 5. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online