Reasoning in Psychology Using Statistics

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Reasoning in PsychologyUsing Statistics

• Psychology 138
• Spring 2006

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Lab Exam 4 Conclusions from Data

• Inferential Statistics Procedures which allow us
  to make claims about the population based on
  sample data

• Hypothesis testing
• Correlation
• Regression
• Chi-squared test
• Estimation
• Point estimates
• Confidence intervals
• 1-sample z test
• 1-sample t test
• Related samples t-test
• Independent samples t-test

• Testing claims about populations (based on data
  collected from samples)

• Using sample statistics to estimate the
  population parameters

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Lab Exam 4 Conclusions from Data

• Inferential Statistics Procedures which allow us
  to make claims about the population based on
  sample data

• Hypothesis testing
• Correlation
• Regression
• Chi-squared test
• Estimation
• Point estimates
• Confidence intervals
• 1-sample z test
• 1-sample t test
• Related samples t-test
• Independent samples t-test

• Testing claims about populations (based on data
  collected from samples)

• Using sample statistics to estimate the
  population parameters

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Estimation

• Two kinds of estimates that use the same basic
  procedure
• The formula is a variation of the test statistic
  formulas

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Estimation in other designs

• Two kinds of estimates that use the same basic
  procedure
• The formula is a variation of the test statistic
  formulas

Different Designs Estimating the mean of the
population from one or two samples, but we dont
know the ?
Depends on the design (what is being estimated)
Use the t-table your confidence level
Depends on the design
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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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Estimation in other designs
Estimating the difference between the population
mean and the sample mean based when the
population standard deviation is not known
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Estimation in one sample t-design
What two critical t-scores do 95 of the data lie
between?
So the confidence interval is 82.94 to 87.06
From the table tcrit 2.064
or 85 2.064
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Estimation in related samples design
Estimating the difference between two population
means based on two related samples
Confidence interval
Diff. Expected by chance
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Estimation in related samples design

• Dr. S. Beach reported on the effectiveness of
  cognitive-behavioral therapy as a treatment for
  anorexia. He examined 12 patients, weighing each
  of them before and after the treatment. Estimate
  the average population weight gain for those
  undergoing the treatment with 90 confidence.

Differences (post treatment - pre treatment
weights) 10, 6, 3, 23, 18, 17, 0, 4, 21, 10,
-2, 10
Related samples estimation
Confidence level 90
CI(90) 5.72 to 14.28
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Estimation in independent samples design
Estimating the difference between two population
means based on two independent samples
Confidence interval
Diff. Expected by chance
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Estimation in independent samples design

• Dr. Mnemonic develops a new treatment for
  patients with a memory disorder. He randomly
  assigns 8 patients to one of two samples. He
  then gives one sample (A) the new treatment but
  not the other (B) and then tests both groups with
  a memory test. Estimate the population difference
  between the two groups with 95 confidence.

Independent samples t-test situation
Confidence level 95
CI(95) -8.73to 19.73
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Relating estimates to hypothesis tests

• If we had instead done a hypothesis test with an
  ? 0.05, what would you expect our conclusion to
  be?

H0 there is no difference between the groups
- Fail to reject the H0
CI(95) -8.73to 19.73
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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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Lab Exam 4 Conclusions from Data

• Inferential Statistics Procedures which allow us
  to make claims about the population based on
  sample data

• Hypothesis testing
• Correlation
• Regression
• Chi-squared test
• Estimation
• Point estimates
• Confidence intervals
• 1-sample z test
• 1-sample t test
• Related samples t-test
• Independent samples t-test

• Testing claims about populations (based on data
  collected from samples)

• Using sample statistics to estimate the
  population parameters

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Performing your inferential statistics

• Analyze the question/problem.
• The design of the research how many groups, how
  many scores per person, is the population ?
  known, etc.

• Write out what information is given
• Is it asking you to test a difference or make an
  estimate?
• What is your critical value of your test
  statistic (z or t from table, youll need youre
  ?-level)

• Now you are ready to do some computations
• Write out all of the formulas that youll need

• Then fill in the numbers as you know them

• Interpret your final answer

• Reject or fail to reject the null hypothesis?
  What does that mean?

• State your confidence interval and what it means

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Which test do I use?

• The design determines the test

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Which test do I use?

• The design determines the test

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Correlation within hypothesis testing
Suppose that you notice that the more you study
for an exam (X hours of study), the better your
exam score typically is (Y exam score). Test if
there is a significant correlation between the
two variables (? 0.05)
A 6 6
B 1 2
C 5 6
D 3 4
E 3 2
Correlation
2-tailed
Reject H0
There is a significant positive correlation
between study time and exam performance
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Which test do I use?

• The design determines the test

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Regression

• The best fitting line is the one that minimizes
  the differences (error or residuals) between the
  predicted scores (the line) and the actual scores
  (the points)

• Directly compute the equation for the best
  fitting line
• Slope
• Intercept

• Also need a measure of error
• r2 (r-squared)
• Sum of the squared residuals SSresidual
  SSerror
• Standard error of estimate

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Prediction with Bi-variate regression
Suppose that you notice that the more you study
for an exam (X hours of study), the better your
exam score typically is (Y exam score). Compute
the regression equation predicting exam score
with study time.
A 6 6
B 1 2
C 5 6
D 3 4
E 3 2
16.0
SSY
Bi-variate regression
15.20
SSX
14.0
SP
r2 0.806
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Hypothesis testing with Regression

• SPSS Regression output gives you a lot of stuff

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Which test do I use?

• The design determines the test

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Crosstabulation and ?2

• When do we use these methods?
• When we have categorical variables

Step 1 State the hypotheses and select an alpha
level
Step 2 Compute your degrees of freedom df
(Cols-1)(Rows-1) Go to Chi-square statistic
table and find the critical value
Step 3 Obtain row and column totals and
calculate the expected frequencies
Step 4 compute the ?2
Step 5 Compare the computed statistic against
the critical value and make a decision about your
hypotheses