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Validity and Introduction to Inferential Statistics

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Title: Validity and Introduction to Inferential Statistics


1
Lecture 7-8
  • Validity and Introduction to Inferential
    Statistics

2
  • Chain of Reasoning for
  • Inferential Statistics

Selection
Sample
Population
Inference
3
  • Hypothesis Testing

4
  • Hypothesis

A statement about what findings are expected and
are used for inferential statistics null
hypothesis statements of valueless statistically
significant relationships of differences "the two
groups will not differ alternative
hypothesis statements of statistically
significant relationships of differences "group A
will do better than group B" "group A and B will
not perform the same"
5
  • Possible Outcomes in
  • Hypothesis Testing

Type I Error Rejecting a True Hypothesis Type
II Error Accepting a False Hypothesis
6
Probability
Statistical probability is the odds that what we
observed in the sample did not occur because of
error (random and/or systematic). In other
words, the probability associated with a
statistic is the level of confidence we have that
the sample group that we measured actually
represents the total population.
7
Two Tail
  • 2.5

2.5
5 region of rejection of null hypothesis Non
directional
8
One Tail
  • 5

5 region of rejection of null hypothesis Directio
nal
9
  • Possible Outcomes in
  • Hypothesis Testing

Type I Error Rejecting a True Hypothesis Type
II Error Accepting a False Hypothesis
10
  • Chain of Reasoning for
  • Inferential Statistics

Selection
Sample
Population
Inference
11
When we conduct a study and obtain our RESULTS,
we would like to have some confidence that our
conclusions are the most plausible explanations
for the results we observed
12
  • Relationship of Variables

confounding variables
independent variables
dependent variables
presumed or possible cause
presumed results
13
  • Confounding Variables Threats to Internal Validity
  • Intervening Variables
  • Independent variables that have not been or can
    not be controlled or measured directly
  • Extraneous Variables
  • those uncontrolled variables (not manipulated by
    the experimenter) that may have a significant
    influence upon the results of the study

14
The extent that we can be confident in our
conclusions is related to the degree of internal
validity we have established in our study
15
Judging Internal Validity
  • Explanation credibility
  • is the study reasonable?
  • problem, lit review, purpose hypotheses

16
Judging Internal Validity
  • Translation fidelity
  • are the operational definitions reasonable
  • 5 Ws and an H
  • Who (subjects)
  • Where (situation)
  • Why (treatment (the cause))
  • What (measurement (the effect))
  • How (method of evaluation)
  • When (procedure)

17
Judging Internal Validity
  • Demonstrated Result
  • Authenticity of the evidence
  • Precedence of cause
  • Presence of effect
  • Congruence of explanation and evidence

18
Judging Internal Validity
  • Rival explanations eliminated
  • There are always rival explanations, it is up to
    the researcher to anticipate as many as possible
    and design a study that eliminates or minimizes
    the most threatening
  • use of comparison groups (control groups)
  • randomization

19
Judging Internal Validity
  • Credible Result
  • the sum of the previous 4 judgements
  • includes an evaluation of this studies findings
    in relation to the literature
  • consistent with previous research
  • inconsistent ----gt why

20
Classical Threats to Internal Validity
  • History
  • Maturation
  • Selection
  • Instrumentation
  • Mortality
  • Cross-Sectional Longitudinal
  • Matching
  • Subject Effect
  • Valid Data (self report)
  • Regression to the mean
  • Correlation - Causality
  • Experimenter Effect
  • Instability
  • Observer/rater Effects
  • Order Effects
  • Sampling Bias
  • Statistical
  • Testing
  • Treatment Confound

21
History
  • When a group of subjects is measured before and
    after exposure to some treatment,
    pretest-posttest change (or lack of) can be
    attributed to something other than the treatment
    that took place outside of the confines of the
    study between the pre and post measurements

22
Maturation
  • Changes in the organism (person) over the course
    of the study may influence the outcome measure

23
Instrumentation
  • Sometimes a measuring instruments ability to
    yield accurate information systematically changes
    over time, like when norms become obsolete

24
Mortality
  • If subjects drop out of a one-group
    pretest-posttest design, or there is differential
    rates of (and reasons) attrition in multi-group
    designs, conclusions about group differences can
    be misleading

25
Selection
  • When two or more groups receive different
    treatments and there is a failure to randomly
    assign subject to groups, treatment differences
    might me confounded with initial group differences

26
Cross-Sectional / Longitudinal
  • Attempts to identify developmental trends by
    studying different age groups (cross-sectional)
    and not by studying one age group over an
    extended time period (longitudinal)

27
Matching
  • The attempt to create equivalent groups at the
    start of a study by selecting specific variable
    and making sure they are equally distributed in
    all your groups

28
Subject Effect
  • The subjects in particular group figure out what
    your study is about and alter their behavior
    (consciously or unconsciously)

29
Valid Data / Self-Report
  • When a subject (consciously or unconsciously)
    reports false data.

30
Regression To The Mean
  • If a group of subject are preselected to receive
    a treatment because they represent an extreme
    group and the pretest has a correlation lower
    than 1.00 with the posttest, the preselected
    group will be less extreme on the posttest
    regardless of the treatment intervention

31
Correlation / Causality
  • Drawing a causal conclusion when the design is
    not an experimental design

32
Experimenter Effect
  • When there are different experimenters and they
    differentially treat the different experimental
    groups, or when one experimenter changes the way
    they treat (react to) a group

33
Instability
  • Sample statistics are estimates of population
    values (parameters) and thus often have limited
    generalizability

34
Observer/Rater Effects
  • Two people viewing the same thing will often see
    and report different things

35
Order Effects
  • Can happen when multiple measuring instruments or
    treatments are administered and the outcome
    response is partially dependent on the specific
    order of presentation.

36
Sampling Bias
  • The use of non-representative (non random)
    samples and trying to generalize back to the
    population

37
Statistical (other than instability and
regression)
  • The use of the wrong statistical test, or
    violation of the assumptions underlying the
    statistical test used

38
Testing
  • People tend to become more normal on subsequent
    testing

39
Treatment Confound
  • When characteristics in the study or experimenter
    characteristics are confounded with the treatment
    administration

40
Methods For Determining Change
  • Method of agreement
  • there is only one instance in common and all else
    differs
  • Method of differences
  • two groups exactly alike except one gets exposed
    to the treatment, the other doesnt
  • Method of concomitant variation
  • used when it is not possible to control the
    situations experimentally
  • Method of Residuals

41
Inferential Statistics
  • Relationship
  • bivariate
  • correlation
  • multivariate
  • Regression
  • Group comparison
  • IV, DV
  • t-test
  • ANOVA
  • Estimation

42
Relationship
43
Pearson Correlation
  • Direction of relationship (linear)
  • positive or negative
  • Magnitude of relationship (-1.0 to 1.0)
  • pencil
  • cigar
  • football
  • watermelon
  • ball

44
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45
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46
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47
Nonlinear Relationship
48
Correlation Interpretation
Coefficient Range Strength of Relationship
0.0 - .20 Very Low
.20 - .40 Low
.40 - .60 Moderate
.60 - .80 High Moderate
.80 - 1.0 Very High
49
Common Correlations
  • Pearson Product Moment Correlation
  • both variables are continuous
  • Spearman Rank-order Correlation
  • both variables are measured as rank data
  • Biserial Correlation
  • one variable is continuous and one is an
    artificial dichotomy with an underlying normal
    distribution
  • Point-Biserial Correlation
  • one variable is continuous and one is a true
    dichotomy
  • Phi Coefficient
  • both variables are true dichotomies

50
More Correlations
  • Tetrachoric Correlation
  • both variables are artificial dichotomies with
    underlying normal distributions
  • Polychoric Correlation
  • both variables are ordinally measured with both
    having underlying normal distributions
  • Polyserial Correlation (rps, Dps)
  • one variable is continuous and one is ordinal
    with an underlying normal distribution
  • Kendall Tau-b
  • measures agreement between two rankings
  • Kendalls Coefficient of Concordance
  • measures of the extent to which members of a set
    of m distinct rank orderings of N things tend to
    be similar
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