Analysis of Count Data

1
Chapter 14

• Analysis of Count Data

2
Example

• You buy a bag of grass seed from Big-K and it
  produced the following lawn.

3
Example
4
Example

• You are concerned because it doesnt seem to be
  the same Varity of grasses that were advertised
  on the bag. You take a representative sample of
  the lawn to Jeff Houge (CRs botany instructor)
  and he gives you the following break down.

5
Example

• Annual Ryegrass 1300 pieces
• Creeping Red Fescue 525 pieces
• Perennial Ryegrass 275 pieces
• Other Grasses 25 pieces
• Weed Other 375 pieces

6
Example
7
How To Tell if Significant Difference?

• We use the Chi-Squared Goodness-of-fit test.
• Data consists of observed counts.
• We calculate what we expect to see based on the
  nulls distribution. Calculate np for each category

8

• The Big Idea
• 1. The data consist of observed countsthat is,
  how many of the items or subjects fall into each
  category.
• 2. We will compute expected counts under Ho, that
  is, the counts that we would expect to see for
  each category if the corresponding null
  hypothesis were true.
• 3. We will compare the observed and expected
  counts to each other via a test statistic that
  will be a measure of how close the observed
  counts are to the expected counts under Ho. So if
  this distance is large, we have some support
  for rejecting Ho.

9
Calculate Chi-Squared
10

• Various Chi-Squared Distributions

11

• Properties of the Chi-Square Distribution
• The distribution is not symmetric and is skewed
  to the right.
• The values are non-negative.
• There is a different chi-square distribution for
  different degrees of freedom.
• The mean of the chi-square distribution is equal
  to its degrees of freedom and is located to the
  right of the mode.
• The variance of the chi-square distribution is
  2(df).

12
Do the Test Page 933

• We could calculate the p-value by hand using the
  TI. To do that well need to know our degrees of
  freedom which is K 1 where K is the number of
  categories.
• I wrote a program MULTNOM that is in your
  calculator to do this test.

13
Lets Do It

• LDI 14.2, 14.3
• Page 936 Exercises 14.6, 14.10, 14.12, 14.13