Chapter 22 Testing Hypotheses in Research

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Chapter 22Testing Hypotheses in Research
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What is a hypothesis?
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What is a hypothesis?

• Testable
• Falsifiable

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Scientific method
1.Define the question 2.Gather information and
resources 3.Form hypothesis 4.Plan
experiment 5.Do experiment and collect
data 6.Analyze data 7.Interpret data and draw
conclusions that serve as a starting point for
new hypotheses 8.Communicate results
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Using Data to Make Decisions

• Examining Confidence Intervals.
• Hypothesis Tests
• Is the sample data statistically significant, or
  could it have happened by chance?

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Steps for Testing Hypotheses

• Determine the null hypothesis and the
  alternative hypothesis.
• Collect data and summarize with a single number
  called a test statistic.
• Determine how unlikely test statistic would be if
  null hypothesis were true.
• Make a decision.

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Step 1. Determine the hypotheses.

• Null hypothesishypothesis that says nothing is
  happening, status quo, no relationship, chance
  only.
• Alternative (research) hypothesis hypothesis is
  reason data being collected researcher suspects
  status quo belief is incorrect or that there is a
  relationship between two variables that has not
  been established before.

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Step 2. Collect data and summarize with a test
statistic.

• Decision in hypothesis test based on single
  summary of data the test statistic.
• chi-square test statistic
• standard Z score.
• Also will see t, F, r, .

.
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Step 3. Determine how unlikely test statistic
would be if null hypothesis true
p-value - If null hypothesis true, how likely to
observe sample results of this magnitude or
larger (in direction of the alternative) just by
chance? P-value often misinterpreted in the
news.
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Step 4. Make a Decision.

• p-value not small enough to convincingly rule out
  chance.
• We cannot reject the null hypothesis as an
  explanation for the results.
• There is no statistically significant difference
  or relationship evidenced by the data.
• p-value small enough to convincingly rule out
  chance.
• We reject the null hypothesis and accept the
  alternative hypothesis.
• There is a statistically significant difference
  or relationship evidenced by the data.

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• What numerical value gives you the answer to the
  question of how unlikely the test statistic would
  be if the null hypothesis were true?
• The p-value
• The confidence interval
• The sample standard deviation

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Thought Question 1
In the courtroom, juries must make a decision
about the guilt or innocence of a defendant.
Which mistake is more serious A. if the jury
claims the suspect is guilty when in fact he or
she is innocent. B. if the jury claims the
suspect is not guilty when in fact he or she is
guilty
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Example A Jury Trial
If on a jury, must presume defendant is innocent
unless enough evidence to conclude is guilty.
Null hypothesis Defendant is innocent. Alternati
ve hypothesis Defendant is guilty.

• Trial held because prosecution believes status
  quo of innocence is incorrect.
• Prosecution collects evidence, like researchers
  collect data, in hope that jurors will be
  convinced that such evidence is extremely
  unlikely if the assumption of innocence were true.

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The Two Types of Errors

• Courtroom Analogy Potential choices and errors

• I. We believe enough evidence to conclude the
  defendant is guilty.
• Potential error An innocent person falsely
  convicted and guilty party remains free.
• usually seen as more serious.
• II. We cannot rule out that defendant is
  innocent, so he or she is set free without
  penalty.
• Potential error A criminal has been erroneously
  freed.

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The Two Types of Errors in Testing

• Type 1 error can only be made if the null
  hypothesis is actually true.
• Type 2 error can only be made if the alternative
  hypothesis is actually true.

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The Power of a Test
The power of a test is the probability of making
the correct decision when the alternative
hypothesis is true.
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Chapter 23Hypothesis Testing Examples and Case
Studies
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How Hypothesis Tests Are Reported in the News

• Determine the null hypothesis and the
  alternative hypothesis.
• Collect and summarize the data into a test
  statistic.
• Use the test statistic to determine the p-value.
• The result is statistically significant if the
  p-value is less than or equal to the level of
  significance.

Often media only presents results of step 4.
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• A p-value is calculated under the assumption that
  the null hypothesis is __________.
• True
• False

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Quitting Smoking with Nicotine Patches
Compared the smoking cessation rates for smokers
randomly assigned to use a nicotine patch versus
a placebo patch.
Null hypothesis The proportion of smokers in the
population who would quit smoking using a
nicotine patch and a placebo patch are the
same. Alternative hypothesis The proportion of
smokers in the population who would quit smoking
using a nicotine patch is higher than the
proportion who would quit using a placebo patch.
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Quitting Smoking with Nicotine Patches
Higher smoking cessation rates were observed in
the active nicotine patch group at 8 weeks (46.7
vs 20) (P lt .001) and at 1 year (27.5 vs 14.2)
(P .011). (Hurt et al., 1994, p. 595)
Conclusion p-values are quite small less than
0.001 for difference after 8 weeks and equal to
0.011 for difference after a year. Therefore,
rates of quitting are significantly higher using
a nicotine patch than using a placebo patch after
8 weeks and after 1 year.
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Role of Sample Size in Statistical Significance
If the sample size is large enough, almost any
null hypothesis can be rejected. There is almost
always a slight relationship between two
variables, or a difference between two groups,
and if you collect enough data, you will find it.
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No Difference versus No Statistically
Significant Difference
If the sample size is too small, an important
relationship or difference can go undetected. In
that case, we would say that the power of the
test is too low.
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• Which of the following conclusions should make
  you suspicious as an educated consumer of
  statistical information?
• a. Based on our sample results we know there is
  no relationship between these two variables in
  the population.
• b. We looked at all possible correlations
  between these 10 variables, and this was the only
  one that was significant, signifying its
  tremendous importance.
• c. All of the above.