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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
© 2012 The McGraw-Hill Companies, Inc.
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
© 2012 The McGraw-Hill Companies, Inc.
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
© 2012 The McGraw-Hill Companies, Inc.
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
© 2012 The McGraw-Hill Companies, Inc.
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
© 2012 The McGraw-Hill Companies, Inc.
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
© 2012 The McGraw-Hill Companies, Inc.
Probability: The Case of ESP Are correct answers due to chance or due to
something more? Sampling Distributions Sample Size
© 2012 The McGraw-Hill Companies, Inc.
t value is a ratio of two aspects of the data The difference between the group means and The variability within groups
© 2012 The McGraw-Hill Companies, Inc.
t= group difference
within-group difference
Degrees of Freedom One-Tailed Two-Tailed Tests The F Test (analysis of variance)
Systematic variance Error variance
© 2012 The McGraw-Hill Companies, Inc.
Calculating Effect Size Confidence Intervals and Statistical
Significance Statistical Significance
© 2012 The McGraw-Hill Companies, Inc.
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.
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.
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.
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
© 2012 The McGraw-Hill Companies, Inc.
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
© 2012 The McGraw-Hill Companies, Inc.
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
© 2012 The McGraw-Hill Companies, Inc.
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
© 2012 The McGraw-Hill Companies, Inc.
One Independent Variable Nominal Scale Data Ordinal Scale Data Interval or Ratio Scale Data
© 2012 The McGraw-Hill Companies, Inc.
© 2012 The McGraw-Hill Companies, Inc.
IV DV Statistical Test
NominalMale-Female
NominalVegetarian – Yes / No
Chi Square
Nominal (2 Groups)Male-Female
Interval / RatioGrade Point Average
t-test
Nominal (3 groups)Study time (Low, Medium, High)
Interval / RatioTest Score
One-way ANOVA
Interval / RatioOptimism Score
Interval / RatioSick Days Last Year
Pearson’s correlation