Statistics for Psychology

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• Statistics for Psychology
• Patrick Murphy
• Department of Statistics
• Room L548
• 5th Floor Library Building
• Patrick.Murphy_at_UCD.IE

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• 12 Lectures
• 2.00 pm Tuesdays
• Theatre L
• Textbook
• Seeing Through Statistics
• by
• Jessica Utts
• Duxbury Press

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• CLASS WEBPAGE
• 1. Go to the Statistics Department Website
• WWW.UCD.IE/Statdept/
• 2. Then click on ClassPages in the left frame
• 3. Finally click on
• Statistics for Psychology

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What do you know about statistics?
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Its boring
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Frogs and Princesses
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There are three kinds of lies

• Lies
• Damned Lies
• and
• Statistics
• - Benjamin Disraeli

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A single death is a tragedy, a million deaths is
a statistic.Joseph Stalin (1879-1953)
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The weaker the data available upon which to base
one's conclusion, thegreater the precision which
should be quoted in order to give the
dataauthenticity.Norman R. Augustine
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Simpsons episode

• Homer is questioned about his newly formed
  vigilante group
• Newscaster Since your group started up, petty
  crime is down 20, but other crimes are up.
• Such as heavy sack beating which is up 800. So
  youre actually increasing crime.
• Homer You can make up statistics to prove
  anything.
• 43 of people know that.

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Misuse of Statistics

• The Great Meryl Streep Apple Juice Cancer Scare
• Asbestos is really bad for you so we need to
  eradicate it from our buildings

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Aeroplanes

• 1/1,000,000 chance of a bomb on a plane
• Aeroplane Engines

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What about Probability?

• The foundation of Probability theory lies in
  problems associated with gambling and games of
  chance
• The Romans used played a game with ASTRAGALI -
  Heel bones of animals

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DICE

• DICE as we know them were invented around 300 BC

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I lied, cheated and stole to become a
millionaire. Now anybody at all can win the
lottery and become a millionaire
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LOTTO 6/42

• What are the chance of winning with one selection
  of 6 numbers?
• Matches Odds
• 6 1 in 5,245,786
• 5 1 in 24,286
• 4 1 in 555

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LOTTO 6/42

• The average time to win each of the prizes is
  given by
• Match 3 with Bonus 2 Years, 6 Weeks
• Match 4 2 Years, 8 Months
• Match 5 116 Years, 9 Months
• Match 5 with Bonus 4323 Years, 5 Months
• Share in Jackpot 25,220 Years

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Why do people still play the lottery?

• If youre not in you cant win!
• You never know your luck until you try!
• My chances of winning a million are better than
  my chances of earning a million.
• The lottery is a tax on the statistically
  challenged.

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Lincoln Kennedy

• Abraham Lincoln was elected to Congress in 1846.
  
• John F Kennedy was elected to Congress in 1946.
• Abraham Lincoln was elected President in 1860.
• John F. Kennedy was elected President in 1960.
• The names Lincoln and Kennedy each contain seven
  letters.
• Both were particularly concerned with civil
  rights.

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Lincoln Kennedy

• Both wives lost a child while living in the White
  House.
• Both Presidents were shot on a Friday.
• Both Presidents were shot in the head.
• Lincoln's secretary was named Kennedy.
• Kennedy's secretary was named Lincoln.
• Both were assassinated by Southerners.

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Lincoln Kennedy

• Both were succeeded by Southerners named Johnson.
  
• Andrew Johnson, who succeeded Lincoln, was born
  in 1808.
• Lyndon Johnson, who succeeded Kennedy, was born
  in 1908.
• John Wilkes Booth, who assassinated Lincoln, was
  born in 1839.
• Lee Harvey Oswald, who assassinated Kennedy, was
  born in 1939.

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Lincoln Kennedy

• Both assassins were known by their three names.
• Both names are composed of fifteen letters.
• Lincoln was shot at the theatre named 'Ford.'
• Kennedy was shot in a car called 'Lincoln.'
• Booth ran from the theatre and was caught in a
  warehouse.
• Oswald ran from a warehouse and was caught in a
  theatre.
• Booth and Oswald were assassinated before their
  trials.

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Lincoln Kennedy

• And here's the clincher.
• A week before Lincoln was shot, he was in
  Monroe, Maryland.
• A week before Kennedy was shot, he was in Marilyn
  Monroe.
• Ohand on the day he died Lincoln pardoned a man
  named
• Patrick Murphy

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Election Which parties have most power?

• Party A - 45
• Party B - 44
• Party C - 7
• Party D - 4

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Were ready to play some games
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An Example

• Experiment Roll Two Dice
• Possible Outcomes Any number from 1 to 6 can
  appear on each die.
• There are 36 possible outcomes
• Each Outcome in the Sample Space is equally
  probable.
• So the probability of each outcome is 1/36
• What is the probability of the Event - get
  combined total of 7 on the dice

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A more interesting example

• Game Show
• Who wants to win a Ferrari?
• 3 doors
• 1 Car 2 Goats
• You pick a door - e.g. 1
• Host knows whats behind all the doors and he
  opens another door, say 3, and shows you a goat
• He then asks if you want to stick with your
  original choice 1, or change to door 2?

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Ask Marilyn.

• Marilyn vos Savant
• Guinness Book of Records -Highest IQ
• Yes you should switch. The first door has a 1/3
  chance of winning while the second has a 2/3
  chance of winning.
• Ph.D.s - Now two doors, 1 goat 1 car so chances
  of winning are 1/2 for door 1 and 1/2 for door
  2.
• You are the goat - Western State University.

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Whos right?

• At the start, the sample space is
• CGG, GCG, GGC
• Pick a door e.g. 1
• 1 in 3 chance of winning
• Host shows you a goat so now
• CGG, GCG, GGC
• So Marilyn was right, you should switch.

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Chapter 1The Beginning

• Statistics is the science of data. This involves
  collecting, analysing and interpreting
  information.
• Descriptive Statistics uses graphical and
  numerical techniques to summarise and display the
  information contained in a dataset.
• Inferential Statistics uses sample data to make
  decisions or predictions about a larger
  population of data

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• More Definitions
• Population The entire collection of individuals
  or objects about which information is desired.
• Sample A part (subset) of the population
  selected in some prescribed manner.
• Variable A characteristic or property of an
  individual unit in the population.
• Representative Sample A selection of data
  chosen from the target population which exhibits
  characteristics typical of the population.
• Representative samples should give unbiased
  estimates

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• More Definitions
• The most common way to select a Representative
  Sample is to choose a Random Sample.
• A Random Sample is a sample selected so that
  each different possible sample of the desired
  size has an equal chance of being the one chosen.
• This implies that each member of the original
  population has an equal chance of being selected
  in any random sample.

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Descriptive vs Inferential Statistics

• Descriptive statistics is only interested in
  describing a dataset, whereas Inferential
  Statistics seeks to make a decision based on the
  data.

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An Example of Descriptive Statistics- UCD
Faculties
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By using Descriptive Statistics to display the
data in this manner we can now analyse the data
more easily to find trends or patterns which
were not immediately obvious in the original
dataset.
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The Basics of Inferential Statistics - An Example

• A Newspaper wants to know whether people are
  happy with the performance of the Government.
  They hire a company to conduct an opinion poll.
  The pollsters select 1000 people and ask them the
  question Are you happy with the performance of
  the Government?
• The Newspaper prints a headline like the
  following
• 70 want the Government to go
• or
• Government achieves record popularity among
  voters

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• How can the newspaper publish things like this?
• They have only got the opinions of less than
  1000 people ( remember the dont knows).
• 1000/2.3 Million 0.00043 or 0.043
• Before the end of this course we will find out
  in great detail whether we should believe these
  polls.

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• For the moment lets examine the procedure
  carried out in this example.
• The newspaper is interested in a certain
  population. What is this Population?
• The newspaper wants to measure some variable for
  each unit of the population. What variable do
  they want to measure?
• The opinion pollsters decide to select a sample
  from the population. What is the sample?
• And what is so special about the sample chosen?
• Is the result reliable?

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How to collect data.

• Before we can begin making inferences about the
  data we need to collect the data itself. Usually
  one gets data in one of 4 different ways.
• Data from a published source
• The data has already been collected and the
  results published, all we need do is draw
  conclusions from the data. This is where
  politicians and economists get most of their
  data. A boring way to get data!!!
• Data from a designed experiment
• Here you design and conduct an experiment to
  measure some characteristic of a population. You
  have strict control over how the experiment is
  carried out. This is the way scientists collect
  their data and it is the method which should
  provide the most accurate results.

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How to collect data continued...

• Data from a survey
• Here you select a representative sample of
  people from the population you are interested in.
  You ask each person some questions and record
  their answers. This method is used by polling
  companies, government statisticians etc. It has
  certain obvious drawbacks relating to the
  truthfulness of responses.
• Data collected observationally
• Here one observes the sample in its normal
  environment and records the variables of
  interest. Used by biologists and psychologists.