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# INTRO TO STATISTIC PSY 3301

Texas State

GPA 3.98

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This 64 page Class Notes was uploaded by Jeromy Hilll on Wednesday September 23, 2015. The Class Notes belongs to PSY 3301 at Texas State University taught by G. Turner in Fall. Since its upload, it has received 18 views. For similar materials see /class/212848/psy-3301-texas-state-university in Psychlogy at Texas State University.

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Date Created: 09/23/15

Terminology Va rlables traits or characteristics of someone differ from one person to the next Values or scores Gender Depression Test Scores Levels the possible values MF Severely Moderate Not at all Percentile Independent divide into groups ex gender vs Dependent see difference in ex type of therapy 39 Scales Of Measurement Nominal ordinal intervalratio quottraditionalquot Nominal rankorder equalinterval quotthe bookquot Same asabove How much information on a variable we actually have Nominal like assigning names to different categories or groups Ex Types of Cereal No real order but can be categorized OrdinalRankOrder Divided into groups Somewhat orderly IntervalRation EqualInterval Difference between the groups stays consistant Adding information as the groups get more complex Discrete versus Continuous Discrete There are gaps in them There really arent any midpoints Continuous Midpoints determined and used Equal interval is generally continuous no breaks Types of Statistics Descriptive Statistics Summarize data sample size Through tables charts and graphs Through central tendency amp variability Inferential Statistics Draw conclusions about large group from small subset of the group Infer to the population from the sample Typically you do not what more than 10 values in a frequency table All groups should be of an equal size In one Comm We have the actual values Start F req u e n cy Ta b es wtth the htghett ehh with the lowest SPSS Stress does it backwards Rating Frequency Percent AI luthei colum 1 O 14 9393 represents the 9 15 9399 frequency How 8 26 172 often each value 7 31 205 occured 6 1 3 86 5 18 1 1 9 4 16 1 06 Percent represents 3 12 79 the actual percent of 2 3 20 scores that were at 1 1 07 that value 0 2 1 3 Note Even values with a frequency of 0 it is listed SPSS does not include them Across the bottem x axis values Height yaxis represents frequency Histograms it unwind Fran Mm Tabla shown here STRESS saints 39 If the bars touch each Iii133 imam 1 other it is continuous data 21 1 425 u 39 Bar Charts 33 1 not shown Can be linked together to shorten the chart Used for discrete data with gaps Sircm Rille Shapes of Distributions Rectangular Unimodal bimodal amp multimodal a Unimodai If the shape of the distribution has one Peak its Unimodal If it has two Peaks its Bimodal bf Appmximmh 3111mm cl Approximately Rectangular Symmetrical Sha 965 Of Distributions General lfyou found a midpoint in the distribution and split it in half it would be like a mirror Skewed Normally distributed a where there isjust a midpoint in the middle that peaks Positively skewed b most scores on the left extreem scores to the ri ht Kurtosis g Negatively skewed most of the scores are higher values with a few extreem scores on the left Descriptive Statistics Used to describe or our measures Measures of Central Tendencv Central Tendency the score value of our variable amp Variability how spread out they are Mode Any scale of measurement Get Frequencies of values Highest frequency wins MODEMOST Mode Example 1 B would be the MODE because it occures the most E 5 15 13 9 2 mUOw gtlgtlt Mode Example 2 122333 4 6 555 0 Mode3 Mode5 0 Can have multiple modes 0 If there are two modes then you have a bimodal distribution 39 If there are more than two tri quador Multi Modal When to use the Mode Nominal data you dont have to put the categories in order to see which had the highest frequency Quick and easy measure tells us the value that occurs most often but doesnt tell us much else Doesn t really tell us much sometimes it can be misleading ex if all values are 1 and one value is 2 One high mode with most other data in the lower range Median MEDIAN MIDDLE 50 above 50 below Ordinal or IntervalRatio Midpoint ofthe values Median Odd of scores List values from high to low Count halfway through 0 Middle value is the median Median Example 1 O 1 4 3 2 3 4 5 3 2 1 Put them in order high to low 5 4 4 3 3 3 2 2 1 1 0 Find middle number 3 Median 3 Median Even of scores List values high to low Locate middle two scores 0 Half way between the two scores is the median Add up those two numbers divide by two Thats the median Median Example 2 4 3 2 4 2 1 5 6 2 1 O 3 Put them in order high to low 6 5 4 4 3 3 2 2 2 1 1 0 Find middle 2 numbers 32 Median 25 When to use the Median Ordinal or IntervalRatio data Extreme scores Skewed Distributions Unknown values Mean MEAN AVERAGE IntervalRatio measurement Numerical Average Sum all values Divide by number of values Sample vs Population Statistical Notation amp Formula M stands for the mean X stands for a score or value N stands for the number of scores 2 stands for the sum of 5m ma 20 Mean Example 1 1 2 2 3 3 3 4 4 5 5 Step 1 Sum the scores 2 X Step 2 Divide by N Mean is 32 lam Ina ma 21 Mean Example 2 Add up15 Calculate 2 X 39 X l f 39 6 2 DivideZbeN l 5 3 Mean is387 4 5 m 3 3 ma 2 0 mm 1 2 45m 22 Add up total Variables When to use the Mean IntervalRatio data Most commonly used 39 NO extreme scores take last example and add a 23 Central Tendency amp Distributions Symmetrical Distribution Normal special symmetrical Negatively skewed Positively skewed 24 mEtrica divide in half and it is a mirror of eachother Mode Median Mode Mean If they are the Same Value its symmetrical 25 The mean median and mode are all equal to eachother Which is symmetrical Mean Median Mode 26 POSitiVEI SkEWEd39pulls the mode to be less than the mean The Meangt Mode ModeltMean Median N eatiVEI SkEWEd mean is less than the mode MeanltMode ModegtMean Mean Median Mode Descriptive Statistics Variability Recognizes that not everyone will fit in the mean or mode 0 How spread out values are Low Variability not spread out very far peaked distribution 0 High Variability scarse flatter distribution 29 Measures of Variability Range Interquartile Range SemiInterquartile Range Deviation Variance Standard Deviation 30 Range Distance between highest and lowest values Descrete Date Range High Low 0 Think pages in a book 39 or Continuous Data Range High Low 1 31 Range Pros and Cons PRO Easy to figu re CON Influenced by extreme scores 32 Deviation Distance between score and mean DXu u is the same as Mean Not used alone because limited information EX M4 OMLCDCDIX 844 642 440 242 044 If you add up the deviation scores it always equals 0 33 Sum of Squared Deviations SS SSZX M2 Sum Squared Score Mean Calculate each deviation score by taking the score and subtracting the mean Square each deviation score Add the squared deviation scores together 34 Variance The sum ofthe squared deviations SS Z X M2 Take the added up squared deviants SS Divide by N for a population 2 G SS N Divide the 33 by the number of scores OR given originally Divide by n 1 for a sample 52 SS n1 35 Standard Deviation Most widely used measure IntervalRatio scale Square root of the variance Helps standardize the measure Standard Deviation amp Mean Formula 36 Using SPSS SPSS works sort of like a spreadsheet ROWS represent cases Columns represent variables SPSS can calculate descriptive statistics for us Have to know which one is appropriate to use Couple of ways to get various descriptive statistics 37 SPSS Menu Analyze Descriptive Statistics Frequencies Descriptives least useful Explore 38 Frequencies Flequencies W Qisplaj frequency tables Flequencies Statistics F39en ntile Values CentralTendency I Mean I Megian I Mgde l um I Values are group rnidpL Distribution 1 Skegness 39 Magimum 39 mesk Fiange 39 5 mean 39 Using Explore Allows you to break things down by group Factor is the same as Independent Variable ependent List Eeset I Eaclm List I Eancel I Help I Label Eases by Gender gender LI Display Enth If Stgt S39tatiticsI Flats gptinm I 4O Getting ready for Inferential Statistics Linear Transformations z Scores Normal Distribution Proportions and more Linear Transformations Take some data What if add a constant to all values What if subtract a constant from all values What if multiple all values by a constant What if divide all values by a constant Statistics 66 66 66 66 66 N Valid Missing 0 0 0 0 Mean 250455 300455 200455 1252273 Median 255000 305000 205000 1275000 Mode 2600quot1 3100quot1 2100quot1 130003 Std Deviation 265116 265116 265116 1325582 Variance 702867 702867 702867 17571678 Range 900 900 900 4500 a Multiple modes exist The smallest value is shown Summarv of changes Add amp Subtract Mean changes SD stays the same Multiple amp Divide Mean Changes SD changes Regardless General quotshapequot stays the same If skewed before transformation remains skewed If normal before transformation remains normal zSco res Special case of Linear Transformation M 0 SD 1 How to get formula zScore Formula To get M O subtract mean from all scores Gives us an individual quotdeviationquot score on top To get SD 1 divide by the SD Gives us an average deviation on bottom In the end the zscore gives us a measure in standard deviation units of the distance of an individual score from the mean zSco res Sign gives direction Value gives distance from the mean in standard deviation units Negative z score is below the mean Positive z score is above the mean Going backwards Can also go from a z score back to a raw score X ZSD M This allows us to take values from one quotscalequot with a given M amp SD and convert them to another quotscalequot with a different M amp SD Transforming Scores Recag Raw to z Score standardize distribution get to a mean of O and SD of 1 z Score to Raw can set new Mean amp SD REMEMBER Linear Transformation does NOT change shape of distribution The Normal Distribution Talked about briefly already last week Special case of symmetrical distribution Mean median amp mode are all equal Has that bell shaped curve Putting stats to work Locating Scores in Distribution How far away from mean is a given score How many standard deviation units Can also determine proportion of scores abovebelow based on calculus and formula for the curve Normal Distribution With zScores 39 Mean0 SD1 O to 1 3414 of scores 1 to 2 14 of scores 1 to 1 6828 of scores 196 to 196 95 of scores 34 between 1 and O Terminoloav Population Parameters Sample Statistics Populatlon Parametet Sample Statistic Usually Unknown Figured from Known Data Basis Scores of entire population Scores of sample only Symbols Mean Standard deviation V at Populations Samples amp Stats With descriptive statistics difference isn t quotasquot important The mean is still the mean But if making a comparison difference is VERY important Issues of inference amp inferential statistics Purpose of Inferential Statistics Take the data from our sampes and draw a conclusion about the population Probabilitv Probability is the proportion of times that a particular event is likely to happen BY CHANCE Randomly assign to groups by flipping a coin 5050 chance they ll end up in a group Roll of a die Possible successful outcomes Probabili ty All possible outcomes Probabilitv contl Is constant Flip a coin 100 times Every time get heads What s probability of heads on 101st flip BUT cumulative probability can be different likelihood of 101 heads showing up might be less unlikely Even though the probability for any single event is the same The Gamblers Fallacy Probabilitv in Svmbols Use the lower case italicized letter p to represent probability p05 means there is a 5 chance or probability ie a proportion of 05 plt05 means that there is less than a 5 chance of the outcome occuring Inferential Stats amp Probabilitv How likely are we to see what we see Most outcomes are probably going to be common but what s less likely to happen Need something that gives us a proportion we could base things on The Normal Distribution We know the proportion of scores that fall in a given region Eg 95 are between 196 amp 196 So if we draw a score at random 95 of the time it s going to be in that range Chance of getting a more extreme score is quotunlikelyquot Example getting a zscore below 196 or above 196 is unlikely will occur less than 5 of the time Frequency dislribu un Anagt DSgt FrequemtexDi 39erEntgmups wiLhin Lhe data Ana gtDSgtEgtq71me Variablestrai39ts or cnara u 39 39 inr r in 39 39 a Types of r k 39 39 DiscrEtE bar n N mirin inr nnnn n n nr k H39imn rnrnbrani nrre nrirnn rnrnn nrri A w subsetofdnegroupirn i Central7 4 39 Niodernost 39 i 39 39 variahilitv now sore out rn mode 39 W 39 Hi39 rivari39abi39ii39tycscaroe atter rii rnnnn n quot 39 Deviau39 D 39 39 M Variance Divide by N for a ooouiation s as or Divide by n71 for a sarnoie s 55 0771 Standard Deviation represent cases Coiurnns representvariabies Liquot a 39 39 39 39 ltn cnanges quotsnaoequot stays tne sarne if skewednonnai before transforma on remains skewednonnai To getM o subuactrnean from aii scores individuai quotdeviationquot score on too To getSD divide by tine SD quotaveragequot deviation 1 1 i f MeanosD10to 1 4 to e H i i alto1 496 to 19695 39 39 LHdH i Measure or centrai tendency describes the typicai or average score ine zcscore is aiso caiied a standardized vaiue Distribution 0 Variance 1 ine word quotfrequencyquot rerers to now rnany scores there are at eacn vaiue K M l X ZSD M 7 Positive N 22w 51943 r 7 39 SD N N Simple data set Score Ana gt Descriptive Statistics gt Frequency Mean Median Mode Experimental Design Two groups Two columns Group 1 or 2Condition IV Score DV Ana gt Descriptive Statistics gt Explore Factor Grouping Correlational Design Ana gt Descriptive Statistics gt Frequ Average overall

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