SNAPSHOT.01 EZESTAT2 旼Page 36컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴� 쿖olmogorov-Smirnov [KS] test of differences in cumulative frequency � 쿭istributions � � � 쿟he KS test is an extremely effective way of determining differences � 쿫etween variables measured at the nominal or ordinal level � � - between two different samples � � - one group measured again after an interval. � � � 쿌s such, it is particularly useful in questionnaire analysis. � � � 쿥orked example "Opinions concerning capital punishment" � � -------------------------------------- � � 1982 旼컴컴컴컴컴컴커 1992 � � Nos. Cum% � ABSOLUTE � Cum% Nos. � � --------- � DIFFERENCES � ---------- � � Strongly opposed 20 20% � 20% � 40% 16 � � Opposed 25 45% � -> 30% � 75% 14 � � In favour 35 80% � 10% � 90% 6 � � Strongly in favour 20 100% � - � 100% 4 � � --- 읕컴컴컴컴컴컴켸 -- � � 100 40 � � [Pg Dn] [Pg Up] � 읕컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴켸 SNAPSHOT.02 EZESTAT2 旼Page 37컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴� 쿖olmogorov-Smirnov Test - calculations � � � 쿔s this evident shift in opinion statistically sigificant or not ? � � � � � Work out the cumulative frequencies in percentages and then find � � the largest ABSOLUTE difference between them (central column). � � /------- � � � We need a difference of 1.358 * / (n1+n2) at the 5% level � � / -------- � � \/ (n1*n2) � � � 퀇here n1,n2 are the sample sizes. If n1=100 and n2=40 then we need at least� �1.358 � ( 140/4000 ) = 0.2541 (25.41%) so 30% is significant at 5% level. � � � 쿢se 1.628 to test at the 1% level. In the example, the figure would work � 쿽ut at 0.3046 (30.46%) which would NOT be significant at the 1% level. � � � 쿟he KS test is much less sensitive to small cell numbers than a � 쿬hisquare test but more powerful as it uses the WHOLE of the distribution. � � � � � � [Pg Dn] [Pg Up] � 읕컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴켸 SNAPSHOT.03 EZESTAT2 旼Page 38컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴� 쿝ecoding data � � � 쿥e may need to recode data to turn CONTINUOUS into CATEGORICAL data... � 쿔NCOME Y_CODE SEX � � 1000 1 1 旼컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴� � � 2000 1 2 � Here we have INCOME (a continuous variable) � � � 3000 1 1 � coded into Y_CODE (a categorical variable) � � � 4000 1 2 � We could now, for example, do a chi- square � � � 5000 2 1 � test on Y_CODE v SEX � � � 6000 2 2 � � � � 7000 2 1 � NB We do lose some of the 'richness' in � � � 8000 2 2 � the data when we code like this. � � � 읕컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴� � � � 쿥e can also COLLAPSE data, which is similar to recoding. If we have a � 퀆ariable CLASS measured on a six-point scale [1-6] then we could recode � �1-3 into a 1 [ Middle class ] � �4-6 into a 2 [ Working Class] � 쿯or easier analysis [ or to reduce the cells ] in a chi-square. � � � � � � [Pg Dn] [Pg Up] � 읕컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴켸 SNAPSHOT.04 EZESTAT2 旼Page 39컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴� 쿎hoice of Test � � � 쿟he choice of test depends upon whether the data is measured at � 퀃he CONTINUOUS or the CATEGORICAL (or ORDINAL) level.. � � � � Variable Type of Statistics � � Statistic � �------------------------------------------------------------------------ � � CONTINUOUS PARAMETRIC Means; Standard Deviations � � (e.g. Incomes) Correlation (Pearson) � � Regression � � 't' tests on means, proportions � � � � CATEGORICAL NON- Frequency Distributions � � (e.g. coding PARAMETRIC Correlation (Spearman) � � number for Chi-square � � SEX) Kolmogorov-Smirnov tests � �------------------------------------------------------------------------- � � � � � � � � [Pg Dn] [Pg Up] � 읕컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴켸