ࡱ> UWRST5@ 0WDbjbj22 +LXX%-\\\\\\\p____a|p dlxexexexeSf`ff$R$j\fSfSfff\\xexer{k{k{kf6\xe\xe{kf{k"{kk\\xed D\_hL 08hpp\\\\(\/ff{kfffffppD8:$%qk pp:Descriptive StatisticsTest DescriptionAssumptionsFormulaAdvantage DisadvantageReference/ExamplePercent, Modes, Frequency, MediansMeasure of central tendency for a descriptive stats (DS) Works for all types of variables. HYPERLINK "http://www.statcan.ca/english/edu/power/ch11/median/median.htm" http://www.statcan.ca/english/edu/power/ch11/median/median.htmMeans/Standard of Deviation (SD)DS - Measure of central tendency (means) & Dispersion (SD)Only works for interval/ratio, because they can be normally distributedRange, Quartiles (medians is second quartile), inter quartilesDS: Measure of dispersions Works for all variables (nominal, ordinal, interval, ratio)ModeMost frequent value in a category - Model Categories is a range measurementIs not reliable on raw data because unless the data is normally distributed, it will be unbalancedSDMeasure of deviation from the central tendency for normal distribution The variance and the closely-related standard deviation are measures of how  HYPERLINK "http://davidmlane.com/hyperstat/A84400.html" spread out a distribution is. The variance is computed as the average squared deviation of each number from its mean HYPERLINK "http://davidmlane.com/hyperstat/A16252.html" http://davidmlane.com/hyperstat/A16252.html Inferential Statistics - Measure of AssociationPhiFor 2x2 cross tables. SquaredNominal & Ordinal level of categories for both D.V and I.V from -1 to 1 How much the I.V. explains the D.V. = (A*D)-(B*C)/[(A+B)(C+D)(A+C)(B+D)] = SQRT(chi squared/N) Squared is a PRE measure Range. Coefficient of contingencyFor large tables where is no clear I.V. or D.V.`C= "(  2 / ( 2 +N))For large tablesNot a good measure and the interpretation is not easy. Its value can vary according to table size HYPERLINK "http://www.ams.sunysb.edu/~finchs/ams315/fall99/lectures/ams315l13.ppt#17" http://www.ams.sunysb.edu/~finchs/ams315/fall99/lectures/ams315l13.ppt#17 Cramers VFor non 2x2 and large tables V=SQRT(X2/(N*(k-1) where k is the smaller number of rows and columns For large tablesNot a Proportional reduction in error (PRE)LambdaReduction in err using info on I.V/Original amt of error (not using I.V. to aid prediction) Any size cross tables Works on ORDINAL or NOMINAL Must know your D.V. and I.V.PRE = (E1-E2)/E1: E1: error no considering (for michael: frequency or manager or clerks) the I.V. E2 error knowing the I.V.PRE MeasureWhen the modes are in the same categories. Must have different modal categories.GammaBoth variables have to be ORDINAL Measures based on proportion of concordant (vary in same direction) vs. non-concordant (vary in opposite direction)Symmetric Indicates a measure of association that produces the same result regardless of which of the 2 variables is the independent and which is the dependent variableProbability of a random pair of observations is concordant probability that the same pair is non-concordant (???) P1-P2 = PPRE MeasureIf there is a lot of ties, gamma is useless as the probability is 0. . HYPERLINK "http://www.uwm.edu/People/chava/chapter7.ppt" http://www.uwm.edu/People/chava/chapter7.ppt Somer DA measure of association where you have to pay attention to which is the independent variable and which is the dependent. It requires clear IV and DVBoth variables have to be ORDINAL PRE HYPERLINK "http://faculty.uccb.ns.ca/cdr/Measures%20of%20association.htm" http://faculty.uccb.ns.ca/cdr/Measures%20of%20association.htm  HYPERLINK "http://www.unlv.edu/faculty/cstream/ppts/QM722/measuresofassociation.ppt" http://www.unlv.edu/faculty/cstream/ppts/QM722/measuresofassociation.ppt Persons RBased on regression equation NOT on cross table Values = [-1,+1] 1 for perfect positive relationship 0 no relationship -1 for negative relationship Both variables have to be INTERVAL OR RATIO level of measurement. Formula  HYPERLINK "http://www.people.vcu.edu/~pdattalo/706SuppRead/Pearson's%20r.html" http://www.people.vcu.edu/~pdattalo/706SuppRead/Pearson's%20r.html PRE HYPERLINK "http://www.people.vcu.edu/~pdattalo/706SuppRead/Pearson's%20r.html" http://www.people.vcu.edu/~pdattalo/706SuppRead/Pearson's%20r.html Unexplained VarianceSum of the difference in actual value and predicted values of Y (D.V.) (y -y)2 : y is actual value of observation and y is the predicted valueExplained VarianceTotal variance  Unexplained varianceExplained V= (y - )2 - (y -y)2Total VarianceTotal sum of Square of observation  grand meanTotal V = (Y- )2Correlation Coefficient R2R2 proportion of total variation in y (DV) explained by x (IV)R2 = Explained Variance/Total Variance (Y- )2- (y -y)2 / (Y- )2 Eta squared (h2)Is the proportion of the total variance that is attributed to an effect from an experiment. It varies from 0 to 1 ETA squared is the proportion of the total variability in the dependent variable account for by knowing the values of the independent variableIV is at least NOMINAL or ORDINAL and DV is INTERNVAL or RATIO and symmetrich2  INCLUDEPICTURE "http://edf5400-01.sp02.fsu.edu/eta.gif" \* MERGEFORMATINET 2 is a PRE measure, but INCLUDEPICTURE "http://edf5400-01.sp02.fsu.edu/eta.gif" \* MERGEFORMATINET  is not. Used when R can not be used  HYPERLINK "http://web.uccs.edu/lbecker/SPSS/glm_effectsize.htm" http://web.uccs.edu/lbecker/SPSS/glm_effectsize.htm  HYPERLINK "http://www.janda.org/c10/Lectures/topic10/R3-bivariate.htm" http://www.janda.org/c10/Lectures/topic10/R3-bivariate.htm  HYPERLINK "http://www.visualstatistics.net/Visual%20Statistics%20Multimedia/nonlinear_regression_analysis.htm" http://www.visualstatistics.net/Visual%20Statistics%20Multimedia/nonlinear_regression_analysis.htm Multiple RegressionFind the best fit for the data. Uni-variate and multivariate refer to the number of IVYou have to know the theoretical model (both the Independent Variables and the DVTauA, B, CBESD Binominal EffectCronbach Alpha> .8 is there is correlation HYPERLINK "http://www.ats.ucla.edu/STAT/SPSS/faq/alpha.html" http://www.ats.ucla.edu/STAT/SPSS/faq/alpha.html Point Biserial RMeasure of Significance (Analysis of variance)Degrees of Freedom (df)Number of categories of first variable -1 * number of categories in second variable -1 so a 2x1 table df = (2*1-2*1) =1Chi Square  2Used for Corsstabs. It is the product of the effect (strength of relationship) * size of the study (sample) Results are looked up in the lookup table. Report the smallest number for which the calculated  2 is bigger. That tells us that it is significant. IV and DV are nominal or ordinal level categories 2= 2 * N =  (O- E) 2/E Observed frequencies in every cell of the cross table  expected frequencies under null hypothesis Any chi square of 15 or bigger is going to be significant at the .01 level or up. Big chi square means that the probability that the null hypothesis is true is small. T TestTest of significance used to compare the means of two groups "t" means in terms of the probability that the null hypothesis is true must be determined by comparing the obtained t to a probability table for the t distribution, examining the row for your degrees of freedom. IV is NOMINAL and has only 2 categories nominal, DV is internal or higher normally distributed r2 * SQRT(df) SQRT(1-r2) Numerator is explained variance Denominator is the unexplained variance Result is size of effect (or strength of the relationship) df = N-2 It can have positive or negative values we can tell which mean is larger on the DV. Requirements for T Interval level of measurement Approximately normal distribution of means within each of the two groups "Homogeneity of variance:" the pattern of variance around the means is such that the two samples could have been drawn from the same population Non parametric tests (Mann-Whtiney U or WilcoxosonData is ranked orders and not normally distributed on the DVANOVA F Test Factorial ANOVAOperation to partition variance. The total variance is the sum of squares of deviations from the grand mean Uni-variate and multivariate refer to the number of DV Single IV nominal or ordinal and 3 or more categories of the IV and Single DV is interval and normally distributed. Explained variance/unexplained variance "F= t SSb= ( (Mk- Mbar) 2 SSw= ( (Mk- Mbar) 2 k is the number of conditions or experiments N: is the sample size SS: Sum of squared of the mean (w: within each group, b: between each group and grand mean) (SSb/k-1) (SSw/N-k) df1 = k-1 df2 = N-k Factorial Designs/MANOVACrosses 2 or more IV with Nominal categories like a cross table but instead of Ns in the cells, we have means on one or more DV Interaction effect between IVs Uni-variate and multivariate refer to the number of DVMANOVA involves the calculation of several sets of composite variables and each set is specific to a particular effect. HYPERLINK "http://www.uwsp.edu/psych/cw/statmanual/manovauses.html" http://www.uwsp.edu/psych/cw/statmanual/manovauses.html  HYPERLINK "http://www.richmond.edu/~pli/psy538/MANOVA/manova1%20copy/3" http://www.richmond.edu/~pli/psy538/MANOVA/manova1%20copy/3 P TableP is determined by using a lookup table that considers size of correlation and size of sampleIV and DV are interval and normally distributed. IV at nominal or ordinal level. DV at the interval or ratio level the square root of F =t Factor AnalysisProve the convergent and discriminate validity of items between within a factor. 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