Upload
jayson-sutton
View
215
Download
0
Tags:
Embed Size (px)
Citation preview
Review of SPSS basics & Displaying Distributions
Statistics for the Social SciencesPsychology 340
Spring 2010
PSY 340Statistics for the
Social Sciences Announcements
• Quizzes (at least quiz 1) should appear soon– Pay attention to the due dates & times
– Don’t wait until the last min.
– Can take up to 3 times, don’t need to do them all at the same time (but only those taken by the due date/time count)
PSY 340Statistics for the
Social Sciences Types of statistics
Descriptive Statistics Used to describe summarize, simplify, and organize data
(distributions of observations) Includes: graphs, tables, measures of shape, center, and
variability Inferential Statistics
Used to test hypotheses about the population based on observations from samples
Includes things like t-tests, ANOVA, correlation & regression analyses
PSY 340Statistics for the
Social Sciences What are samples?
• Who do we test?– Population
• The set of all individuals of interest
– Sample• A subset of the population from whom data is collected
Typically we don’t have access to all of the population
We test these folks and then generalize the results to the population as a whole
PSY 340Statistics for the
Social Sciences What are samples?
– “Sample” - may also be used to refer to the participants (randomly) assigned to a particular condition of the experiment
condition A
condition B condition C
condition D
– Sample• A subset of the population from whom data is collected
PSY 340Statistics for the
Social SciencesLet’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– Which day of the week is your busiest?– On a scale of 1 (“hate it”) to 7 (“love it”) rate how you feel about
statistics
PSY 340Statistics 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 person’s value on a variable
PSY 340Statistics for the
Social Sciences Measurement issues
• Understand what the measurements mean– The correspondence between the way you measure the
variable and the variable (i.e., what your observations mean)
– Impacts what kind of statistics you can do, what kind of comparisons you can make
PSY 340Statistics for the
Social Sciences 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
PSY 340Statistics for the
Social Sciences Scales 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
PSY 340Statistics for the
Social Sciences Scales 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 scale20º40º
“Not Twice as hot”
PSY 340Statistics for the
Social Sciences Scales 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.
Ratio versus interval: Ask what a score of zero means on your scale. If it is the absence of that variable then you have a ratio scale.
SPSS doesn’t distinguish between these, collapses them into ‘scale’ measurements
PSY 340Statistics for the
Social Sciences Scales & Units of measurement
• Nominal scale
• Ordinal scale
• Interval scale
• Ratio scale
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
Discrete variables– Broken into a finite number of discrete categories that can’t be broken down– E.g., In my family I can have
2, or 2.5 cookies
1 kid or 2 kids, but not 2.5
PSY 340Statistics 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– Which day of the week is your busiest?– On a scale of 1 (“hate it”) to 7 (“love it”) rate how you feel about
statistics
PSY 340Statistics 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 you’ve got the data)– Three basic characteristics are used to describe
distributions• Shape
– How do the observations ‘stack up’, symmetry, skew, number of peaks, etc.
• Center– Where do most of the observations fall
• Variability– How similar/dissimilar are the observations to one another
PSY 340Statistics for the
Social Sciences Distribution Example
• Get the height (in inches) distribution
– If we just look at the data in an unorganized way it is hard to get a sense of how the observations are distributed
PSY 340Statistics 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 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
– Also ways to describe distributions numerically
PSY 340Statistics for the
Social Sciences Frequency distribution tables
• Allow us to organize large data sets• Properties of distribution easier to “see”• Most common score, range of scores, etc.
PSY 340Statistics for the
Social SciencesSteps for Making a Frequency Table(done for the ‘likability’ variable from a previous class)
• Make a list down the page of each possible value, from highest to lowest
The values of the variable
X f % c%
7 1 2.3 100
6 1 2.3 97.8
5 9 20.5 95.5
4 14 31.8 75
3 8 18.2 43.2
2 6 13.6 25
1 5 11.4 11.4
PSY 340Statistics for the
Social SciencesSteps 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
X f % c%
7 1 2.3 100
6 1 2.3 97.8
5 9 20.5 95.5
4 14 31.8 75
3 8 18.2 43.2
2 6 13.6 25
1 5 11.4 11.4
PSY 340Statistics for the
Social SciencesSteps 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
X f % c%
7 1 2.3 100
6 1 2.3 97.8
5 9 20.5 95.5
4 14 31.8 75
3 8 18.2 43.2
2 6 13.6 25
1 5 11.4 11.4
PSY 340Statistics for the
Social SciencesSteps 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 – percentile ranks
X f % c%
7 1 2.3 100
6 1 2.3 97.8
5 9 20.5 95.5
4 14 31.8 75
3 8 18.2 43.2
2 6 13.6 25
1 5 11.4 11.4
PSY 340Statistics for the
Social Sciences
Grouped Frequency Table(do this for height variable)
A frequency table that uses intervals (range of values) instead of single values
Create this one on the whiteboard Figure out how many intervals you want, figure out the
range of values (max-min), and create your interval size Count up the number of observations in each interval
PSY 340Statistics for the
Social Sciences Distributions (Data) in SPSS
• Let’s enter some data into SPSS.
• The nature of your data determines how you enter the data into SPSS– The nature of your variables
• Scales of measurement
– The design of a study• Are the variables independent or dependent (related)
• Does SPSS need to know certain numbers are related with one another
PSY 340Statistics for the
Social Sciences Brief review of SPSS
Two view windows:
Data view
This is where you type in all of the data
To switch between the views click on the tabs
PSY 340Statistics for the
Social Sciences Brief review of SPSS
Two view windows:
Variable view
This is where you specify the details about the variables
PSY 340Statistics for the
Social Sciences The Data View
Each row corresponds to an experimental unit(called “cases” in SPSS lingo)
So each column in the data view corresponds to a row in the variable view
Each column corresponds to a variable
PSY 340Statistics for the
Social Sciences Entering Data into SPSS
• I recommend that you start by defining your variables and their properties in the variable view
• Alternative – can enter data first, SPSS will set up the variables, but it may not get all the properties correct.
PSY 340Statistics for the
Social Sciences Variable view
Name of the variable
Type of variable: numeric, text, monetary, date, etc.
PSY 340Statistics for the
Social Sciences Categorical variables in SPSS
• SPSS ‘likes’ numbers for analyses– If you plan to analyze a variable, enter it in as a
number– If it is categorical (nominal or ordinal) you can
label the values (give SPSS names to go along with the numbers)
• This includes Levels of between groups Independent variable
PSY 340Statistics for the
Social SciencesSteps for Making a Frequency Table
• Using SPSS– Analyze Descriptive Statistics -> Frequencies– Select the variable that you want a table for and click on the arrow– Click ok
• note1 : you can also select the statistics and charts options to get more than just the Freq Dist Table
• Note2 : SPSS uses every score that appears for the variable, but leaves out those for which there were 0 instances. This can influence how you interpret the scores relative to each other.
• Note3: SPSS does not create grouped frequency tables (although it essentially does when it creates histograms, more on this later)
PSY 340Statistics for the
Social Sciences Distributions
• Three basic characteristics are used to describe distributions– Shape
• Many different ways to display distribution– Frequency distribution table
– Graphs
– Center
– Variability
PSY 340Statistics for the
Social Sciences Shapes of Frequency Distributions
Unimodal, bimodal, and rectangular
PSY 340Statistics for the
Social Sciences Shapes of Frequency Distributions
Symmetrical and skewed distributions
Normal and kurtotic distributions
PSY 340Statistics for the
Social Sciences Frequency Graphs
Histogram Plot the
different values against the frequency of each value
PSY 340Statistics for the
Social Sciences Frequency Graphs
Histogram by hand (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
PSY 340Statistics for the
Social Sciences Frequency Graphs
Histogram using SPSS (create one for class height) Graphs -> Legacy -> histogram Enter your variable into ‘variable’
To change interval width, double click the graph to get into the chart editor, and then double click the bottom axis. Click on ‘scale’ and change the intervals to desired widths
Note: you can also get one from the descriptive statistics frequency menu under the ‘charts’ option
PSY 340Statistics for the
Social Sciences Frequency Graphs
Frequency polygon - essentially the same, put uses lines instead of bars
PSY 340Statistics 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
PSY 340Statistics for the
Social Sciences Bar graphs
• Plot a bar graph of men and women in the class– Graphs -> bar– Simple, click define– N-cases (the default)– Enter Gender into Category axis, click ‘okay’
PSY 340Statistics for the
Social Sciences Bar graphs
• Plot a bar graph of shoes in closet crossed with men and women– What should we plot? (and why?)
• Average number of shoes for each group?– Graphs -> bar
– Simple, click define
– Other statistic (default is ‘mean’) – enter pairs of shoes
– Enter Gender into Category axis, click ‘okay’
PSY 340Statistics for the
Social Sciences Scatterplot
• Useful for seeing the relationship between the variables– Graphs -> Legacy Dialogs– Scatter/Dot– Simple Scatter, click ‘define’– Enter your X & Y variables, click ‘okay’
• Can add a ‘fit line’ in the chart editor
• Plot a scatterplot of soda and bottled water drinking