Transcript Inferential Statistics

Inferential Statistics
The Logic of Inferential Statistics
Makes inferences about a population from
a sample
 Assumes a random sample to estimate
error
 Uses tests of significance which are rooted
in the logic of probability sampling
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Making a Statistical Decision
Step 1: Establishing Type I and Type II Error
Risk Levels
 Step 2: Selecting the appropriate statistical test
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– Parametric and Nonparametric Statistics
– Statistics of Difference and Relationship
Step 3: Computing the test statistic
 Step 4: Consulting the appropriate statistical
table
 Step 5: Deciding whether or not to reject the
null hypothesis.
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Chi Square
Nonparametric Statistic of difference
 Used to identify differences in frequency data.
 One Sample Chi Square compares the frequency
of attributes of a variable measured at the
nominal level.
 Chi Square for Contingency Tables compares the
frequency of attributes of two or more variables
measured at the nominal level.
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T-test
Parametric statistic of difference
 Measures the difference between attributes of
an independent variable measured at the
nominal level on some dependent variable
measured at the interval or ratio level.
 The Independent Samples T-test is used when
the two groups (independent variable) are
independent.
 The Paired Samples T-test is used when the two
groups (independent variable) are related.
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Analysis of Variance (ANOVA)
Parametric test of difference
Assesses the extent to which attributes of
independent variables measured at the nominal
level differ on some dependent variable
measured at the interval or ratio level.
 A one-way ANOVA is used when there are more
than two attributes of a single independent
variable measured at the nominal level.
 A factorial ANOVA is used when there are more
than one independent variables measured at the
nominal level.
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Pearson Product-Moment
Correlation
Parametric statistic of relationship
 Assess the degree to which two variables
measured at the interval or ratio level are
linearly related to one another.
 A correlation coefficient can range from -1.00 (a
perfect negative relationship) to +1.00 (perfect
positive relationship)
 The coefficient of determination indicates the
percentage of variation of one variable that is
predicted by knowledge of the other variable.
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