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Lecture 6

PSYC 2002 Lecture Notes - Lecture 6: Level Of Measurement, Standard Score, Null Hypothesis


Department
Psychology
Course Code
PSYC 2002
Professor
Angel Mackenzie
Lecture
6

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Thursday, February 11th, 2016
PSYC 2002 – t-test (dependent)
Summary from last week:
- Hypothesis testing w/ Z-tests
- Confidence Intervals
oAlternative to hypothesis testing
- Effect size
oMeasure of size of difference b/w means, unaffected by sample size
- Power
Lecture Outline:
- Recap of concepts covered to date
- Power revisited
- Hypothesis testing w/ 2 sample means (t-tests)
Recap:
- Measures of central tendency
oMean, median, mode
oMean most important in stats
- Population vs. sample
oRandom sampling
oPopulation “parameters” vs. Sample “statistics”
Mean: μ = population, M = sample (generic)
Variance: σ2 = population, s2 = sample, SD2 = generic
Standard Deviation: σ = population, s = sample, SD = generic
- Variance
oMeasure of variability of scores around mean SD2 =
oNot that useful on its own (due to squared units)
- Standard deviation
oSq. root of variance
oUseful measure b/c it uses “real” units (not squared units)
- The normal distribution
oProbability & proportions
- Z-score
oPopulation parameters known, calculate standardized score for raw data
o Z = X – μ
σ
- Sampling distribution of means
oTheoretical construct (not “real”)

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oAllows us to compare sample mean to distribution of means, & relate sample to
pop.
- Hypothesis testing
oRelate sample to pop. using sampling distribution
oNull & alternate hypotheses
oSet decision criterion (α) based on probability
- Standard error
oMeasure of variability of distribution of means
oSD + influenced by sample size
- Z-statistic
oZ-score calculated for a mean (within set of means)
- Confidence Interval
oRange of values (interval) likely to contain μ
oSet level of confidence – how “confident” that μ is contained in interval
- Effect size
oMeasure of “true” difference (overlap_ b/w 2 populations, unaffected by n
Statistical power defined:
-Statistical power: probability of achieving significant result when H1 (research
hypothesis) is true
- Studies w/ sufficient power have high probability of rejecting null hypothesis if research
hypothesis really is true
-
- Example:
o2 distributions of means (H0 & H1)
oNote size of power region when μ1μ2 is small

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- Example:
oNote how size of power region changes when μ1μ2 is larger
oNote effect on probability of sample means exceeding alpha
Calculating statistical power:
-
- Calculating power using x-test:
1. Plot 2 (sampling) distributions: H1 & H0
oUsing µNH and µRH
2. Determine raw score corresponding to alpha value (i.e., value that separates rejection
region from remainder of H0 distribution)
oCalculate this using population parameters , µ & Zcritical
oUse Z-statistic formula & “works backwards”
3. Plot corresponding point on H1 plot (same value on H1 distribution)
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