Social Science Reasoning Using Statistics

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Social Science Reasoning Using Statistics

• Psychology 138
• Spring 2005

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Estimation

• So far weve been dealing with situations where
  we know the population mean. However, we often
  dont know it.

• Use what we do know

• Sample information

• Two kinds of estimation
• Point estimates
• A single score
• Interval estimates
• A range of scores

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Estimation
Estimate the number of people attending lecture
today
How confident are you that your estimate is
correct?
Not real confident, maybe 20
65 students
Fairly confident, maybe 90
somewhere between 40 and 90 students
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Estimation
Kinds of estimation
Point estimate
65 students
Interval estimate
somewhere between 40 and 90 students
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Estimation

• Both kinds of estimates use the same basic
  procedure
• The formula is a variation of the test statistic
  formulas (well start with the z-score)

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Estimation

• Both kinds of estimates use the same basic
  procedure
• The formula is a variation of the test statistic
  formulas (well start with the z-score)

1) It is often the only piece of evidence that we
have, so it is our best guess. 2) Most sample
means will be pretty close to the population
mean, so we have a good chance that our sample
mean is close.
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Estimation

• Both kinds of estimates use the same basic
  procedure
• The formula is a variation of the test statistic
  formulas (well start with the z-score)

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Estimation

• Finding the right test statistic (z or t)

• You begin by making a reasonable estimation of
  what the z (or t) value should be for your
  estimate.
• For a point estimation, you want what?

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Estimation

• Finding the right test statistic (z or t)

• You begin by making a reasonable estimation of
  what the z (or t) value should be for your
  estimate.
• For a point estimation, you want what? z (or t)
  0, right in the middle

• For an interval, your values will depend on how
  confident you want to be in your estimate

• What do I mean by confident?
• 90 confidence means that 90 of confidence
  interval estimates of this sample size will
  include the actual population mean

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Estimation

• Finding the right test statistic (z or t)

• You begin by making a reasonable estimation of
  what the z (or t) value should be for your
  estimate.
• For a point estimation, you want what? z (or t)
  0, right in the middle
• For an interval, your values will depend on how
  confident you want to be in your estimate
• Computing the point estimate or the confidence
  interval

• take your reasonable estimate for your test
  statistic
• put it into the formula
• solve for the unknown population parameter.

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Estimates with z-scores
So the point estimate is the sample mean
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Estimates with z-scores
What two z-scores do 95 of the data lie between?
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Estimates with z-scores
What two z-scores do 95 of the data lie between?
So the confidence interval is 83.04 to 86.96
or 85 1.96
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Estimates with z-scores
What two z-scores do 90 of the data lie between?
From the table z(1.65) .0500
So the confidence interval is 83.35 to 86.65
or 85 1.65
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Estimates with z-scores
What two z-scores do 90 of the data lie between?
From the table z(1.65) .0500
So the confidence interval is 80.88 to 89.13
or 85 4.13
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Estimation

• The size of the margin of error related to

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Estimation in other designs
Estimating the mean of the population from one
sample, but we dont know the ?
Use the t-table
Confidence interval
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Estimates with t-scores
Confidence intervals always involve a margin of
error
This is similar to a two-tailed test, so in the
t-table, always use the proportion in two tails
heading, and select the ?-level corresponding to
(1 - Confidence level)
What is the tcrit needed for a 95 confidence
interval?
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Estimates with t-scores
What two critical t-scores do 95 of the data lie
between?
From the table tcrit 2.064
So the confidence interval is 82.94 to 87.06
95 confidence
or 85 2.064
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Estimation in other designs
Estimating the difference between two population
means based on two related samples
Confidence interval
Diff. Expected by chance
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Estimation in other designs
Estimating the difference between two population
means based on two independent samples
Confidence interval
Diff. Expected by chance
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Estimation Summary
Design
Estimation
(Estimated) Standard error
One sample, ? known
One sample, ? unknown
Two related samples, ? unknown
Two independent samples, ? unknown
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In labs

• Practice computing and interpreting confidence
  intervals