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Lecture 4

# PSYB07H3 Lecture Notes - Lecture 4: Interquartile Range, Statistical Inference, Quartile

by OC1062122

Department

PsychologyCourse Code

PSYB07H3Professor

Dwayne PareLecture

4This

**preview**shows pages 1-3. to view the full**12 pages of the document.**Lecture Notes September 28, 2016

Lecture #4 – PSYB07 – Descriptive Statistics II

Lecture #4 – Descriptive Statistics II

Unbiased

Unbiased estimator

Expected value of =μ

o From an individual sample may not =μ (of a population)

sample may not equal population

oIf I average the from many samples, the average (mean of the means)

would = μ

Sample of 10 may or may not be a representation of the entire

class (population) – it depends

If you do a sample of 10, another sample of 10, another sample

of 10, then you get the average of these then average their

results, that is a better representation of the population and

therefore unbiased

oNot true for median nor mode

Example

Population = 6, 6, 8, 8, 9, 9, 10, 11, 14

µ (population mean) = 9

Median = 9

Collect a sample

à µ

Sample median à Population median

median

is

biased to the sample you take in the

picture on the right ^

Efficiency

1

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Lecture Notes September 28, 2016

Lecture #4 – PSYB07 – Descriptive Statistics II

Estimate µ (or population median) = 9

oSample means cluster more closely to 9

Because we know the data is all being used, every time we take

a sample, that sample is closer to 9 than the median may be

Mean is more efficient in this way

omean à More efficient

- Too get more efficiency: Take one sample with a large N – gives us a close

approximation to the population parameter

Summary

Mean:

o✗ Resistant - gets pulled be outliers

o✓ Sufficient – uses all of the data

o✓ Unbiased – when you get a sample statistic the expected value is =

to population

o✓ Efficient – the means efficient and that increases with the larger

sample

Inferential

oSample mean à Population mean

oThe requirement for these inferential statistics which is the

sample mean is inferring the population mean

oInferential statistics make predictions about a population from

observations and analyses of a sample (with the use of statistical tests)

oRather than doing multiple samples, we can just do a large sample and

we can figure out if our results are valued

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Lecture Notes September 28, 2016

Lecture #4 – PSYB07 – Descriptive Statistics II

Variability

Measures of Variability

Variability/Spread

oHow far is the rest of your data from the centre of the distribution?

Small variability (49&51) they are not very far away from the

middle

Mean of an exam =70, then we see the variability is between

(68-72)

oBlue graph = very little variability

oRed = lots of variability (data across the entire spectrum)

Range

oDistance between lowest and highest score

Interquartile Range (IQR)

oDistance between 1st and 3rd quartile

Variance & Standard Deviation (MOST IMPORTANT ASPECT OF

VARIABILITY BECAUSE IT IS A MEASURE THAT IS USED IN EVERYTHING

WE DO IN STATISTICS)

o“Average” distance from the mean

Range

Range = highest score – lowest score

Population = 6, 6, 8, 8, 9, 9, 10, 11, 14

oRange = 14 – 6 = 8

Low Resistance - sensitive to outliers

oLet’s say someone watched for 20 hours and someone watches for 3

hours… they are more extreme and therefore it would not be a good

representation of the true range

Interquartile Range (IQR)

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