1. UNDERSTANDING RESEARCH RESULTS: STATISTICAL INFERENCE
CHAPTER 13
UNDERSTANDING RESEARCH RESULTS: STATISTICAL INFERENCE
© 2012 The McGraw-Hill Companies, Inc
© 2012 The McGraw-Hill Companies, Inc.

2. LEARNING OBJECTIVES
Explain how researchers use inferential statistics to evaluate sample data
Distinguish between the null hypothesis and the research hypothesis
Discuss probability in statistical inference, including the meaning of statistical significance
© 2012 The McGraw-Hill Companies, Inc.

3. LEARNING OBJECTIVES
Describe the t test, and explain the difference between one-tailed and two-tailed tests
Describe the F test, including systematic variance and error variance
Distinguish between Type I and Type II errors
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4. LEARNING OBJECTIVES
Discuss the factors that influence the probability of a Type II error
Discuss the reasons a researcher may obtain nonsignificant results
Define power of a statistical test
Describe the criteria for selecting an appropriate statistical test
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5. SAMPLES AND POPULATIONS
Inferential statistics are necessary because
the results of a given study are based on data obtained from a single sample of researcher participants and
Data are not based on an entire population of scores
Allows conclusions on the basis of sample data
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6. INFERENTIAL STATISTICS
Allow researchers to make inferences about the true differences in populations of scores based on a sample of data from that population
Allows that the difference between sample means may reflect random error rather than a real difference
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7. NULL AND RESEARCH HYPOTHESES
Null Hypothesis
H0: The means of the populations from which the samples were drawn equal
Research Hypothesis
H1: The means of the populations from which the samples were drawn equal
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8. PROBABILITY AND SAMPLING DISTRIBUTIONS
Probability: The Case of ESP
Are correct answers due to chance or due to something more?
Sampling Distributions
Sample Size
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9. within-group difference
THE t TEST
t value is a ratio of two aspects of the data
The difference between the group means and
The variability within groups t=
group difference
within-group difference
© 2012 The McGraw-Hill Companies, Inc.

10. SAMPLING DISTRIBUTION OF t VALUES
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11. EXAMPLE: THE t AND F TESTS
Degrees of Freedom
One-Tailed
Two-Tailed Tests
The F Test (analysis of variance)
Systematic variance
Error variance
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12. EXAMPLE: THE t AND F TESTS
Calculating Effect Size
Confidence Intervals and Statistical Significance
Statistical Significance
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13. TYPE I AND ERRORS Type I Errors
Made when the null hypothesis is rejected but the null hypothesis is actually true
Obtained when a large value of t or F is obtained by chance alone
© 2012 The McGraw-Hill Companies, Inc.

14. TYPE II ERRORS Type II Errors
Made when the null hypothesis is accepted although in the population the research hypothesis is true
Factors related to making a Type II error
Significance (alpha) level
Sample size
Effect size
© 2012 The McGraw-Hill Companies, Inc.

15. THE EVERYDAY CONTEXT OF TYPE I AND TYPE II ERRORS
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© 2012 The McGraw-Hill Companies, Inc.

16. SIGNIFICANCE LEVEL
Researchers traditionally have used either a .05 or a .01 significance level in the decision to reject the null hypothesis
There is universal agreement that the consequences of making a Type I error are more serious than those associated with a Type II error
© 2012 The McGraw-Hill Companies, Inc.

17. CHOOSING A SAMPLE SIZE: POWER ANALYSIS
Power is a statistical test that determines optimal sample size based on probability of correctly rejecting the null hypothesis
Power = 1 – p (probability of Type II error)
Effect sizes range and desired power
Smaller effect sizes require larger samples to be significant
Higher desired power demands a greater sample size
Researchers usually strive power between .70 and .90
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18. IMPORTANCE OF REPLICATIONS
Scientists attach little importance to results of a single study
Detailed understanding requires numerous studies examining same variables
Researchers look at the results of studies that replicate previous investigations
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19. SIGNIFICANE OF PEARSON’S r CORRELATION COEFFICIENT
Is the relationship statistically significant?
H0: r = 0 and
H1: r ≠ 0
It is proper to conduct a t-test to compare the
r-value with the null correlation of 0.00
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20. COMPUTER ANALYSIS OF DATA
Software Programs include
SPSS
SAS
Minitab
Microsoft Excel
Steps in analysis
Input data
Rows represent cases or each participant’s scores
Columns represent for a participant’s score for a specific variable
Conduct analysis
Interpret output
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21. SELECTING THE APPROPRIATE SIGNIFICANCE TEST
One Independent Variable
Nominal Scale Data
Ordinal Scale Data
Interval or Ratio Scale Data
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22. SELECTING THE APPROPRIATE SIGNIFICANCE TESTIV DV
Statistical Test
Nominal
Male-Female
Vegetarian – Yes / No
Chi Square
Nominal (2 Groups)
Interval / Ratio
Grade Point Average
t-test
Nominal (3 groups)
Study time (Low, Medium, High)
Test Score
One-way ANOVA
Optimism Score
Sick Days Last Year
Pearson’s correlation
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23. SELECTING THE APPROPRIATE SIGNIFICANCE TEST
Multiple Independent Variables
Nominal Scale Data – Factorial Design
Ordinal Scale Data – no appropriate test is available
Interval or Ratio Scale Data – Multiple Regression
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