Hypothesistesting with Ordinal Nominal Variables:

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Hypothesis-testing with Ordinal/ Nominal
Variables

• Use (t-test) when one variable is measured at the
  interval/ratio level , and the other variable
  involves 2 groups. However, when testing a
  hypothesis with two variables measured at the
  nominal or ordinal level you should use the
  chi-square statistic.
• With nominal measurement we categorizes a
  variable at the ordinal level we have enough
  information to rank-order a variable in terms of
  greater of less than.

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• Ordinal measurement
• What is your annual gross income?
• 1. less than 10,000
• 2. 10,000 to 19,999
• 3. 20,000 to 34,999
• 4. 35,000 to 59,999
• 5. 60,000 to 89,999
• 6. 90,000 or more
• Nominal measurement
• Your religious affiliation is
• 1. Protestant
• 2. Catholic
• 3. Other religion

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Hypothesis-testing with Ordinal/ Nominal
Variables

• At the interval or ratio level, a variable
  includes enough information about a social
  phenomenon that we can measure it using constant
  units that provide equal intervals on the
  measurement scale.
• Please enter you gross income last year on the
  line below
• ____________________
  
• How may siblings do you have? ________
• How old are you? I am __________
  years old.
• How concerned are you about rising tuition fees?
• 0 ---------- 1 ---------- 2
  ---------- 3 ---------- 4 ---------- 5
• Not Concerned
  Very Concerned
  

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• Statistical tests tell us when observed data
  differ so much from what we would expect by
  chance, that we can conclude that a real
  difference exists. Hypothesis testing assesses
  differences between what we expect if the null
  hypothesis is true, and what is in our data.the
  t-ratio does this for means proportions
  chi-square for frequency counts.
• Chi-square tells us if observed frequencies
  differ so much from what we would expect from
  chance that we can reject the null hypothesis.

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• H1 The Professor tends to assign particular
  correct responses in multiple-choice exams. The
  Professor favors A and B as answers, and
  avoids D as an answer category.
• H0 The Professor has no tendency to assign
  particular correct responses in multiple-choice
  exams. Answers A to E have an equal chance of
  being selected.
• The observed frequencies are those we see in the
  data the expected frequencies are those we
  expect to see by chance. SPSS calculates the
  expected frequencies as an option.

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• The null hypothesis is there are no sex
  differences (or at least no difference big enough
  to rule out chance) in the reasons students give
  for attending university.
• The research hypothesis is there are sex
  differences in the reasons students give for
  attending university.
• If the difference between observed and expected
  frequencies is so large that it is unlikely due
  to chance, we reject the null hypothesis.,

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