statistics for the social sciences psychology 340 fall 2006 distributions
TRANSCRIPT
Statistics for the Social Sciences
Psychology 340Fall 2006
Distributions
Statistics for the Social Sciences
Outline (for week)
• Variables: IV, DV, scales of measurement– Discuss each variable and it’s scale of measurement
• Characteristics of Distributions– Using graphs– Using numbers (center and variability)
• Descriptive statistics decision tree
• Locating scores: z-scores and other transformations
Statistics for the Social Sciences
Let’s get some data
• On a sheet of paper (that you’ll turn in) write out these pieces of information:– Male or female– Height (in inches)– How many pairs of shoes in your closet– Typical number of servings of soda per day– Typical number of servings of water per day
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Basic Concepts
Variable– A condition or characteristic that can have different values
Value– A possible number or category that a score can have
Score– A particular person’s value on a variable
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Basic Concepts
Kinds of Variables– A condition or characteristic that can have different values– Experiment:
– Independent - manipulated by experimenter– Dependent - measured by experimenter
– Observational:– Explanatory - observed variable to do the explaining
– Response - variable to be predicted
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Measurement
• Properties of our measurement?– Units of measurement - whether the measurement has a minimum sized unit or not
– Levels (Scales) of measurement - the correspondence between the numbers representing the properties that we’re measuring
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Units of Measurement
• Continuous variables– Variables can take any number and can be infinitely broken down into smaller and smaller units
– E.g., For lunch I can have2,3,or 2.5 cookies
• Discrete variables– Broken into a finite number of discrete categories that can’t be broken down– E.g., In my family I can have1 kidor 2 kids, but not 2.5
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Units of Measurement
• Continuous or discrete?:– Male or female– Height (in inches)– How many pairs of shoes in your closet– Typical number of servings of soda per day– Typical number of servings of water per day
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Levels (scales) of measurement
• Nominal Scale: Consists of a set of
categories that have different names. – Measurements on a nominal scale label and categorize observations, but do not make any quantitative distinctions between observations.
– Example:•Eye color:
blue,
green,
brown,
hazel
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Levels of measurement
• Ordinal Scale: Consists of a set of categories that are organized in an ordered sequence. – Measurements on an ordinal scale rank observations in terms of size or magnitude.
– Example: • T-shirt size:
Small,Med,Lrg,XL, XXL
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Levels of measurement
• Interval Scale: Consists of ordered categories where all of the categories are intervals of exactly the same size. – With an interval scale, equal differences between numbers on the scale reflect equal differences in magnitude.
– Ratios of magnitudes are not meaningful.– Example:
• Fahrenheit temperature scale 20º
40º“Not Twice as
hot”
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Levels of measurement
• Ratio scale: An interval scale with the additional feature of an absolute zero point. – With a ratio scale, ratios of numbers DO reflect ratios of magnitude.
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Levels of measurement
• What kind of measurement is used for each of these variables?:– Male or female– Height (in inches)– How many pairs of shoes in your closet– Typical number of servings of soda per day– Typical number of servings of water per day
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Distributions
• The distribution of a variable is a description of all of the tokens of the variable within in sample (or population if you’ve got the data)– A picture of the distribution is usually helpful• Gives a good sense of the properties of the distribution
– Many different ways to display distribution• Frequency distribution table• Graphs
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Steps for Making a Frequency Table(do this for class soda drinking variable)
• Make a list down the page of each possible value, from highest to lowest
X f % c% 12 11 10 9 8 7 6 5 4 3 2
The values of the variable
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Steps for Making a Frequency Table
• Go one by one through the scores, making a mark for each next to its value on the list, count up how frequently each value appears and include this in the table
X f % c% 12 11 10 9 8 7 6 5 4 3 2
The values of the variable
The number of tokens of each variable
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Steps for Making a Frequency Table
• Figure the percentage (or proportion) of scores for each value
X f % c% 12 11 10 9 8 7 6 5 4 3 2
The values of the variable
The number of tokens of each variable
N=total% = (f/N)*100
The percentage of tokens at each value
Statistics for the Social Sciences
Steps for Making a Frequency Table
• Figure the cumulative percentage (or proportion) of scores for each value
X f % c% 12 11 10 9 8 7 6 5 4 3 2
The values of the variable
The number of tokens of each variable
N=total% = (f/N)*100
The percentage of tokens at each valueCumulative percentage
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Grouped Frequency Table(do this for class height variable)
A frequency table that uses intervals (range of values) instead of single values
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Frequency Graphs
Histogram Plot the different values against the frequency of each value
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Frequency Graphs
Histogram (create one for class height) Step 1: make a frequency distribution table (may use grouped frequency tables)
Step 2: put the values along the bottom, left to right, lowest to highest
Step 3: make a scale of frequencies along left edge
Step 4: make a bar above each value with a height for the frequency of that value
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Frequency Graphs
Frequency polygon - essentially the same, put uses lines instead of bars
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Properties of distributions
• Distributions are typically summarized with three features
•Shape•Center•Variability (Spread)
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Shapes of Frequency Distributions
Unimodal, bimodal, and rectangular
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Shapes of Frequency Distributions
Symmetrical and skewed distributions
Normal and kurtotic distributions
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Displaying two variables
Bar graphs Can be used in a number of ways (including displaying one or more variables)
Best used for categorical variables
Scatterplots Best used for continuous variables
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Bar graphs
• Plot a bar graph of men and women in the class
• Plot a bar graph of shoes in closet crossed with men and women– What should we plot? (and why?)
•Total number of shoes for each group?•Average number of shoes for each group?
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Scatterplot
• Plot a scatterplot of soda and bottled water drinking– Useful for seeing the relationship between the variables
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Next time
• In addition to using tables and graphs to describe distributions, we also can provide numerical summaries