Primary Scales Nominal Scales Numbers serve only as labels frequency counts i e Modes percentages Ordinal Scales Ranking No difference between figures centile based stats i e percentile quartile etc Interval Scale Equal distances represent equal values y a bx nom ord techniques mean std dev etc Ratio Scales Like interval but possesses absolute 0 point y bx all statistical techniques Scaling Techniques Comparative Non Comparative Comparative direct comparisons between objects Only ordinal or ran order properties Paired Comparison compare one object to another based off criterion ex Which one do you prefer Rank Order rank each object Constant Sum ex Allocate 100 points to each object Non Comparative each object is scaled independently interval or ratio scaled Continuous Rating Scale rate by placing mark at appropriate position on a line that runs from one extreme to another Itemized Rating Scale Respondents are provided with a scale that has a number or brief description with each category Semantic Differential 7 point rating scale with bipolar labels 1 7 or 3 3 Stapel Scale 5 to 5 vertical scale 0 is neutral point Likert Scale indicate level of agreement or disagreement from 5 levels ex 1 5 PNC has poor customer service XO Observed Score XT True Score XS Systematic Error XR Random Error Reliability extent to which scale produces consistent results if repeated Related to XR Validity Extent to which differences in observed scale scores reflect true differences among objects No systematic or random error Questionnaire Design structured technique for data collection consisting of a series of questions written or verbal Open Ended Q s Adv easy quick Disadv Costly interview bias various responses Multiple Choice Needs to be mutually exclusive collectively exhaustive can t find answer Adv Easy data coding less bias Disadv Position Bias tendency to choose option based on position Dichotomous Questions T F Y N etc Pre testing to identify and eliminate potential problems Sampling Error when sample is not reflective of population Non Sampling Error all other errors besides sampling measurement analysis response bias etc Sampling Frame representation of the elements of the target population ex Phone directory listserv Probability Sampling SRS each element in population has equal chance of selection Systematic start at random point and pick every ith element Stratified population is split into sub populations Take samples then compare the populations Cluster Sampling samples are selected from geographic locations Non Probability Sampling Convenience Sampling taking a sample from those most convenient Judgmental Sampling experiences individual selects sample based off judgement Ex Test Markets Quota Sampling Ex We know student population is 40 male 60 female We choose a sample where 40 are male Snowball Sampling respondents are asked to refer researcher to other potential respondents Data Analysis Methods Standard Dev SQRT sum of X X bar n 1 Z p where SQRT p 1 p n Type I Error Rejecting Null when Null is True Type II Error Failing to reject Null when Null is False Power 1 Probability of Rejecting the Null when it if False Rejecting when you should Cross Tabulation describes two or more variables simultaneously Chi Sqare X2 Null Hypothesis No association between variables df r 1 c 1 Expected Frequency in row in column total sample size X2 observed expected 2 Total t Distribution assumes normal distribution and mean is unknown Paired Sample t Test Null Hypothesis something t X bar s df n 1 sX S sqrt n HO of Differences 0 Ha of Differences 0 df n 1 tn 1 D bar subD s subD sqrt n One Way ANOVA used to test means for two or more populations Must have a dependent variable that is metric interval or ratio and independent nominal or ordinal called factors Ho All means of each of the populations are equal Ha At least one mean is different df within c 1 and df error N c SSy SS between SS within or Total Variation SSx SS error F SS between c 1 SS within or MSx MS error Product Moment Correlation summarizes strength of association between two metric variables interval or ratio Measures strength and direction Ho Two variables are not related Ha Two variables are related Eta Square 2 SSx SSy Regression Analysis Y 0 1X where Y dependent variable X independent variable 0 intercept 1 slope For each individual observation Yi 0 1 Xi ei where e error i ith observation Ho 1 0 Ha 1 0 t b SEb