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Statistics for the Social Sciences Psychology 340 Fall 2006 Distributions

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Statistics for the Social Sciences Outline (for week) Variables: IV, DV, scales of measurement –Discuss each variable and its scale of measurement Characteristics of Distributions –Using graphs –Using numbers (center and variability) Descriptive statistics decision tree Locating scores: z-scores and other transformations

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Statistics for the Social Sciences Lets get some data On a sheet of paper (that youll 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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Statistics for the Social Sciences 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 persons value on a variable

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Statistics for the Social Sciences 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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Statistics for the Social Sciences 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 were measuring

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Statistics for the Social Sciences 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 have 2, 3,or 2.5 cookies Discrete variables – Broken into a finite number of discrete categories that cant be broken down – E.g., In my family I can have 1 kid or 2 kids, but not 2.5

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Statistics for the Social Sciences 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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Statistics for the Social Sciences 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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Statistics for the Social Sciences 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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Statistics for the Social Sciences 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 20º40º Not Twice as hot

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Statistics for the Social Sciences 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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Statistics for the Social Sciences 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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Statistics for the Social Sciences Distributions The distribution of a variable is a description of all of the tokens of the variable within in sample (or population if youve 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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Statistics for the Social Sciences 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 The values of the variable

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Statistics for the Social Sciences 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 The values of the variable The number of tokens of each variable

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Statistics for the Social Sciences Steps for Making a Frequency Table Figure the percentage (or proportion) of scores for each value The values of the variable The number of tokens of each variable N=total% = (f/N)*100 The percentage of tokens at each value

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Statistics for the Social Sciences Steps for Making a Frequency Table Figure the cumulative percentage (or proportion) of scores for each value The values of the variable The number of tokens of each variable N=total% = (f/N)*100 The percentage of tokens at each value Cumulative percentage

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Statistics for the Social Sciences 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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Statistics for the Social Sciences Frequency Graphs Histogram Plot the different values against the frequency of each value

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Statistics for the Social Sciences 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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Statistics for the Social Sciences Frequency Graphs Frequency polygon - essentially the same, put uses lines instead of bars

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Statistics for the Social Sciences Properties of distributions Distributions are typically summarized with three features Shape Center Variability (Spread)

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Statistics for the Social Sciences Shapes of Frequency Distributions Unimodal, bimodal, and rectangular

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Statistics for the Social Sciences Shapes of Frequency Distributions Symmetrical and skewed distributions Normal and kurtotic distributions

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Statistics for the Social Sciences 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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Statistics for the Social Sciences 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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Statistics for the Social Sciences Scatterplot Plot a scatterplot of soda and bottled water drinking –Useful for seeing the relationship between the variables

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Statistics for the Social Sciences Next time In addition to using tables and graphs to describe distributions, we also can provide numerical summaries

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