PSYCH 302: Statistics - Week 2 Notes
PSYCH 302: Statistics - Week 2 Notes PSY 302
Popular in Statistical Meth Psych
Popular in Psychlogy
This 5 page Class Notes was uploaded by Shannon Hardman on Thursday October 8, 2015. The Class Notes belongs to PSY 302 at University of Oregon taught by Laurent S in Fall 2015. Since its upload, it has received 9 views. For similar materials see Statistical Meth Psych in Psychlogy at University of Oregon.
Reviews for PSYCH 302: Statistics - Week 2 Notes
Report this Material
What is Karma?
Karma is the currency of StudySoup.
Date Created: 10/08/15
PSY 302 WEEK 2 NOTES TUESDAY CENTRAL TENDENCY ContinuingFinishing lecture 2 O Visualizing Data 0 The quotNormalquot Curve The distribution is called quotnormalquot because many naturally occurring distributions approximate this curve ie heights weights number of leaves on a tree 0 Helps determine the average looks like a normal distribution with the more normal scores converging at the center and the extremes trailing off on the outside 0 Debate Can one person be a population or can they only be a sample 0 They can be a population because if one person is tracking their own habits for example they are not trying to generalize that information to the rest of a population 0 Central Tendency 0 What is it 0 A single number that summarizes information about a distribution 0 It39s the score that is quotmost representativequot of a whole set of scores 0 The mean M for samples mu for populations Mean arithmetic average of a set of scores 0 The quotbalancequot point in a set of numbers 0 Mmu igmaXN I Sigma X All scores added together I N the amount of scores there are 0 Advantages uses ALL information has cool properties for stats I Properties Will be on the quiz 0 Sensitive Changing one number in a set always changes the mean 0 Adding or removing one number usually changes the mean unless that number is the same as M 0 Adding or subtracting the same constant to every score increases the mean by that constant 0 If M5 and 4 was added to every score then M9 Multiplyingdividing by the same constant multiplies or divides the mean by that same constant 0 If M20 and every score was divided by 4 then M5 Disadvantage influenced by extreme numbers 0 The Median Center of an organized set of scores 0 To find list all the scores in the set in order of size find the middle number 0 If there39s an even amount of numbers take the middle two numbers and average them 0 The Mode Most common or frequently appearing score in a set I If have 3 4 4 5 5 5 6 The quotmodal responsequot is 5 If there are two scores appearing the same amount of times and both appear with the highest frequencies then there are bimodal or multi modal distributions 0 Relationships to Distributions n symmetric distributions the mean median and mode are all the same They are not the same in skewed distributions 0 If you just have mean median and mode and they39re all the same or all different then you39ll know if you have a symmetric or skewed distribution 0 Apply it 0 Find the mean median and mode 10 8 5 7 8 9 4 6 5 8 7 0 Order them I 4 5 5 6 7 7 8 8 8 9 10 0 Mean 7 0 Median 7 0 Mode 8 This is a fairly symmetrical distribution slightly skewed 0 When to use what The mean is preferred for its ability to use all information and to summarize the middle well Median is sometimes used when distributions are skewed badly Modes are all that can be used when dealing with nominal data ie frequencies of categories The Not To BeUnderestimated Importance of Variability 0 While measures of central tendency tell us about the middle of a distribution measures of variability tell us about how spread out the distribution is 0 How different are the scores Together these two measures tell us a lot about the distribution 0 What a typical score looks like How close together or far apart are scores 0 The Range A Crude Measure 0 Subtract the lowest score from the highest to see the overall quotspreadquot of scores The book provides the definition of MaxMin1 0 This includes the real upper and lower limits 0 Many texts and SPSS use MaxMin 0 Doesn39t really matter range is not super informative alone Better measures use all of the data like sum of squares variance standard deviation 0 How far away from the mean are the scores 0 Deviations alone don39t tell us much about overall variability because they always sum to zero 0 Le 3 3 0 Not helpful 0 Instead we calculate the sum of squares the sum of squared deviations from the mean NOTE Deviations and squared deviations from the mean are NOT the same thing 39 SS Sigmax muquot2 0 How to find them 0 Find the mean mu 0 Subtract it from each score x mu 0 If all the scores 0 after subtracting mu you did it right 0 Square the resulting values x muquot2 Add all the results from the last step together NOTE If you ever see computational formulas in the textbook use this instead 0 From Population SS to Population Variance Get the sums of squares 0 Then you can get the variance 0 Variance is SSN Variance MS SigmaXmuquot2N O From Population Variance to Population Standard Deviation 0 Get the sums of squares 0 Get the variance 0 Then you can get standard deviation 0 Take the positive square root of the variance 0 Conceptually you are getting back to the same metric as your original scores I We used squared deviations so now we take the square root of the sum to get our original scale back I This represents the quottypicalquot deviation of scores from the mean in our original units THURSDAY VARIANCE STANDARD DEVIATION AND ZSCORES 0 Sample Variance squot2 and Standard Deviation s also SD 0 A small but important difference for samples 0 Samples only estimate population variance and standard deviation 0 Actually they underestimate it because n is smaller than N we see less of the total variability Statisticians have determined that we can correct for this bias easily 39 Instead of dividing SS by N divide by n 1 0 A smaller denominator leads to larger final value 0 This corrects for the bias 0 Nl is also known as the degrees offreedom df QUESTION What measure of central tendency is best to use when data are on a nominal scale 0 Mean median mode or standard deviation 0 Standard deviation is not the answer as it is not a measure of central tendency 0 Mean is not the answer you can39t calculate a mean from nominal data 0 Mode is the answer as it is what occurs most 0 The definitional formula for a sample standard deviation is O S sqrtZxMquot2n1 0 Why Z Scores Locate a score on a distribution relative to other scores 0 Why are they needed 0 To understand where a score is relative to other scores I Tells us how rare or common is a score 0 2 indicates the precise location of each score in a distribution I This can also tell you the distance between your score and any other score 0 EX If you heard you scored a 12 on likeableness does this mean you are likeable 0 We don39t know because there39s no units at the moment But What if the quotaveragequot likeableness was 8 is 12 much more likeable than the average 0 What do we need to answer this question 0 If your likeableness is 12 and the average likeableness is 8 and s6 are you particularly likeable The two numbers that bracket the average is 2 and 14 Your score is 12 This means your score is within the brackets meaning it39s a typical score 0 What if the standard deviation was 15 instead 0 The brackets are now 65 and 95 two brackets out are 5 and 11 You39re at 12 This means you are very likeable O The z Score Formula 0 Z is a ratio of how much X deviates from the mean compared to how much scores typically deviate from the mean I The Zscore tells us how far X is from the mean in SD units I It does NOT change or move your score it just changes the unit of measurement 0 Population Equation 2 X musigma 0 Sample Equation 2 XMsigma I Same formula different notation The sign of the z score or signifies whether a score is above or below the mean 0 The value of the z score specifies the distance from the mean in standard deviation units I Z15 indicates a score that is 15 standard deviation units above the mean Standardized Distributions 0 Properties of z score distributions 0 Mean 0 Variance 1 0 Standard deviation 1 0 When a set of scores is transformed into z scores that distribution is called a standardized distribution 0 Can be transformed back into raw scores with a set M amp SD eg SAT IQ O The shape of the distribution of z scores is the same as the original distribution of 2 scores all you are doing is relabeling the values for the scores Uses of z scores 0 Within a distribution 0 Compare different people on the same test 0 Across distributions Compare same person across different measures I Eg compare your SAT performance to GRE performance I Eg compare your class standing in this class versus another class 0 Compare different people across different measures I Eg compare IQ scores of individuals given different IQ tests 0 Key Points 0 2 scores used to understand where on a distribution a score is relative to other scores 0 Created using mean and standard deviation 0 Tells you how extreme a score is in standard deviation units 0 Looking Ahead 0 We can use z scores to make decisions about whether a score is extreme and unexpected for that distribution