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Introducing Inferential Statistics

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Descriptive statistics provide basic measures of a distribution of scores ... A NEW TWIST TO p .05. A statement of probability, e.g., p .05 ... – PowerPoint PPT presentation

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Title: Introducing Inferential Statistics


1
Chapter 8
  • Introducing Inferential Statistics

2006 Prentice Hall, Salkind.
2
CHAPTER OVERVIEW
  • Say Hello to Inferential Statistics
  • The Idea of Statistical Significance
  • Tests of Significance
  • Significance Versus Meaningfulness
  • Meta-analysis

3
SAY HELLO TO INFERENTIAL STATISTICS
  • Descriptive statistics provide basic measures of
    a distribution of scores
  • Inferential statistics allow inferences to a
    larger population from the sample

4
HOW INFERENCE WORKS
  • Representative samples from two groups are
    selected
  • Participants are tested
  • Means from each group are compared
  • Researcher concludes that measured differences
    between groups either
  • Result from chance, or
  • Reflect true differences
  • A conclusion is drawn regarding the role group
    membership plays in observed differences

5
THE ROLE OF CHANCE
  • Chance is the first explanation for observed
    differences
  • Chance is unexplained variability
  • The goal of science is to
  • Control sources of variability, thus
  • Reducing the role of chance as an explanation

6
THE CENTRAL LIMIT THEOREM
  • The means of samples drawn from a population will
    be normally distributed
  • This is so regardless of the shape of the
    population distribution
  • This demonstrates the power of inference

7
AN EXAMPLE OF THE CENTRAL LIMIT THEOREM
8
THE IDEA OF STATISTICAL SIGNIFICANCE
  • Because sampling is imperfect
  • Samples may not ideally match the population,
    and
  • Because hypotheses cannot be directly tested
  • Inference is subject to error

9
STATISTICAL SIGNIFICANCE
  • The degree of risk that you are willing to take
    that you will reject a null hypothesis when it is
    actually true

10
MAKING A DECISION
11
TYPE I AND TYPE II ERRORS
  • The probability of making a Type I error
  • Set by researcher
  • e.g., .01 1 chance of rejecting null when it
    is true
  • e.g., .05 5 chance of rejecting null when it
    is true
  • Not the probability of making one or more Type I
    errors on multiple tests of null!
  • The probability of making a Type II error
  • Not directly controlled by researcher
  • Reduced by increasing sample size

12
HOW A TEST OF SIGNIFICANCE WORKS
  • Each type of null hypothesis is tested with a
    particular statistic
  • Each statistic is characterized by a unique
    distribution of values that are used to evaluate
    the sample data

13
USING A STATISTICAL TEST
  • State the null hypothesis
  • Ho µ 1 µ2
  • Establish significance level
  • e.g., p .05
  • e.g., p .01

14
USING A STATISTICAL TEST
  • Select appropriate test statistic
  • Compute test statistic (obtained value)
  • Determine value needed to reject null (critical
    value), which depends on
  • Level of significance chosen (e.g., p 0.5)
  • Degrees of freedom (based on sample size)
  • Compare obtained value to critical value
  • If obtained value gt critical value, reject null
  • If obtained value ? critical value, accept null

15
t-TEST FOR INDEPENDENT MEANS Used to test null
hypothesis when two independent, unrelated groups
are compared E.g., Chen and Stevenson (1989)
  • State null
  • Establish level of risk
  • Select test statistic
  • Compute value
  • Determine critical value
  • Compare obtained value
  • Ho µ 1980 µ 1984
  • p .05
  • t-test
  • 2.00
  • 1.980
  • 2.00 gt 1.980 p lt .05

16
WHAT DOES t120 2.00, p lt .05 Really Mean?
  • t type of test
  • 120 degrees of freedom
  • (related to sample size)
  • 2.00 obtained value of t test
  • p probability
  • .05 level of significance
  • (Type I error rate)

17
A NEW TWIST TO p lt .05
  • A statement of probability, e.g.,
  • p lt .05
  • indicates that the probability of making a Type
    I error on a test is less than .05
  • But SPSS and other data analysis software compute
    exact probabilities, e.g.,
  • p .0375

18
(No Transcript)
19
LOOKING AT DIFFERENCES BETWEEN GROUPS
20
t-TEST FOR DEPENDENT MEANS
  • State null
  • Establish level of risk
  • Select test statistic
  • Compute value
  • Determine critical value
  • Compare obtained value
  • Ho µ 1A µ 1B
  • p .01
  • t-test
  • 4. 2.581
  • 5. 2.771
  • 2.581 lt 2.771
  • p gt .01

 
 
 
 
 
21
LOOKING AT RELATIONSHIPS BETWEEN VARIABLES
22
MULTIVARIATE ANALYSIS OF VARIANCE (MANOVA)
  • Simultaneously tests differences between groups
    on multiple dependent variables, but
  • Because dependent variables might be related
  • True Type I Error rate is inflated
  • 1 (1 - )k
  • Type I error rate
  • k number of pairwise comparisons
  • So, MANOVA takes these possible relationships
    into account

23
FACTOR ANALYSIS
  • A factor groups several related measures into one
    construct
  • The new construct is treated as a dependent
    variable
  • This technique allows a researcher to more
    efficiently examine how these sets of variables
    are related

24
SIGNIFICANCE VERSUS MEANINGFULNESS
  • Statistical significance refers to the
  • Probability that chance influenced observed
    differences
  • Not to the meaningfulness or importance of
    observed differences
  • Statistical significance must be interpreted
    within a larger context

25
META-ANALYSIS
  • Compares the results of multiple independent
    studies that have examined the same conceptual,
    dependent variable
  • Allows examination of trends and patterns that
    may exist in many different groups in many
    different studies

26
HOW META-ANALYLSES ARE DONE
  • An adequate sample of studies is collected
  • Results from these studies are converted to a
    common measureusually effect size
  • Important aspects of the study are coded
  • Descriptive and correlational techniques are used
    to look for trends or common patterns in the
    outcomes of the group of studies
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