Hpothesis Testing of Proportions:

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Hpothesis Testing of Proportions

• In most research, we want to test hypotheses
  about the differences between two or more groups
  or levels of a variable.
• For example, you are studying the efficacy of a
  new drug for treating AIDS. One group of
  patients receives the existing drug of choice
  the other group receives a new drug. After 12
  months you find..
• 
  New Drug Old Drug
• Proportion surviving .75
  .70
• Initial Sample Size 100
  100

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• Although the findings are promising, we must test
  if the difference in the proportion surviving is
  statistically significant.
• A statistically significant difference implies
  that the difference in the proportion surviving
  using the old new drugs is so large that we can
  rule out chance or random sampling error as
  explanations for the difference.
• A significant difference means the new AIDS drug
  has a real, beneficial effect on survival.

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Steps in testing a statistical hypothesis

• Formulate the Research Hypothesis (H1)
• Formulate the Null Hypothesis (H0)
• Select the appropriate test statistic

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Steps in testing a statistical hypothesis

• Formulate the Research Hypothesis (H1)
• Formulate the Null Hypothesis (H0)
• Select the appropriate test statistic
• Choose level of significance (e.g., sig. .05,
  .01, .001)

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Steps in testing a statistical hypothesis

• Formulate the Research Hypothesis (H1)
• Formulate the Null Hypothesis (H0)
• Select the appropriate test statistic
• Choose level of significance (e.g., sig. .05,
  .01, .001)
• Decide if you can reject the Null Hypothesis (H0)

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• IF THE ABSOLUTE VALUE OF YOUR CALCULATED t-ratio
  (t-calculated) EXCEEDS THE VALUE OF THE t-ratio
  OBTAINED FROM THE TABLE (t-critical) THEN
  REJECT THE NULL HYPOTHESIS!

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Hypothesis-testing with Ordinal/ Nominal
Variables

• The t-ratio (t-test) is appropriate when one
  variable is measured at the interval/ ratio level
  , and the other variable involves two groups.
  However, when testing a hypothesis that involves
  two variables measured at the nominal or ordinal
  level you should use the chi-square statistic.
• At the nominal level of measurement a variable
  categorizes a social phenomenon at the ordinal
  level a variable includes enough information that
  we can rank-order a social phenomenon 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 of hypotheses tell us when our
  observed data differ so much from what we would
  expect by chance alone that we can conclude that
  a real difference exists between two groups or
  levels of a variable.
• Hypothesis testing assesses differences between
  what we would expect if the null hypothesis was
  true, and what is actually in our data.t-ratio
  does this for means proportions chi-square for
  frequency counts. Chi-square tells us if our
  observed frequencies differ so much from what we
  would expect from chance alone that we can reject
  the null hypothesis.

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• H1 The Professor tends to assign particular
  correct responses in multiple-choice exams.
  Specifically, the Professor favors A and B as
  answer categories, and avoids D as an answer
  category.
• H0 The Professor has no tendency to assign
  particular correct responses in multiple-choice
  exams. All answer categories A through E
  have an equal chance of being selected.
• The observed frequencies are those we actually
  see in the data the expected frequencies are
  those we expect to see by chance alone.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 our observed
  frequencies and expected frequencies is so large
  that it is unlikely due to chance, we reject the
  null hypothesis.,

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