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222-03 Outline.docx - Lecture 3

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John Kervin

SOC 222 -- MEASURING the SOCIAL WORLD Session #3 -- MEANS & VARIATION Sep 2013 RELATIONSHIPS: CATEGORIES & RATIO VARIABLES A typical Research Question: Do science students get higher marks than social science, or humanities, students? The only difference b/w a hypotheses and RQ is the whether it’s a statement or question. IV: Type of students – DV: marks NOTE: 1. This RQ has 2 variables. IV is a categorical variable (academic area). 2. DV is a ratio variable, which goes from 0-100% (marks) (if it’s the other way around, complicated statistical procedure – for this course, ratio variable will always be DV) RECODING VARIABLES Chem Eng Elec and Comp Eng East Asian Studies English Microbiology Botany Geography Economics Sociology Science Chem Eng Elec and Comp Eng Microbiology Botany Social Science Geography Economics Sociology Humanities East Asian Studies English • Linneman covers this in ch. 1: 27-33 Have 9 departments, which we want to divide into 3 groups - recoding SPSS: Recoding Procedure Purpose: original variable (called “input”) recoded to new variable (called “output”) Example: recode “Department” into “Academic Area” • Data set: Students-4 1. Menu bar, Transform, Recode into Different Variables • This brings up a box called “Recode into Different Variables” • Expand it sideways • On the left: the familiar list of variables (by labels, names in square brackets • In the middle, a working area. Called “Input Variable  Output Variable:” • On right, another area called “Output Variable” • We’ll use all three of these • On the bottom, three rows of buttons: 1. “Old and New Values…” we’ll use this 2. “If” IGNORE 3. The same old action buttons. Only “OK” and “Reset” matter. 2. Move your input variable into the middle working area • “depart” • SPSS adds an arrow and “?” to tell you it’s waiting for the output variable 3. In the right area: • Type in the name of your new variable (“AcadArea”) • Type in a longer label (“Academic Area”) • Click Change button • Your output variable shows up in the middle working area 4. Click on “Old and New Values” • This opens a new sub-box for you to enter values • What are “values”? • They’re the numbers used to identify the categories of category variables • How do we find them? 1. Go to data set 2. Variable view 3. Find your variable name or label 4. Column after “label” is “Values” 5. Click on that cell (“Values” for your variable) • Up comes a little blue button on the right of the cell 6. Click the little blue button • Up comes a box called “Value Labels” • It will have the number assigned to each category of your variable • Write them down • SPSS won’t let you work in another box when it expects something in the one you just opened • When you’re done, close the “Value Labels” box • Here are the values for Department: Chem Eng 1 Elec and Comp Eng 3 East Asian Studies 12 English 13 Microbiology 32 Botany 42 Geography 45 Economics 62 Sociology 65 Nominal #s so doesn’t matter what # is assigned. • We need values for our output variable, AcadArea • We’ll use these: Science 1 Social Science 2 Humanities 3 5. In the sub-box “Old and New Variables”: • Left side is “Old Value” • Right is “New Value” • Three action buttons at bottom • Enter first old value in the “Value” working area (top left) • “1” for Chem Engineering • Enter the new value in the “Value” working area (top right) • “1” for Science • Click on “Add” button • Old and new values show up in the working area • Enter next pair of old and new values • “3” for Elec and Comp Eng • “1” for Science • Click “Add” • Continue to last pair: • “65” for Sociology • “2” for Social Science • Click Add • When finished, click “Continue” to exit this sub-box 6. Click “OK” in the “Recode” box • Your output window opens to tell you you’ve done a recode (at the bottom) • Your data shows: • Variable View: Your new variable at the bottom • Data View: Your new variable at the far right, with the new values 7. To double check and confirm: • Run a crosstab • Input variable and output variable • “Department” and “Academic Area” - OK • Confirm each category of Input is in correct category of Output CENTRAL TENDENCY • What’s the typical mark in each one? Another term for typical is central tendency. 3 ways to get there: 1. Median • Linneman pp. 76-78 • Kranzler pp. 44-45 The idea: • Put all your cases in rank order on the variable • The middle case is the “most typical value” • Called median EG: 21, 24, 24, 26, 27 • median is “24” • it’s in the middle NOTES: 1. Can only be done with cases that have an order (B/c have to rank order) – cannot use nominal #s; only applies to ratio and ordinal #s 2. What do you do with an even number of cases – 2 #s in the middle? EG: 21, 21, 24, 25, 27, 28 • median is the mid-point between these two • median here is 24.5 The average of the two numbers Advantage: • Not affected much by a few outliers (Linneman, p. 77) • outlier is: an extremely high/low value compared to the rest of the values (example: 21, 21, 24, 25, 27, 28, 92  median does not change – outliers do not distort central tendency) Disadvantage: don’t give equal weight to all the cases (in some cases we want this) 2. Mode • Linneman pp. 76-78 • Kranzler p. 45 The idea: look at all values and find out which occurs the most often – most frequent value • The one value that occurs most often • This is the modal value, or mode EG: 21, 21, 24, 25, 27, 28, 29 NOTE: • If there are two modal values (21, 21, 24, 25, 27, 27, 29) • The set of scores on that variable is said to be bi-modal - Not useful for ratio variables 3. Mean EG: the distribution (of ages in a grad student seminar) is : 21, 21, 24, 25, 27, 27, 29 xi means the value of the ithcase. EG: x3is 24. ∑ (“sigma”) means sum EG: ∑x i is 174 Putting these symbols together: xi x= ∑ n • The x with the bar over it means the mean (average) • The equal sign tells us how to get the mean • The sigma sign tells us to add something up • The numerator (top of the fraction) • x with the subscript i tells us to sum up all the values of x • The denominator (bottom) • n tells us to divide that sum The result is the mean EG: mean of this set of values: 3, 5, 7, 9 3,5,7,9 24 x = ∑ = = 6 4 4 NOTES: we normally mean “mean” when we say average but not always (mode, median) Advantages of the mean: 1. in deciding typical value, it considers ALL values (nothing is left out) 2. a lot easier to use i
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