STATISTICAL INFERENCE
UNDERSTANDING RESEARCH RESULTS: STATISTICAL INFERENCE
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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
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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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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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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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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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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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Probability: The Case of ESP
Are correct answers due to chance or due to something more?
Sampling Distributions
Sample Size
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t value is a ratio of two aspects of the data
The difference between the group means and
The variability within groups
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| t= | group difference |
| within-group difference |
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Degrees of Freedom
One-Tailed
Two-Tailed Tests
The F Test (analysis of variance)
Systematic variance
Error variance
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Calculating Effect Size
Confidence Intervals and Statistical Significance
Statistical Significance
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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
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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
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Researchers traditionally have used either a .05 or a .01 significance level in the decision to reject the null hypothesis
The significance level chosen is usually dependent on the consequences of making a Type I vs. Type II error.
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- 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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- 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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- 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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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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One Independent Variable
Nominal Scale Data
Ordinal Scale Data
Interval or Ratio Scale Data
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| IV | DV | Statistical Test |
| Nominal Male-Female | Nominal Vegetarian – Yes / No | Chi Square |
| Nominal (2 Groups) Male-Female | Interval / Ratio Grade Point Average | t-test |
| Nominal (3 groups) Study time (Low, Medium, High) | Interval / Ratio Test Score | One-way ANOVA |
| Interval / Ratio Optimism Score | Interval / Ratio Sick Days Last Year | Pearson’s correlation |
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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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