Psy 202, Week 2 Notes
Psy 202, Week 2 Notes Psy 202
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This 7 page Class Notes was uploaded by Anna Ballard on Tuesday September 6, 2016. The Class Notes belongs to Psy 202 at University of Mississippi taught by Mervin R Matthew in Fall 2016. Since its upload, it has received 16 views. For similar materials see Elementary Statistics in Psychology at University of Mississippi.
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Date Created: 09/06/16
Lecture 3 8/29 Ch. 2 ––> Describing Quantitative Data w/ Frequency Distributions To make a collection of Data… - Put the data in some sort of order - Frequency tables –> organize in descending order and count each group o Also works for smaller sets of data Simple Frequency Table - Shows number of times a piece of data shows up Y F(Y) F(y) –> raw scores 75 2 74 3 73 4 … … 57 0 Include all possible values between high … … and low! Use 0 for values not in table 18 7 Group Frequency Distributions • Grouping values –> used when there is a large range of data • Groups we are dealing with (intervals) - How many intervals - How wide should the intervals be? AKA how many values • How many intervals should we have? - Between 10 and 20, depending on distance between low and high values • How wide should our intervals be? - 2, 3, 5, or a multiple of 5, depending on the number of values used and subsequently, intervals. Grouped Simple Frequency Table • Evenly spaced, includes all values between high and low; inclusive - f(y) –> cumulative frequencies of raw scores with each interval Relative and Cumulative Frequency Distribution • How much is “a lot” –> must be relative to something f(y)/n ––––> n refers to the total number of scores - rf(y) = f(y)/n ….. 14/150 = 0.093 - always round to at least 2 decimal places - rf(y) always add up to be about 1.00 Grouped Cumulative Simple Frequency Table • Start with “n” and subtract f(y) as you descend - simple frequency and grouped cumulative should match up at the end - should end with last f(y) Histograms (simple and relative frequencies) • Great graph when there is a lot of data • X-axis –> values of raw scores - values of raw scores in ascending order (either ungrouped or grouped) • Y-axis –> frequencies (either simple or relative) • Vertical bar for each group (and touching)… compares scores for us Frequency Polygons (Similar to Histograms) • X-axis: still values from lowest to highest) • Point for each f(y) value • Connected points suggest values for scores on a continuum - points just outside of range touch the x-axis Lecture 4 8/31 Ch. 2 cont’d OGIVES • X-axis still • Y axis –> cumulative frequencies (simple or relative) - highest cf(y) is always equal to n (simple) or 1.00 (relative) - points not necessarily connected by lines Stem and Leaf Displays • Intervals: ex: 16-20, 21-25, 26-30, etc.. - shows shape and distribution and individual scores 7 5 5 Ones column with scores in 7 0 0 0 1 1 1 1 2 3 3 3 3 ascending/descending order 4 4 4 & Each score in each interval 6 0 1 2 2 2 2 3 3 3 3 4 displayed 5 5 6 6 6 6 8 8 8 8 9 9 ex: the number “62) shows up 4 times in the data, whereas the number 55 shows up once • intervals divide evenly into 10 Salient Characteristics of…. 2 characteristics (and a couple other important ones) Kurtosis Skewness (peak) Central Tendency Measur Central Tendency – 1 score that summarizes entire distribution Variabili ty - how accurate central tendency is –> smaller number = higher dependency of CT Measure of Variability – numbers further away from central tendency – tells us how accurate CT is –> smaller number = higher number of dependency o if most scores are around the same number as CT, higher dependency o if most scores are way greater than or way less than, and just average to be CT, there is lower dependency Skewness – how symmetrical distribution is (if it leans 1 way or the other… our example leans more to the right) Kurtosis – how curved… high kurtosis –> scores increased and lower than point; lower kurtosis is flatter. - Want kurtosis to be fairly average (not too low, not too high) Computer Analysis and learning R • Object oriented Program - Be specific –> tell it exactly what you want it to do (set.color(RED)) - Type in correct function - Arguments: give as much info as possible • R makes copies of original scores - Can tell one to do something - Never need to put a code in twice RED – protocol before • For group simple frequency table (and OGIVE and Histogram) GREEN – what to interval width –> how many you want in each interval change so R knows what you’re talking - Do not use 10! Look at rules from lecture 3 Type Protocol To Use How To Use It Ungrouped table(variable) table(scores) simple frequency table Grouped table(cut(variable,breaks=seq(lowest value- table(cut(scores,breaks=seq(low- simple 1,highest value,by=interval width))) 1,high,by=2))) frequency table Relative hist(variable,prob=TRUE,breaks=seq(lowest hist(scores,prob=TRUE,breaks=seq(low- frequency value-0.5,highest value+0.5,by=interval 0.5,high+0.5,by=2)) histogram width)) lines(density(scores)) with density distribution line Grouped plot(cumsum(table(cut(variable,breaks=seq(lo plot(cumsum(table(cut(scores,breaks=se OGIVE plot west value-1,highest value,by=interval q(low-1,high,by=2)))), type="o") width)))), type="o") Lecture 5 9/2 Ch. 3 –> Describing Quantitative Data with Summary Statistics Intro • Kurtosis • Skewness • Central Tendency • Measure of variability Measures of Central Tendency What score best represents the distribution Mode – which score that has highest relative frequency (aka the score that occurs the most) 0 2 2 2 3 4 4 5 7 8 9 - Our class does not like mode because it could be far away from the central tendency - There can also be more than one mode - Mode does not consider anything else in a distribution - Only use mode when you absolutely have to because it only gives us info on category membership Median – score that has 50% distribution below and above 0 2 2 2 3 4 4 5 7 8 9 - If 2 different scores straddle median… average the 2 - We like this more than mode because it tells us about rank - Missing info: does not give us distance between scores Mean – preferred because it includes the most information (category, rank, and distance) - Incorporates how much the scores weigh - The average of all the scores n µ = ∑ Yi/n µ –> population mean i = 1 –> start with this score n (above ∑) –> finish with this score Y –>raw score; sum all of these scores –> inclusive The Mean as a Balance Point n Deviations from mean (if negative it means ∑ (Yi - µY) = raw score is below or to the L of mean) 0 ** Deviation Scores will Always Sum to 0 ** i Y µY Y - µ 1 1 4 3- The Mean as a Least-Squares Estimate • Look for squared errors –> the one that 2 2 4 -2 gives you lowest square errors is the one that gives the best estimate 3 3 4 -1 - mean gives you the smallest square errors 4 4 4 0 5 10 4 6 Total error when Properties predicting that Yi = µ of the ∑ 20 20 0 Measures of Central Tendency Mode – use for things that are categorical Benefit: applies to all data (not always preferred because gives least amount of info) Median – used for anything that can be used in rank order Benefit: usable with all shapes (symmetrical or asymmetrical distribution) Not preferred because no distance info but better when there are outliers Mean – can give distance info (along with categorical and rank info) Benefit: uses all available info but is most sensitive to outliers We like mean because it can give us info about populations Outliers –> score far from what rest of scores are. Variability Vs. Ç√ Ç√ 20 40 60 35 40 45 More variability –> less confident The Range • Everything between highest score and lowest score (subtract low from high) - super duper sensitive to outliers What is similar to range but gets rid of outliers? |––––––I––––––|––––––I––––––| low high Chop off lower and upper 25% - interquartile range - gives true representation on how spread out the data is
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