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Lecture 3

lecture three

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University of Toronto Mississauga
John Kervin

SOC 222 -- MEASURING the SOCIAL WORLD Session #3 -- MEANS & VARIATION Sep 2013 Agenda: Announcements Where we are Today’s Objectives: Know … Terms to Know Ratio (Quantitative) Variables- also known as quantitative measures Frequency Distributions for Rat Vars Frequency Distribution Histograms in SPSS 1. Skewed Distributions 2. Outliers Central Tendency Mode Median Mean Comparing Measures of Central Tendency SPSS: Central Tendency Variation 1. Range 2. Variance Standard Deviation (SD) 3. Inter-quartile range Individual Uniqueness Z scores Normal Curve Distributions CatRat Relationships Comparing Means Other Stuff in the Text Tutorial Vote Today’s Objectives: Know 1. How to get a histogram frequency distribution 2. Skewness and outliers 3. Three measures of central tendency, and pros and cons of each 4. How to get central tendency and variation measures with SPSS 5. Variation as distance from the mean 6. Three measures of variation 7. How to assess the uniqueness of a specific case with Z scores and percentiles 8. Difference between experimental and non-experimental designs 9. Comparing means as effect size for cat  rat relationships Terms to Know quantitative variable valid percent normal curve histogram skewness positive and negative skewness outlier mode, median, mean bimodal distribution variance, range, standard deviation, inter-quartile range percentile Z score true experiment, quasi-experiment RATIO (QUANTITATIVE) VARIABLES • Counts – ex. University classes • Amounts- ex. Cost of texts for each class FREQUENCY DISTRIBUTIONS for RAT VARS • Hard to use to find modes and medians Reminder: note the difference between “Percent” and “Valid Percent” • Need it because we have to get to shape of the distribution • Distribution shape is important because • normal curve • This is a bell-shaped curve Frequency Distribution Histograms in SPSS The graphic of a frequency distribution is called a histogram - go to analyze and click on frequencies, put variable we want in box,(average percent mark), go to charts and click on histogram- click on “show the normal curve”- and delete the display frequency tables Revised SPSS Guide is posted: SPSS Frequency Distributions Open data set • Click on “Analyze” on menu bar • Choose “Descriptive statistics” from dropdown menu • Choose “Frequencies” This opens a box called “Frequencies” Expand the box to read the variable labels • List of variables on the left • In the middle: an empty working area called “Variable(s)” • Option buttons on the right • Action buttons on the bottom Click on the variable you want • Click on the arrow to move it to the Variables area For a Frequency Distribution Table • Click on OK • This opens your output window with a frequency distribution table. For a Frequency Distribution Histogram • Click on “Charts…” option button • Select Histogram, Normal curve • Continue • In main Frequencies box • Uncheck “Display frequency tables” • OK • This opens your output window with a Histogram The variable has approximately a normal curve shape • Missing some cases in the middle range 1. Skewed Distributions These are distributions which stretch out in one direction We say this distribution is skewed. • positively skewed.- not normal distribution 2. Outliers • Outliers are extreme values – extreme values, noticeably different from the rest, can distort conclusions you come up with • Shows an outlier at around 5. CENTRAL TENDENCY The underlying question: • What’s the “typical value” of a variable? There 3 common measures, mode medians and means Texts: • Linneman: 76-84 • Kranzler: 43-47 Mode Mode: The value with the most cases EG: Ages: 21, 21, 24, 25, 27, 28, 29 • The value “21” occurs twice • All other ages occur just once • The mode is “21” NOTE: • two modes • bimodal EG: 21, 21, 24, 25, 27, 27, 29 • This distribution is bimodal Median • Median: The value of the “middle” case • When all cases are sorted in rank order EG: 21, 24, 24, 26, 27 • median is “24” • it’s in the middle NOTES: 1. Only applies to ordinal and ratio variables 2. What if you have an even # of cases? EG: 21, 21, 24, 25, 27, 28 • median is the mid-point between these two • median here is 24.5 Mean • Mean: The average value EG: the distribution (of ages in a grad student seminar) is : 21, 21, 24, 25, 27, 27, 29 xi means the value of the ihcase. EG: x is 24. 3 ∑ (“sigma”) means sum EG: ∑xi is 174 x x= ∑ i n Interpretation: • The x with the bar over it means the mean • 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 EG: mean of this set of values: 3, 5, 7, 9 3,5,7,9 24 x = ∑ = = 6 4 4 NOTES: Comparing Measures of Central Tendency Nominal category: can only use the mode Ordinal category: can use mode and the median- best measure depends on kind of question you are asking, if asking about what happens more often then its mode, if asking about what’s in the middle, then report the median Quantitative: can use any of the 3 • Mode: not very useful, typically question imply we want central value, not most frequent • Median • Advantage of the median: not affected by outliers • outliers (Linneman, p. 77) EG: 21, 21, 24, 25, 27, 28, 29 • median is “25” EG: 21, 21, 24, 25, 27, 28, 92 • median is still “25” • Disadvantage of the median: • Doesn’t take each score into account equally, scores at the ends don’t count as much • Mean • Advantages of the mean: 1. it considers all other values 2. statistical formulas 3. mathematically at it has some useful properties • Disadvantage of the mean: 1. outliers 2. skewed distributions How to get central tendency on SPSS -analyze descriptive stats, hit stat button and and click on mean median and mode if that’s what y
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