Statistical Methods

1
Statistical Methods

• What is statistics
• Set of methods and rules for organizing,
  summarizing, and interpreting information
• e.g., mean or average snow for the current year
  were significantly more murders committed this
  year do stroke patients differ significantly
  from age-matched controls in the number of errors
  they make when performing activities of daily
  living

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Statistical Methods

• Why learn statistics
• Its necessary in order to understand and
  critically evaluate what you hear and read in
  everyday life
• e.g., is a new medical treatment (expensive)
  significantly better than a conventional
  treatment (covered by OHIP)?
• e.g., is a new marketing strategy effective?

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Statistical Methods

• Why learn statistics
• It is a tool that those of you who are planning
  to become psychologists, social scientists, or
  who plan to use the tools of these disciplines
  need to know how to use as well as understand

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Statistical Methods

• Why learn statistics
• Statistics is useful
• one goal of this course will be to teach you
  techniques (Lecture) will follow book
• Second goal will be to teach you how to apply
  these techniques (Lab)
• Teach you SPSS, a computerized statistical
  package
• Use this package to analyze data from an
  experiment that this class will carry out

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Statistical Methods

• Populations and samples
• Population
• Set of individuals of interest in a study
• e.g., psychology often studies individual people
  but population could be set of families, small
  businesses in Canada, parts produced by a factory
• -population generally refers to the set of
  individuals about whom you are interested in
  studying

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Statistical Methods

• Populations and samples
• Sample
• Usually most investigators select a sample of
  individuals from this sample
• Sample refers to a set of individuals selected
  from the population. The sample is usually
  intended to represent the population
• Examples of populations and samples
• census, polls, psychological studies

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Statistical Methods

• Populations and samples
• Populations and samples are described in terms of
  their features or characteristics
• Parameter is a value or characteristic that
  describes a population.
• e.g., population of Canada parameters include
  mean age ratio of male to female mean income

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Statistical Methods

• Populations and samples
• Populations and samples are described in terms of
  their features or characteristics
• Statistic is a value that describes a sample
• Random sample of Canadians statistics include
  mean age ratio of male to female mean income,
  etc.
• Note every population parameter can have a
  corresponding sample statistic one important
  question statistics considers is the relation
  between sample statistics and population
  parameters

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Statistical Methods

• Descriptive and inferential statistics
• Descriptive statistics attempt summarize and
  organize data
• e.g., mean score on a test range of scores on a
  test table or graph summarizing a test score

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Statistical Methods

• Descriptive and inferential statistics
• inferential statistics techniques that allow us
  to study samples and then make generalizations
  about the populations from which they were
  selected.

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Statistical Methods

• Note it is important to note that if you take a
  sample from a population, the sample statistics
  will deviate somewhat from the corresponding
  population parameter
• e.g., small island with 10 people having ages
  20, 45, 13, 1, 57, 45, 21, 80, 90, 77
• Mean age of population is 449/1044.9
• sample statistic will vary depending upon the
  size of the sample you select, and the
  individuals included in the sample 44, 48, .

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Statistical Methods

• Sampling error
• Refers to the discrepancy or the amount of error
  between a sample statistic and the corresponding
  population parameter
• e.g., you hear about sampling error when results
  from political polls are presented results are
  within/- 4 19 times out of 20

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Statistical Methods

• See example 1.1 page 9 in book
• Stages of study
• 1. Purpose.
• 2. Method. Design and procedure
• 3. Collect data
• 4. Results Descriptive inferential stats
• 5. Discussion

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Statistical Methods

• Issues to discuss
• Is the sampling procedure representative?
• Descriptive statistics
• Mean, standard deviation
• Inferential statistics
• do the means differ significantly from each
  other

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Statistical Methods

• Random sampling or random selection
• In this procedure, every individual in the
  population has the same chance of being selected
  in the sample. A sample obtained by random
  selection is called a random sample.
• Experiment with 2 conditions first 10
  participants in condition 1 2nd 10 participants
  in condition 2 is this a random sample?

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Statistical Methods

• Random sampling or random selection
• Making sure that your sampling procedure is
  random
• e.g. random assignment of participant to
  condition use table of random digits
• Provide an example

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Statistical Methods

• Variable
• Characteristic or condition that changes or has
  different values for different individuals
• e.g., characteristics of participants (e.g., sex,
  age)
• e.g., characteristics of a study (e.g.,
  conditions of an experiment such as learning
  condition)
• -

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Statistical Methods

• Techniques for investigating relationships
• Most studies are concerned with investigating the
  relation between two or more variables
• Approaches
• Correlational observe two variables to see if
  there is a relationship
• E.g., does the fox and rabbit population covary?
  How would you investigate?
• E.g., do memory performance and grades covary?
• Limitation does not tell you whether there is a
  cause-effect relation

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Statistical Methods

• Techniques for investigating relationships
• Experimental
• Goal is to understand what effect one variable
  has on another variable.
• Manipulate one (or more) variable(s) and observe
  changes in one or more other variables
• hold constant (or randomize) other factors (or
  variables) that are not under investigation
• E.g., effect of delay between study and test on
  memory performance (hold constant environmental
  factors) randomly assign participants to
  condition (delayshort vs long)

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Statistical Methods

• Techniques for investigating relationships
• Experimental
• Independent variable variable manipulated by
  the experimenter
• Dependent variable variable observed by
  experimenter
• In previous slide which is the independent and
  dependent variable

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Statistical Methods

• Confounding variable
• Refers to a variable or factor that covaries with
  the independent variable
• E.g., comparison of effect of delay on recall in
  two groups using two different sets of materials
• What are the confounds? How can you prevent a
  confound?

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Statistical Methods

• Quasi-experimental method
• In this type of experiment the experimenter does
  not manipulate the variable
• Common types of variables that are not
  manipulated
• Subject variables gender, personality attribute
• Time variables time since injury

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Statistical Methods

• Theory
• Importance identify factors to manipulate,
  control, or randomize
• Many studies attempt to evaluate theories by
  assessing hypotheses that are implied by theory
• Hypothesis
• Prediction about relation between variables

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Statistical Methods

• Constructs
• Theories contain constructs or hypothetical
  concepts, which describe mechanisms that underlie
  behavioural phenomena

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Visual/Gestural input
Visual/Object Input
Visual analysis (motion)
Visual analysis (static)
Action input lexicon
Structural Description System
Auditory/ Verbal Input
Tactile Analysis
Tactile/ Proprioceptive Input
Semantic knowledge
Auditory analysis
Action output lexicon
Motor programmes
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Statistical Methods

• Scales of measurement
• Nominal scale
• A form of measurement in which there is a set of
  categories with different names that cannot be
  reasonably ordered
• E.g., sex, location (province), type of course
  taken (psychology, sociology)

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Statistical Methods

• Scales of measurement
• Ordinal scale
• Categories that can be ordered, but differences
  between scores are not meaningful
• E.g., scores of 3, 4, and 5 on scale meaningful
  to state that the people differ not meaningful to
  say that difference between person 1 and 2 is
  equal to the difference between person 2 and 3
• This means that you cannot add and subtract
  ordinal scale measures (e.g., you cannot
  calculate mean)

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Statistical Methods

• Scales of measurement
• Interval and ratio scales
• Interval scale ordered categories in which
  differences between categories are meaningful
• Measures of distance, time, etc.

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Statistical Methods

• Discrete versus continuous variables
• Discrete separate indivisible categories
• E.g., number of children, number of correct
  responses
• Continuous
• Infinite number of possible values
• E.g., time, length, weight

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Statistical Methods

• Frequency distribution
• Points to note the sum of the frequencies equals
  the total
• Mean (arithmetic average)
• Sum of all the scores divided by the number of
  scores
• What is the mean of the scores on the previous
  table can you think of another way to calculate
  the mean?

32
Statistical Methods

• Frequency distribution
• Proportion measures the fraction of the total
  group that is associated with each score
• Proportion p f/N where f frequency of a
  particular score and N total number of scores
• Percentage proportion 100 p 100
• f100/N

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Statistical Methods

• Frequency distribution
• Organized tabulation of individuals located in
  each category on the scale of measurement
• Table
• Graph

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Statistical Methods

• Frequency distribution
• 20, 20, 30, 40, 50, 50, 80, 80, 80, 90

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Statistical Methods

• Grouped frequency distribution table
• When a set of data contain a wide range of values
  it is necessary to group data into intervals so
  as to be able to produce an informative table
• See book for further details about grouped
  frequency distribution table

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Frequency distributions

• Frequency distribution graphs
• Represent pictorially frequency distribution
  tables
• The x-axis or abscissa depicts the independent
  variable
• The y-axis or ordinate depicts the dependent
  variable

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Statistical Methods

• Frequency distribution
• 20, 20, 30, 40, 50, 50, 80, 80, 80, 90

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Statistical Methods

• requency distribution
• 20, 20, 30, 40, 50, 50, 80, 80, 80, 90

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Statistical Methods

• Shapes of frequency distributions
• Symmetrical distributions
• Distribution in which it is possible to draw a
  vertical line through the middle of a frequency
  distribution and each side is the mirror image of
  the other
• Skewed distribution
• Distribution in which the scores tail of at one
  end
• Positively skewed ?tail is at the positive or
  right end of the distribution
• Negatively skewed ? tail is at the negative or
  left end of the distribution

42
Statistical Methods

• Percentiles and percentile ranks
• used to describe an individuals performance
  relative to the performance of a sample
• Rank or percentile rank refers to the percentage
  of individuals in the distribution with scores at
  or below the particular value
• E.g., amnesics are defined as individuals whose
  memory performance scores fall at or below the 2
  percentile range, but whose performance on other
  cognitive tasks is in the normal range.GRE
  scores are frequently reported as percentile
  scores

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Statistical Methods

• Percentiles and percentile ranks
• cumulative frequency (cf) number of individuals
  with scores at or below a given score
• Cumulative percentage c cf100/N

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