1. Review of SPSS basics & Displaying Distributions Statistics for the Social Sciences Psychology 340 Spring 2010

2. PSY 340 Statistics 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)

3. PSY 340 Statistics 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

4. PSY 340 Statistics 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

5. PSY 340 Statistics 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

6. PSY 340 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 –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

7. PSY 340 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 person’s value on a variable

8. PSY 340 Statistics 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

9. PSY 340 Statistics 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

10. PSY 340 Statistics 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

11. PSY 340 Statistics 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 scale 20º40º “Not Twice as hot”

12. PSY 340 Statistics 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

13. PSY 340 Statistics 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

14. PSY 340 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 –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

15. PSY 340 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 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

16. PSY 340 Statistics 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

17. PSY 340 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 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

18. PSY 340 Statistics 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.

19. PSY 340 Statistics for the Social Sciences Steps 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 Xf%c% 712.3100 612.397.8 5920.595.5 41431.875 3818.243.2 2613.625 1511.4

20. PSY 340 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 Xf%c% 712.3100 612.397.8 5920.595.5 41431.875 3818.243.2 2613.625 1511.4

21. PSY 340 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 Xf%c% 712.3100 612.397.8 5920.595.5 41431.875 3818.243.2 2613.625 1511.4

22. PSY 340 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 – percentile ranks Xf%c% 712.3100 612.397.8 5920.595.5 41431.875 3818.243.2 2613.625 1511.4

23. PSY 340 Statistics 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

24. PSY 340 Statistics 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

25. PSY 340 Statistics 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

26. PSY 340 Statistics for the Social Sciences Brief review of SPSS Two view windows: Variable view This is where you specify the details about the variables

27. PSY 340 Statistics 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

28. PSY 340 Statistics 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.

29. PSY 340 Statistics for the Social Sciences Variable view Name of the variable Type of variable: numeric, text, monetary, date, etc.

30. PSY 340 Statistics 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

31. PSY 340 Statistics for the Social Sciences Steps 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)

32. PSY 340 Statistics 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

33. PSY 340 Statistics for the Social Sciences Shapes of Frequency Distributions  Unimodal, bimodal, and rectangular

34. PSY 340 Statistics for the Social Sciences Shapes of Frequency Distributions  Symmetrical and skewed distributions  Normal and kurtotic distributions

35. PSY 340 Statistics for the Social Sciences Frequency Graphs  Histogram  Plot the different values against the frequency of each value

36. PSY 340 Statistics 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

37. PSY 340 Statistics 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

38. PSY 340 Statistics for the Social Sciences Frequency Graphs  Frequency polygon - essentially the same, put uses lines instead of bars

39. PSY 340 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

40. PSY 340 Statistics 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’

41. PSY 340 Statistics 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’

42. PSY 340 Statistics 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