Chisquare

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Lecture 12

• Chi-square

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• 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.

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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

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1. Calculating Chi-square (X2)

• X2 S  (O - E)2 /E
• (where E expected frequencies,
• O observed frequencies)

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ExampleDoes the gender ratio of this class
differ from our hypothesized 73 ratio? (total
student number 50)

• Expected frequencies

• Observed frequencies

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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

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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

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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

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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.