Hypothesis TestingHypothesis Testing

Chapter 13

Hypothesis TestingHypothesis Testing

Decision-making processStatistics used as a tool to assist with

decision-makingScientific hypothesis is a statement of the

predicted relationship amongst the variablesNull hypothesis is a statement of no

relationship amongst the variables

Null Hypothesis Not RejectedNull Hypothesis Not Rejected

Total Population

Samplereared inenrichedenvironment

Samplereared insterileenvironment

Null Hypothesis RejectedNull Hypothesis Rejected

Total populationof rats reared insterile environment

Sample usedin study

Total populationof rats reared inenriched environment

Sample usedin study

Hypothesis TestingHypothesis TestingIn Experimental StudiesIn Experimental Studies

Your research design determines the kind of statistical test you will use.

Experimental studies test hypotheses while quasi-experimental studies tend to focus more on generating hypotheses.

Research Research Designs/ApproachesDesigns/Approaches

Type Purpose Time frame

Degree of control

Examples

Experi-mental

Test for cause/

effect relationships

current High Comparing two types of treatments for anxiety.

Quasi-experi-mental

Test for cause/

effect relationships without full control

Current or past

Moderate to high

Gender differences in visual/spatial abilities

Research Research Designs/ApproachesDesigns/Approaches

Type Purpose Time frame

Degree of control

Examples

Non-experimental - corre-lational

Examine relationship between two variables

Current (cross-sectional) or past

Low to medium

Relationship between studying style and grade point average.

Ex post facto

Examine the effect of past event on current functioning.

Past & current

Low to medium

Relationship between history of child abuse & depression.

Research Research Designs/ApproachesDesigns/Approaches

Type Purpose Time frame

Degree of control

Examples

Non-experimental -corre-lational

Examine relat. betw. 2 var. where 1 is measured later.

Future -predictive

Low to moderate

Relat. betw. history of depression & development of cancer.

Cohort-sequen-tial

Examine change in a var. over time in overlapping groups.

Future Low to moderate

How mother-child negativity changed over adolescence.

Research Research Designs/ApproachesDesigns/Approaches

Type Purpose Time frame

Degree of control

Examples

Survey Assess opinions or characteristics that exist at a given time.

Current None or low

Voting preferences before an election.

Quali-tative

Discover potential relationships; descriptive.

Past or current

None or Low

People’s experiences of quitting smoking.

Tests of SignificanceTests of SignificanceThe Question Null Hypothesis Statistical Test

Group Difference between means of 2 diff. groups

H0: g1 = g2 t-independent

Diff. betw. 2 means of related groups

H0: g1a = g1b t-dependent

Diff. betw. means of 3 groups

H0: g1 = g2 = g3 ANOVA

Group Relationships: betw. 2 variables

H0: xy = 0 t-test for sig. Of correlation

Group Relationships: betw. 2 correlations

H0: ab = cd t-test for sig. Of diff. betw. 2 corr.

Experimental DesignsExperimental DesignsExamines differences between experimentally

manipulated groups or variables (e.g., one group gets a certain drug and the other gets a placebo).

At minimum, experimental (independent) variable has two levels (e.g., drug vs. placebo).– Advantage is that you can determine causality.– Disadvantage is cost and many variables cannot

be experimentally manipulated (e.g., smoke exposure over time).

Null HypothesisNull HypothesisSignificance TestingSignificance Testing

Null hypothesis– Results are due to “chance” – H0

Alternative (scientific) hypothesis– Results are due to a true “effect”– H1

Null HypothesisNull HypothesisSignificance TestingSignificance Testing

Null hypothesis– Results are due to “chance” (H0)

Alternative (scientific) hypothesis– Results are due to a true “effect” (H1)

Assess– Assuming H0 is true, what is the probability or

“chance” of obtaining the data we did?

Null HypothesisNull HypothesisSignificance TestingSignificance Testing

Null hypothesis– Results are due to “chance” (H0)

Alternative (scientific) hypothesis– Results are due to a true “effect” (H1)

Assess– Assuming H0 is true, what is the probability or

“chance” of obtaining the data we did?Decide

– If the chance is small enough, reject H0 and infer the “effect” is real.

Experimental Designs:Experimental Designs:Hypothesis TestingHypothesis Testing

Type of Experim ental Research Design

In d ep en d en tsam p les t-tes

Tw o g rou p s

O n e-w ayA N O V A

M ore th antw o g rou p s

O n e in d ep en d en tvariab le

Tw o-w ayA N O V A

Tw o in d ep en d en tvariab les

N u m b er o fin d ep en d en t

variab les

B etw eenS u b jec t

C orre la tedt-tes ts

Tw o g rou p s o rtw o leve ls o f th e

in d ep en d en t va riab le

R ep ea ted m easu resA N O V A

M ore th an tw o g rou p sor m ore th en tw o leve ls o fth e in d ep en d en t va riab le

N u m b er o f g rou p sor leve ls o f th e

in d ep en d en t va riab le

W ith inS u b jec t

Parametric Vs. Non-Parametric Parametric Vs. Non-Parametric Statistics: Two-Sample CasesStatistics: Two-Sample Cases

Level of measurement

Related Samples Independent Samples

Nominal McNemar test Fisher exactX2 test

Ordinal Sign testWilcoxon matched-pairs sign test

Median testMann-Witney U test

Interval T-test for matched pairs

T-independent test

Parametric Vs. Non-Parametric Parametric Vs. Non-Parametric Statistics: > 2-Sample CasesStatistics: > 2-Sample Cases

Level of measurement

Related Samples Independent Samples

Nominal Cochran Q test X2 test

Ordinal Friedman 2-way ANOVA

Kruskal-Wallis one-way ANOVA

Interval Repeated measures ANOVA

ANOVA

Parametric Vs. Non-Parametric Parametric Vs. Non-Parametric Statistics: > 2-Sample CasesStatistics: > 2-Sample Cases

Level of measurement

Correlation

Nominal Contingency coefficient

Ordinal Spearman rank correlationKendall rank correlation, etc.

Interval Pearson’s Correlation Coefficient

Sampling Distribution of Mean Sampling Distribution of Mean Difference ScoresDifference Scores

0

0.5

1

1.5

2

2.5

3

3.5

4

4.5

Normal Curve

95% of all cases

99% of all cases 0

Critical Values of TCritical Values of T

Need to determine the degrees of freedom– df = N-2

Need to determine the p value for rejecting the null hypothesis (alpha)

Need to determine if this is a 1-tailed or 2-tailed level of significance.

T-ValuesT-Values

T120 = 2.00, p < 0.05

What is one of the major What is one of the major criticisms of employing criticisms of employing

statistical tests of the null statistical tests of the null hypothesis to determine if hypothesis to determine if

effects are true?effects are true?

Limitations of Statistical Tests Limitations of Statistical Tests of the Null Hypothesisof the Null Hypothesis

Does not take into account the size of the difference between means (effect size)

Analysis of Variance (ANOVA)Analysis of Variance (ANOVA)

F-ratio = MSbet

MSwithin

Essentially is the between group variance divided by the within group variance.

If the groups come from similar populations, the variances between the groups will be similar to the variance within groups (null hypothesis is not rejected).

ANOVAANOVABetween group variance consists of:

– Variability due to the effect of the independent variable (treatment effect)

– Variability due to chance factors

Within group variance consists of:– Variability in data with the treatment groups that

is due to chance since if treatment effect was consistent, all subjects within a treatment group would experience similar magnitude of effect.

Analysis of Variance (ANOVA)Analysis of Variance (ANOVA)

F-ratio = MSbet

MSwithin

The MS refers to the mean square and is the sums of squares divided by the appropriate degrees of freedom.

Df for MSbet is the number of groups minus 1.

Df for MSwithin is the total number of scores in the experiment minus the number of groups.

ANOVAANOVA

MSbet = treatment effect + chance variability

MSwithin = chance variability

Ratio will be 1 if there is no treatment effectF(2,144) = 5.56, p < 0.05.

Two-Way ANOVATwo-Way ANOVA

Where you have 2 independent variables, each having at least 2 levels. For example,– Drug dose (none vs. 5 mg)– Delivery mood (intravenous vs. oral)

Factorial design so you can test both main effects and interaction effects

Mixed Model:Mixed Model:2 Between Subject Factors2 Between Subject Factors

1 within Subject Factor1 within Subject Factor Where you have 2 independent variables, each having

at least 2 levels. For example,– Drug dose (none vs. 5 mg)– Delivery mood (intravenous vs. oral)

One within subject factor with for example 3 levels– Pre-treatment, 3 and 6 months follow-up

Factorial design so you can test both main effects and interaction effects (3-way interaction effects)

Rejecting the Null HypothesisRejecting the Null HypothesisNull hypothesis can be rejected but not

acceptedArguments made for allowing some

flexibility in being able to conclude the null hypothesis is true;– No other studies of the phenomenon have

rejected the null hypothesis– P value for the test of the null hypothesis is

large (e.g., > .20 or .40).– Research design is sufficiently powerful

Errors in Statistical Errors in Statistical Decision-MakingDecision-Making

Type I error – falsely reject the null hypothesis– At p < .05 there is a 5% chance (5 in 100) of

falsely rejecting null hypothesis

Type II error – failing to reject the null hypothesis when it is false

External ValidityExternal Validity

Chapter 14

Goals of Psychology Goals of Psychology ResearchResearch

Goal is to understand the underlying laws governing the behaviour of organisms.

The extent to which the results of your study help inform one about these underlying laws, the more valuable the findings.

Limits to the importance of the findings are the internal/external validity.

External ValidityExternal ValidityExtent to which the results of the study can

be generalized across different persons, settings, and times.

Typically think of generalizing to specific populations (e.g., North American elementary school students) than world at large.

Best safeguard is random selection but not usually feasible.

Threats to External ValidityThreats to External Validity

Lack of population validityLack of ecological validityLack of time validity

Population ValidityPopulation Validity

Generalizing to the defined population (i.e., target population) from which the sample was drawn.

Sample is the experimentally accessible population.

Population ValidityPopulation Validity

TargetPopulation

Experimentallyaccessiblepopulation

Sample

Population ValidityPopulation Validity

Threatened by a selection by treatment interaction:– Treatment results may not be exactly

reproducible in target population.

Even willingness to volunteer for studies have been shown to result in a selection by treatment interaction effect.

Ecological ValidityEcological Validity

Extent to which the results can be generalized across settings or environmental conditions.– E.g., Would the treatment effect observed in

patients recruited from a 1st class medical centre be the same as the the treatment effect observed in patients recruited from a local community hospital?

Ecological ValidityEcological Validity

Multiple-Treatment Interference– Sequencing effect whereby exposure to one

treatment influences responses to another treatment; or

– Exposure to one experiment influences response in another experiment (e.g., sophisticated participants).

Ecological ValidityEcological Validity

Hawthorne Effect– Knowing one is in a study can affect one’s

behaviour– Participant bias effects (e.g., social

acceptability, compliance)

Novelty or Disruption Effect– Effects are simply due to novelty and wear off

once novelty diminishes.

Ecological ValidityEcological Validity

Experimenter Effect– Enthusiastic experimenter/clinician may get

different effects than a clinician who is implementing the treatment in routine care.

Pre-testing Effect– Administering a pre-test may sensitive the

participant in such a way that he/she may respond differently to the experiment than what would have occurred without a pre-test.

Temporal ValidityTemporal Validity

Extent to which the results would generalize to other times– Results might vary depending on the time

elapsed between presentation of the independent variable and the measurement of the dependent variable.

Temporal ValidityTemporal Validity

Seasonal Variation– Variation that appears regularly over time (e.g.,

change in traffic accident rates between daylight savings time and non-daylight savings time).

– Fixed-time variation – variation at specific, predictable time points

– Variable-time variation – don’t know when variation will occur but when it occurs, there are predictable responses.

Temporal ValidityTemporal Validity

Cyclical Variation– Predictable variation within people or other

organisms

Personological Variation– Variation in the characteristics of the individual

over time

Internal Vs. External ValidityInternal Vs. External ValidityTends to be an inverse relationship

– Internal validity ; external validityIn testing for between group differences,

you want to minimize within group variability and maximize between group differences

To do so you want to ensure high control over factors that could confound the results but this often results in increasingly artificial experimental conditions.

When Is External Validity Less When Is External Validity Less ImportantImportant

When you don’t need to demonstrate that “X” will happen but rather “X” can happen.

Sometimes the main goal is to test a theory and extent to which it reflects “real-life” is less important.