Non-Experimental designs: Developmental designs

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Non-Experimental designs Developmental designs
Small-N designs

• Psych 231 Research Methods in Psychology

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Announcements

• Journal Summary 2 due this week
• Bring your group project data to labs this week
• Decide how to analyze it
• What test
• Organize the data
• Somebody from each group is encouraged to visit
  an office hour next week to finish the group
  project data analysis

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Developmental designs

• Used to study changes in behavior that occur as a
  function of age changes

• Three major types
• Cross-sectional
• Age is subject variable treated as a
  between-subjects variable
• Longitudinal
• Cohort-sequential

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Developmental designs

• Longitudinal design

• Follow the same individual or group over time
• Age is treated as a within-subjects variable
• Rather than comparing groups, the same
  individuals are compared to themselves at
  different times
• Repeated measurements over extended period of
  time
• Changes in dependent variable reflect changes due
  to aging process
• Changes in performance are compared on an
  individual basis and overall

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Developmental designs

• Longitudinal design

• Advantages
• Can see developmental changes clearly
• Avoid some cohort effects (participants are all
  from same generation, so changes are more likely
  to be due to aging)
• Can measure differences within individuals

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Developmental designs

• Longitudinal design

• Disadvantages
• Can be very time-consuming
• Can have cross-generational effects
• Conclusions based on members of one generation
  may not apply to other generations
• Numerous threats to internal validity
• Attrition/mortality
• History
• Practice effects
• Improved performance over multiple tests may be
  due to practice taking the test
• Cannot determine causality

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Developmental designs

• Cohort-sequential design

• Measure groups of participants as they age
• Example measure a group of 5 year olds, then the
  same group 5 years later, as well as another
  group of 5 year olds
• Age is both between and within subjects variable
• Combines elements of cross-sectional and
  longitudinal designs
• Addresses some of the concerns raised by other
  designs
• For example, allows to evaluate the contribution
  of generation effects

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Developmental designs

• Cohort-sequential design

• Advantages
• Can measure generation effect
• Less time-consuming than longitudinal
• Disadvantages
• Still time-consuming
• Still cannot make causal claims

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Small N designs

• What are they?
• Review Chapter 13
• One or a few participants
• Data are not analyzed statistically rather rely
  on visual interpretation of the data
• Basic method
• Observations begin in the absence of treatment
  (BASELINE)
• Look for stable level
• Then treatment is implemented
• Changes in frequency, magnitude, or intensity of
  behavior are recorded

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Statistics

• Why do we use them?
• Descriptive statistics
• Used to describe, simplify, organize data sets
• Inferential statistics
• Used to test claims about the population, based
  on data gathered from samples
• Takes sampling error into account, are the
  results above and beyond what youd expect by
  random chance

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Distributions

• Recall that a variable is a characteristic that
  can take different values.
• The distribution of a variable is a summary of
  all the different values of a variable
• both type (each value) and token (each instance)

How much do you like psy231? 1 - 2 - 3 - 4 -
5 Hate it Love it
5 values (1, 2, 3, 4, 5)
7 tokens (1,1,2,3,4,5,5)
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Distribution

• Example Distribution of scores on an exam
• A frequency histogram

Frequency
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Distributions

• A picture of the distribution is usually helpful
• Gives a good sense of the properties of the
  distribution
• Many different ways to display distribution
• Graphs
• Continuous variable
• histogram, line graph (frequency polygons)
• Categorical variable
• pie chart, bar chart
• Table
• Frequency distribution table
• Stem and leaf plot

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Graphs for continuous variables

• Histogram

• Line graph

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Graphs for categorical variables

• Bar chart

• Pie chart

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Frequency distribution table
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Distribution

• Properties of a distribution
• Shape
• Symmetric v. asymmetric (skew)
• Unimodal v. multimodal
• Center
• Where most of the data in the distribution are
• Mean, Median, Mode
• Spread (variability)
• How similar/dissimilar are the scores in the
  distribution?
• Standard deviation (variance), Range

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Shape

• Symmetric

• Asymmetric

Positive Skew
Negative Skew
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Shape

• Unimodal (one mode)

• Multimodal
• Bimodal examples

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Center

• There are three main measures of center
• Mean (M) the arithmetic average
• Add up all of the scores and divide by the total
  number
• Most used measure of center
• Median (Mdn) the middle score in terms of
  location
• The score that cuts off the top 50 of the from
  the bottom 50
• Good for skewed distributions (e.g. net worth)
• Mode the most frequent score
• Good for nominal scales (e.g. eye color)
• A must for multi-modal distributions

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The Mean

• The most commonly used measure of center
• The arithmetic average
• Computing the mean

• The formula for the population mean is (a
  parameter)

• The formula for the sample mean is (a
  statistic)

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The Mean

• The most commonly used measure of center
• The arithmetic average
• Computing the mean

Our population
2, 4, 6, 8
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Spread (Variability)

• How similar are the scores?
• Range the maximum value - minimum value
• Only takes two scores from the distribution into
  account
• Influenced by extreme values (outliers)
• Standard deviation (SD) (essentially) the
  average amount that the scores in the
  distribution deviate from the mean
• Takes all of the scores into account
• Also influenced by extreme values (but not as
  much as the range)
• Variance standard deviation squared

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Variability

• High variability
• The scores are fairly dissimilar

• Low variability
• The scores are fairly similar

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Standard deviation

• The standard deviation is the most popular and
  most important measure of variability.
• In essence, the standard deviation measures how
  far off all of the individuals in the
  distribution are from a standard, where that
  standard is the mean of the distribution.
  Essentially, the average of the deviations.

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Computing standard deviation (population)

• Step 1 To get a measure of the deviation we need
  to subtract the population mean from every
  individual in our distribution.

Our population
2, 4, 6, 8
X - ? deviation scores
2 - 5 -3
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Computing standard deviation (population)

• Step 1 To get a measure of the deviation we need
  to subtract the population mean from every
  individual in our distribution.

Our population
2, 4, 6, 8
X - ? deviation scores
2 - 5 -3
4 - 5 -1
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Computing standard deviation (population)

• Step 1 To get a measure of the deviation we need
  to subtract the population mean from every
  individual in our distribution.

Our population
2, 4, 6, 8
X - ? deviation scores
2 - 5 -3
6 - 5 1
4 - 5 -1
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Computing standard deviation (population)

• Step 1 To get a measure of the deviation we need
  to subtract the population mean from every
  individual in our distribution.

Our population
2, 4, 6, 8
X - ? deviation scores
2 - 5 -3
6 - 5 1
Notice that if you add up all of the deviations
they must equal 0.
4 - 5 -1
8 - 5 3
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Computing standard deviation (population)

• Step 2 So what we have to do is get rid of the
  negative signs. We do this by squaring the
  deviations and then taking the square root of the
  sum of the squared deviations (SS).

SS ? (X - ?)2
(-3)2
(-1)2
(1)2
(3)2
9 1 1 9 20
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Computing standard deviation (population)

• Step 3 Now we have the sum of squares (SS), but
  to get the Variance which is simply the average
  of the squared deviations
• we want the population variance not just the SS,
  because the SS depends on the number of
  individuals in the population, so we want the
  mean
• So to get the mean, we need to divide by the
  number of individuals in the population.

variance ?2 SS/N
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Computing standard deviation (population)

• Step 4 However the population variance isnt
  exactly what we want, we want the standard
  deviation from the mean of the population. To
  get this we need to take the square root of the
  population variance.

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Computing standard deviation (population)

• To review
• Step 1 compute deviation scores
• Step 2 compute the SS
• either by using definitional formula or the
  computational formula
• Step 3 determine the variance
• take the average of the squared deviations
• divide the SS by the N
• Step 4 determine the standard deviation
• take the square root of the variance