Ch15 data exploration (ii)
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Transcript of Ch15 data exploration (ii)
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Research Methods, 9th Edition
Theresa L. White and Donald H. McBurney
Chapter 15Data Exploration Part 2:
Inferential Statistics
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Some basic terms
Empirical data Facts derived from experience
Population All members of some group
Sample A subset of a population
Statistic A quantity computed from a sample
Parameter A quantity computed from a population
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Statistics
Descriptive Statistics Summarize a set of data Chapter 14
Inferential Statistics Assist in drawing conclusions about
populations by examining a sample drawn from the population.
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Sampling Distributions
Distribution of means of samples from a population
Standard Error of the Mean Standard
Deviation of a sampling distribution
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Sampling Distributions
Three properties: The sampling distribution has the same
mean as the original distribution. The sampling distribution has a smaller
standard deviation than the population distribution.
The larger the size of the samples that are drawn from the population, the smaller the standard deviation of the sample distribution.
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Sampling Distributions
The standard error of the mean is the standard deviation of the population divided by the square root of the sample size
The sample size becomes larger, the shape of the distribution approaches a normal distribution, regardless of the shape of the population from which the samples are drawn.
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Hypothesis Testing
H1 (Alternative) vs H0 (Null)
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Hypothesis Testing
H1 (Alternative) vs H0 (Null)
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Hypothesis Testing
H1 (Alternative) vs H0 (Null)
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Hypothesis Testing
H1 (Alternative) vs H0 (Null)
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Hypothesis Testing
Directional hypothesis An alternative hypothesis that predicts that the results of
one condition will be greater (or less) than another, rather than a prediction that they will simply differ.
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Hypothesis Testing
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Hypothesis Testing
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Hypothesis Testing
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Hypothesis Testing
One-tailed hypothesis test Statistical test of a directional hypothesis
Two-tailed hypothesis test Statistical test of a nondirectional hypothesis
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Hypothesis Testing
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Hypothesis Testing
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Hypothesis Testing
Statistical significance is the probability that a result happened by chance
Alpha is the probability of deciding that the null hypothesis is false when it’s actually true. Probability of a Type I error
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Hypothesis Testing
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Hypothesis Testing
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Hypothesis Testing
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Hypothesis Testing
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Significance
Probability that an experimental result happened by chance
Generally alpha less than .05 (statistical significance)
Does not necessarily mean that the result was important or large
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Significance
The significance of significance Size of result is measured with Effect Size
Effect size shows the strength of the relationship between the independent and dependent variables.
Be measured by practice or by Cohen’s d (eta-squared)
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Significance
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Power of the Test of the Null Hypothesis Against the Alternative
Power is the probability of rejecting the null hypothesis when it actually IS false
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Power of the Test of the Null Hypothesis Against the Alternative Power
Three things influence the power of a test The value of alpha
The smaller your alpha level, the smaller your power. Experimental error Sample sizes
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Chi Square Statistic
Tests Frequency Data to determine whether two categorical variables are related.
Expected Frequency vs Observed Frequency
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Chi Square Statistic
contingency table also referred to as cross tabulation or crosstab In statistics, a contingency table is a type of table in a
matrix format that displays the (multivariate) frequency distribution of the variables.
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Chi Square Statistic
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ANOVA
Compares more than two conditions For only two, use a t-test
Tests the significance of a difference among several conditions in an experiment by making two different estimates of the variability that would be expected if the null hypothesis is true. Between variability Within variability
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T test
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ANOVA
Ha: at least two means differ(Note the alternative hypothesis is sometimes stated as "at least one mean differs")
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ANOVA
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ANOVA
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How to Read an ANOVA Table
Between Subjects Single Factor Design
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How to Read an ANOVA Table
Within Subjects Single Factor Design
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How to Read an ANOVA Table
Between Subjects Factorial Design