GNRS 713

Week 3

T-tests

Statistics

Descriptive Inferential

Correlational

Relationships

GeneralizingOrganizing, summarising & describing data

Significance

3

1. Experimental Design• Experiment

– Treatment: something that researchers administer to experimental units

– Factor: controlled independent variable whose levels are set by the experimenter

• Experimental design– Control– Treatment

• Placebo effect• Blind

– single blind, double blind, triple blind

4

1. Experimental Design• Randomization

– Completely randomized design• The computer generated sequence:

4,8,3,2,7,2,6,6,3,4,2,1,6,2,0,…….

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1. Experimental Design• Methods of Sampling

– Random sampling– Systematic sampling– Convenience sampling– Stratified sampling

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1. Experimental Design• Random Sampling

– Selection so that each individual member has an equal chance of being selected

• Systematic Sampling– Select some starting point and then select every k

th element in the population

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1. Experimental Design• Convenience Sampling

– Use results that are easy to get

8

1. Experimental Design• Stratified Sampling

– Draw a sample from each stratum

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2. Descriptive Statistics & Distributions

• Standard normal distribution: – Mean 0, variance 1

Example Hypotheses: Isometric Torque

• Is there any difference in the length of time that males and females can sustain an isometric muscular contraction?

Null Hypothesis

There is not a significant difference in the DV between males and females

Alternative Hypothesis

There is a significant difference in the DV between males and females.

Example Hypotheses: Isometric Torque

• Is there any difference in the length of time that males and females can sustain an isometric muscular contraction?

Energy Intake (calories per day)

1500 2500 3500 4500 5500

Nu

mb

er o

f P

eo

ple

0

20

40

60

80

100

120

140

160

16 17 18 19 20

Sustained Isometric Torque (seconds)

N♂N♀

n♂n♀

Statistical Errors• Type 1 Errors-Rejecting H0 when it is actually true -Concluding a difference when one does not actually exist

• Type 2 Errors-Accepting H0 when it is actually false (e.g. previous

slide)-Concluding no difference when one does exist

Energy Intake (calories per day)

1500 2500 3500 4500 5500

Nu

mb

er o

f P

eo

ple

0

20

40

60

80

100

120

140

160

16 17 18 19 20

Sustained Isometric Torque (seconds)

n♂n♀

Independent t-test: Calculation

Mean SD n

♀ 18.5 1.74 25

♂ 17.5 1.72 25

• Problem: Sam Sleep researcher hypothesizes that people who are allowed to sleep for only four hours will score significantly lower than people who are allowed to sleep for eight hours on a cognitive skills test. He brings sixteen participants into his sleep lab and randomly assigns them to one of two groups. In one group he has participants sleep for eight hours and in the other group he has them sleep for four. The next morning he administers the SCAT (Sam's Cognitive Ability Test) to all participants.

• 8 hours sleep group (X) 5 7 5 3 5 3 3 9

• 4 hours sleep group (Y) 8 1 4 6 6 4 1 2

Scores on the SCAT range from 1-9 with high scores representing better performance.