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Using Statistics To Make Inferences 1

Summary

What is an experiment 

What is an hypothesis 

What is a p-value

 

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Goals

To lay the foundations for the course.

To be able to interpret a p-value. 

Practical

Graphical methods applied to sampling.

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What might we test?

1. Men are taller than women2. Women are taller than men3. Men and women are the same height

1 & 2 are typical examples of a one tail test (< or >).

3 is a typical example of a two tail test for equality(=). As opposed to not equal to (≠).

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Height

Fre

qu

en

cy

9080706050403020100

FemaleMale

Sex

Histogram of Height

What might we test?

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What might we test?

1. Men are more competitive than women are.2. Women are more co-operative than men are.3. Lung cancer is more common among

smokers.4. 80% of traffic accidents are caused by

excessive speed.5. Colour blindness is more common among

men.6. Men find women with a smaller waist to hip

ratio more attractive.

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What might we test?

7. Women find men with more symmetric features more attractive.

8. 87% of the population support the present Prime Minister.

9. More young people are vegetarians.10. Children are more likely to be killed by step-

fathers than fathers.11. 67% of people own mobile phones.

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What might we test?

12. Students are more likely than staff to own mobile phones.

13. Poorer people commit more crimes.14. Extroverts are more successful.15. 32% surveyed prefer organically grown

vegetables.

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Sampling

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Notation

Sample Population

Mean μ

Standard deviation

s σ

x

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Sampling Distributions

The means of the samples range from 41.6 to 46.8.

The overall mean is 45.56

Sample 1 52 42 46 45 49 2 40 53 52 45 43 3 55 40 45 50 43 4 41 46 52 41 28 5 49 52 39 46 45

Mean46.8046.6046.6041.6046.2045.56

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Testing Hypothesis

Null hypothesis

H0

Assumes that there is no real

effect present

Alternate hypothesis

H1

Assumes that there

is some effect

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Testing Hypothesis Recall that a null hypothesis (Ho) states that the findings of the experiment are no different to those that would have been expected to occur by chance. Statistical hypothesis testing involves calculating the probability of achieving the observed results if the null hypothesis were true. If this probability is low (conventionally p < 0.05), the null hypothesis is rejected and the findings are said to be “statistically significant” (unlikely) at that accepted level.

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One Tail Test

95%Accept H0Result notsignificant

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Two Tail Test

95%

Accept H0

Result notsignificant

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Accepting Or Rejecting The Null Hypothesis - p-

Valuep-value Significance Decision

p>0.1 Not significant at the 10% level

Accept H0

0.1>p>0.05 Significant at the 10% level, but not at 5%

Accept H0, investigate further

0.05>p>0.01

Significant at the 5% level

Reject H0

0.01>p>0.001

Significant at the 1% level

Reject H0, with some confidence

0.001>p Significant beyond the 0.1% level

Reject H0, with reasonable certainty

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Interpretation Of p-Values

0 Reject H0, with reasonable certainty

0.001 Reject H0, with some confidence

0.01 Reject H0

0.05 Accept H0, investigate further

0.1 Accept H0 1

p-axis

A commentary on p values

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Review The Steps Involved In Finding A p Value

1. We formulate a null.2. Assuming the null is true, we display that

null model.3. We superimpose in the null model on our

sample data (usually a statistic like t or chi square)

4. We find the area(s) in the null model that are as extreme or more extreme than our sample data are.

5. That extreme area is the p value.

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What Does It Mean?

The p value represents the area in the null model that is more extreme than our sample data given we assume the null is true.

A large p value means that our sample data do not look unusual given the null model.

A very low p value suggests a misfit between our data and the null model.

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What Does It Mean?

The smaller the p value is, the more discrepant our sample results look compared to what they should look like under the null model.

What does the p value prove?

Actually nothing.

If we retain the null with a large p value, it does NOT prove that the null is true. If we reject the null with a low p value it does NOT prove that the null is false.

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What Does It Mean?

At best, low p values suggest to you that the null model is not looking too good since the sample data conflict with it.

Does rejecting the null tell you how strong an effect is? NO

Does rejecting the null tell you how important an effect is? NO

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What is the average height of 19 year old

males? Type of study parameter estimation

Sample 10 members of the class

Sampling method

choose at random

Population students studying PSY1011

Type of population

finite19 year old males

Target population

not of UK 19 year olds in general, only first year psychology students

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What is the average weight of female

students? Type of study parameter estimation

Sample 10 members of the class

Sampling method

ask for volunteers

Population students studying PSY1011

Type of population

finiteall female students

Target population

not of female students in general, only first year psychology students

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Is there any evidence for extra-sensory perception? Method Test whether an individual has extra-

sensory perception, by identifying the shape, from five possible, on a concealed card.

Infinite population

Repeat to obtain a sample of the required size

Random variable

Number of successful predictions

Null hypothesis

If guessing should be correct one time in 5.

If there were 12 correct response in 50 trials, would this be sufficient evidence for extra-sensory perception? See the Binomial section later.

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Does alcohol slow down reaction times?

Method Choose a representative sample

Run experiment One group is given alcohol, the control group a placebo, both are presented with an identical stimulus and their reaction times recorded.

Test Do reaction times differ between the groups

Method Choose a representative sample

The appropriate method of analysis will be covered later.

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Does a new method of teaching mathematics

improve scores? The average score obtained by all children completing a mathematics test is 56%. In an experiment 100 children, selected at random, are taught by a novel method and their scores

noted. To test the result either estimate the sample average score together with a confidence interval or test whether the average score differs significantly from the national average.

The appropriate method of analysis will be covered later.

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Suggested Texts

• Introduction to Statistics in Psychology by Dennis Howitt and Duncan Cramer, ISBN: 0130173142

• First Steps In Research and Statistics: A Practical Workbook for Psychology Students by Dennis Howitt and Duncan Cramer, ISBN 0203457323 (electronic book) 0415201012

• Statistics For The Behavioural Sciences An Introduction by Riccardo Russo, ISBN 0203641574 (electronic book) 1841693200

• An Introduction to Statistics and Research Methods: Becoming a Psychological Detective by Stephen F. Davis and Randolph A. Smith, Prentice Hall, 2005, ISBN 0131505114

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Read

Read Howitt and Cramer pages 3-8

Read Howitt and Cramer (e-text) pages 3-8

Read Russo pages (e-text) 78-94

Read Davis and Smith pages 14-15, 42-43

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Practical 1

This material is available from the module web page.

http://www.staff.ncl.ac.uk/mike.cox

Module Web Page

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Practical 1

This material for the practical is available.

Instructions for the practical

Practical 1

Material for the practicalPractical 1

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Best Access Route

For technical reasons the best performance for the material (SPSS and e-books) used in this module is obtained using a web page via RAS.

Enter ras.ncl.ac.uk into your favourite web browser.

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Best Access Route

Then select

Communications and Browsers > IE For on Campus Web Pages

and enter www.staff.ncl.ac.uk/mike.coxin the available address box

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Best Access Route

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Whoops!

Experts disagree over the issue, with some saying there is no proof light drinking harms the baby, while others believe the evidence is inconclusive.

The Independent

21 January 2009

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Whoops!Why pay less when you could pay more?