Chisquare - PowerPoint PPT Presentation

1 / 10
About This Presentation
Title:

Chisquare

Description:

... chi-square. Goodness-of-fit test. 1. Calculating Chi-square (X2) X2 ... Once the chi-square value is known, the goodness-of-fit test determines whether ... – PowerPoint PPT presentation

Number of Views:20
Avg rating:3.0/5.0
Slides: 11
Provided by: hyoso
Category:
Tags: chisquare

less

Transcript and Presenter's Notes

Title: Chisquare


1
Lecture 12
  • Chi-square

2
  • Statistics is a necessary evil
  • Statistics is necessary when you follow the
    scientific method of research
  • In order to have valid and reliable results, any
    question must be analyzed using some type of
    statistics (in quantitative method)

3
Some inferential statistical methods
  • Chi-square
  • T-test
  • Correlation
  • You will not calculate statistics by hand, but
    you have to understand the basic logic behind the
    statistic.

4
Chi-square (X2) test
  • When variables of interest are categorical
  • (categorical vs. numerical variables)
  • Compare the observed frequencies of a phenomenon
    with the expected frequencies
  • 2 step process
  • Calculating chi-square
  • Goodness-of-fit test

5
1. Calculating Chi-square (X2)
  • X2 S  (O - E)2 /E
  • (where E expected frequencies,
  • O observed frequencies)

6
ExampleDoes the gender ratio of this class
differ from our hypothesized 73 ratio? (total
student number 50)
  • Expected frequencies
  • Observed frequencies

7
Steps
  • X2 S  (O - E)2 /E
  • 1. For each category, subtract the expected
    frequency from the observed frequency. Square
    this figure and then divide this figure by the
    expected frequency
  • (40-35)2 / 35 0.71
  • (10-15)2 / 15 1.67
  • 2. Add up the resulting figures for each
    category to get the chi-square value
  • 0.71 1.67 2.38

8
2. Goodness-of-fit Test
  • Once the chi-square value is known, the
    goodness-of-fit test determines whether this
    value represents a significant difference in
    frequencies
  • To do this, 2 values are necessary
  • Probability level (predetermined by the
    researcher) p lt .05
  • Degrees of freedom (df) the number of scores in
    any particular test that are free to vary in
    value
  • number of categories - 1

9
Steps
  • 1. Calculate the degrees of freedom, which equal
    the number of categories minus 1
  • ex) 2 1 1
  • 2. Consult a chi-square significance table (p.
    437)
  • 3. If the calculated chi-square value equals or
    exceeds the value found in the table, the
    differences in the observed frequencies are
    considered to be statistically significant if
    the calculated value is smaller, the results are
    nonsignificant
  • ex) 2.38 lt 3.841
  • -gt the difference is not significant

10
Examples
  • H1 The distribution of party proportions differ
    from the traditional norm values of 442.
  • H2 TV set sales of four major manufacturers are
    significantly different this year from those of
    the previous year.
Write a Comment
User Comments (0)
About PowerShow.com