1. Sampling

2. BASIC DEFINITIONS Population=aggregate set of all case that conform some set of specifications Subpopulation=population stratum = stratum Population element =single member of population Census=count of elements in population, determination of characteristics of the population based on info on all members Sample=selection of some elements of population Representative sampling plan carries the insurance that say, 90% of the time (confidence level) the population estimates based on the sample differ no more than 5% (margin of error) from the real value

3. Nonprobability sampling Accidental Samplesselect the first population elements you encounter. danger: underrepresentation of minorities, females, etc. Quota Samplingaccidental sample while taking care to have all strata represented in the sample as in the population. danger: “own-friends”-bias Purposive Samplespick cases that are judged to be “typical” of the target population. danger: judgement... Probability sampling Simple Random Samples selection based on random numbers such that each population element has equal and independent probability of being sampled Stratified Random Sample Cluster Sample

4. Determine a proper sample size

5. Lambda ( ) (Goodman & Kruskal, 1954) To what extent does prediction of rows (columns) improve if the column (row) is known in a 2  2 contingency table? Divorce. LowHigh Marriage % Low18523 High61925 24 Marriage rate predicted WITHOUT knowledge of divorce rate : High (25>23) Marriage rate predicted WITH knowledge of divorce rate : High if Divorce% high Low if Divorce% low

6. :To what extent does prediction of rows (columns) improve if the column (row) is known in a 2  2 contingency table? Generalization r² :To what extent does prediction of y improve if this prediction is based on X substituted in the regression line y=ax+b than if this prediction were made without knowing that line? Generalization: correlation between continuous variables Sum of squares of errors WITHOUT knowing X Sum of squared errors WITH knowledge of X Improvement:

7. Correlation between one continuous variable and one dichotomous variable puzzles solved by Autocratic Teams Democratic Teams 810 12 79 11 1213 mean=9.611.0 Dummy variable Autocratic = 0 Democratic = 1 y = 9.6 + 1.4x Regression line

8. Computation of r² If we know the leadership style in a team, then we can predict their productivity 15% better than without that knowledge

9. r² depends on the difference between the group averages and the variance within the groups Higher r²

10. Relation between r and t-test H 0 :there is no relation between a dichotomous variable x (group) and a continuous variable y H 0 is not likely to be true if r² is high. WHAT IS HIGH? Statistics  if in the population no relation exists between x and y then the samplingdistribution of has a t-distribution

11. Student t-distribution versus Normal distribution -3-20123 N(0,1) t(100) t(5).4.3.2.1 Type I error

12. Voorbeeld – leadership style and productivity r² for leadersship style and productivity equals.15 (N=10 teams, r =.39) Concluson: the obtained result is NOT strong enough to reject the nulhypothesis that states that leadership style and productivity are unrelated … WHICH IS NOT THE SAME AS “H 0 IS TRUE” !!

13. Classical approach to t-test Autocratic teamsDemocratic teams

14. Attention! Statistically significant  Theoretically relevant You can always find a sample size N for which you get a significant test result r=.04 r²=.0016 N=3000 yields t = 2,19