Week 2 Notes - Psychology 211
Week 2 Notes - Psychology 211 Psychology 211
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This 13 page Class Notes was uploaded by Kennedy Patterson on Friday January 23, 2015. The Class Notes belongs to Psychology 211 at University of Alabama - Tuscaloosa taught by Andre Souza in Spring2015. Since its upload, it has received 941 views. For similar materials see Psychology 211-003 Elem Statistical Methods in Psychlogy at University of Alabama - Tuscaloosa.
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Date Created: 01/23/15
Chapter 2 11215 1 How do you guarantee the sample is a presentation of population a Random sampling b If there is no accurate re resentation results wont be accurate representation of population number summarizes sample number 99quot Sample Mea UniversePopulation o Variants of Sample 5 Sample S2 Mean Age IJ 5 in the absence of all cases from a population we need to make inferences about the population arameter based on a sample 6 h a Response dependent variable variation interested in y axis Drinking explanatory independent influencing the variation of the Drinking response variable xaxis a can only take on specific values categories ex siblings Beaut b can take any real number value ex reaction time Chapter 2 11215 variables characterized as a set of categories two or more categories or levels 1 Name things 2 3 Ex transportation two categories or levels 1 2 Ex yes or no two or more categories 1 Order or Rank things 2 3 Ex social class am can only assume a specific number of values 1 Nominal dichotomous ordinal b 39 variables characterized by a numerical value i numerical values in which the intervals between the values are assumed to be the same 1 Equal intervals represent equal differences 2 Ex professor s annual salary numerical values with a meaningful zero point ex height Zero represents the absence of the variable 1 Allow us to use phrases such as half as muchquot iv v 5 ugly 5 beauty 0 Interval not the absence of beauty Ratio absence of not caring to rate beauty Chapter 2 11215 the values of data measured on this scale can be a number or name but can be rank ordered 2 the values of data measured on this scale can be rank ordered The differences between two adjacent ranks are e ual 3 h the values of data measured on this scale are labels or names 4 values measured on this scale can be compared such that ou can sa one value is twice as big as another value 5 H the allocation or assignment of participants to groups by a random process Sigma Z Greek letter symbol indicating summation Summation notation a ZX sum of the x s add up or sum what follows b N all the values c 1 starting with the first value lm N EX 1 d ZX2 sum all x s then square e 2X2 square all the x s then sum 8 a Height in Inches Continuous b Number of pets in household Discrete c Pounds of Chocolate consumed in past year Continuous d Number of countries ever visited Discrete e Shoe Size Discrete 9 a Relationship between parent s ages and their parenting practices 20 couples that have 10yearold daughters b Mom s ages x Dad s ages y i Sum of mom s ages 788 EX 788 ii Sum of dad s ages 852 Zy 852 iii Sum of differences in ages 9 Zyx 1 Zyx 2852788 2 Z 64 iv Dad s age 10 years ago 9 Zy10 Z v10 Zy N x 10 Zy 20 x 10 852200 652 Zy10 652 WhWNll Chapter 3 11415 a End up with a lot of numbers ii Identify center of data any unusual feature spread amp shape b variable that classifies into categories i List the categories and show the frequency number of observations in each category 2 listing of possible values for a variable together with the number of observations at each value a i Survey about students cell phone Model and SMS Usage 1 Variables model 6 models 2 Categorical list of variables Model Frequency Relative Frequency iPhone 4 2 014 iPhone 4s 1 007 iPhone 5 3 022 Galaxy SII 3 022 Galaxy SIII 4 028 Nokia 1 007 Total 14 1 3 proportion percentage of the observations that fall in that category 4 frequency distributions are also useful for quantitative variables Intervals Frequency Relative Frequency 1 50 7 05 51 100 2 014 101 150 1 007 151 200 2 014 201 250 1 007 251 300 0 0 301 250 1 007 Number Frequency Number Total 5 extreme observation that falls far from the rest of the data a Such observations are troublesome to many statistical procedures b Cause exaggerated estimates and instability c Important to identify extreme observations and examine the source of the data more closely Chapter 3 11415 d i There was a typo ii Not meant for study iii Indicates deeper trend or phenomenon 6 good amp bad a Explore patterns b Visualization 7 a relationship between number of emails and U grade on exams i Number of emails Quantitative explanatory 5 ii Grade on exams Qualitative responsive O 10 20 3O 4O 50 8 Email a relationship between beauty a 42 40 and high grades 393 i Grade numeric 5 9 Beauty a Categorical Data b Histogram graph in which a rectangle is used to represent frequencies of observations within each interval i Relative frequency distribution density for a quantitative variable 1 a Reports how often each value of the variable occurred b Is often a first step of organizing the data into logical order c Distribution in which the values of the variable are tabled or plotted against their frequency of occurrence d Spring Fall Fall Spring Summer Fall Winter Spring Season Students Sp ng 3 Summer 1 Fall 3 Winter 1 Chapter 3 11415 3 Point halfway between the bottom of one interval and the top of the one below it 4 the point halfway between the top of one interval and the bottom of the one above it center of the interval average of the upper and lower limits frequency of occurrence of each value of X ordinate yaXis abscissa Xaxis measure of the degree to which a distribution is asymmetrical a distribution that trails off to the right b distribution that trails off to the left 10 graphical display presenting original data arranged into a histogram 11 a set of techniques developed bu Turkey for presenting data in visually meaningful ways 12 most significant digits leftmost digits of a number 13 vertical axis of display containing the leading digits 14 less significant digits digits to the right of the leading digits 15 horizontal aXis of display containing the trailing digits EOSDNP S Supply a main title Always label the axes Try to start both the X and Y aXis at 0 zero Pie charts Don t use very hard to read accurately Try to never plot in more than two dimensions a b c d e f Don t add nonessential material having the same shape on both sides of the center a distribution having two distinct peaks a distribution having one distinct peak the number of meaningful peaks in a frequency distribution of the data agom 2 Negatively Skewed vs Positively Skewed Chapter 3 11415 Row Data Stem Leaf 0 1 1 223444555667777889 0 01122344455566677778899 9 1 0111222333334445555556666666666 2 777888899 10 11 11 11 12 12 12 13 13 13 13 13 14 3 00112233444455667889 14 14 15 15 15 15 15 15 16 16 16 16 16 005 16 16 16 16 16 16 17 17 17 18 18 18 18 19 19 20 20 21 21 22 22 23 23 24 24 24 24 25 25 26 26 27 28 28 29 30 30 35 Missed Class Stem Attended Often Regularly 8 18 5 5 19 20 21 8 5 22 9 7 3 2 23 0 24 1 3 6 9 6660 25 024456 8441 26 123444577 74400 27 Code 25 6 256 8 30 31 0 32 0 1 8 012366788 28 012488 29 0112346678 Chapter 4 1161512115 an object with rows and columns different observations contain the values of different variables US What affects student s grades i Age H Gender iii Relationship status iv Hours spent on Facebook v Number of friends on Facebook vi Drinking habits a 6 columns b X amount of rows c Cannot have more than 1 column to represent data Male Female Wrong lID Yes No 3 a Everything varies yet measurements often cluster around certain values b Shows what the t ical observation is 4 Sample Statistic I Sample Statistics are not the same everything varies amp varies around Sample Statistic 2 2 central number X y etc always lower case X age y relationship status individual values i X1 X2 X3 c Individual values of the variable are represented by subscript i lnX 23 32 45 65 77 ii X1 23 X2 32 X5 77 d To refer to a single score without saying which one it is we use Xi e Sometimes subscripts may be omitted g OOIO Chapter 4 f 1161512115 i Z sum of everything that follows ii 2X sum of all the X s 1 Example if there are 30 values for X a X1 12 X2 45 X3 44Xn 21 we say n 30 N 2X sum of all X s from i1 to in 1 202 is different than 28 i X 1112 X y XV 2X 5 1 20 20 z 2 25 1 19 19 220 12121222 7 1 19 19 X 2 19 38 ArithmeticMean a b X bar I the mean is the sum of all the data points ZX divided by the number of data points n Mathematically i A a ZXn n 1112 i 54 Answers the question if all the data points had the same value what would the value be If I want all the data points to be the same and still have the same sum what would this number be What ifI asked these people to give me all the money they have Ca os250 Kevin 153 Stephanie 76 Mary 198 Total 677 I ZXn 9 6774 16925 Mean 16925 16925 X 4 677 Chapter 4 1161512115 g h i J C m 321 222 n 3 ZX 6 na zx 32 3 Mean 1 2 9 number to replace every data set to keep same total 9 a Mean equals the proportion observations that equal 1 b asked 9 women how many men they have dated in the past 12 months Boyfriend 0 O I ZXn 49 1 1 is recorded 4 times 1 9 is the total number 0 O 1 1 9 O c Arithmetic mean is the only single number for which the defined as the difference each data point amp the mean sum to zero X 3 21 iL 1 21 14oo 12 220 2 2 i2 Residual O Chapter 1161512115 1 middle score in an ordered set or data a b The score corresponding to the point having 50 of the observations below it when the observations are arranged in numerical order the location of the median in an ordered series 2 a b 32 34 35 35 36 38 38 42 42 42 44 44 100 i Middle value 38 ii 13 12 7th number 9 median 38 c F i 12 12 65 9 between 6 amp 7 1 Average of number median 9 avg of 38 amp 38 38 3 a The median like the arithmetic mean is appropriate for b Since it requires ordered data the median is also appropriate for c The median is which makes it an appropriate measure for skewed distributions d The median is not very informative for discrete data that takes only a few values e The US Census asked how many relationships have you had in the last 12 months i Only 6 distinct responses occurred O12345 and 638 of them was 1 ii The median is 1 because more than 50 of the total was 1 4 l the sum of the scores divided by the number of scores avera e 5 mean after discarding fixed percentage of extreme observations a take one or more of the largest and smallest values in the sample set them aside and take the mean of what remains b For a 10 trimmed mean we would set aside the largest 10 of the observations and the lowest 10 of the observations the mean of what remained would be the 10 trimmed mean 6 a For processes that change multiplicatively rather than additively arithmetic mean is not a good measure b Th xk n Chapter 4 1161512115 Also indicates the central tendency but uses the product x instead of Ex x x x 30 9 x i Multiili the same numbers to get same product record the cumulative amounts of tweets written in last 6 months Month Number of Tweets Increase Rate July 132 August 158 1997 September 169 697 October 188 1124 November 221 1755 December 240 86 i How to find increase rate Take the first value subtract from the second value and divide by the first value 1 158132 1997 132 Percentage not independent of each other Increase rate depends on previous month nnx x 511997 x 697 x 1124 x 1755 x 86 1187 1187 Geometric Mean Arithmetic means are good for independent events scores on a test Geometric Means are good for the numbers that are not independent of each other percentages i n x ZXi The same loiic aiilies to the claeometric mean i Axn x Chapter 4 1161512115 7 the most common value highest region of distribution a Commonly used with highly discrete variables such as categorical variables through it is appropriate for all types of data b F c number of girls dated in the past 12 months i Mode quot2quot amp Mexico 1 2 is in the chart 3 times 2 Mexico has the most number of girls Nationalitv Number of Girls Brazil 3 Russia India Mexico Peru Cmumbm United States Canada NLNmVNI t