Inferential statistics.ppt


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Inferential statistics.ppt

  1. 1.
  2. 2. INFERENIAL STATISTICSinvestigate questions, models andhypotheses. In many cases, theconclusions from inferential statisticsextend beyond the immediate dataalone.Statistics that use sample data tomake decision or inferences about apopulationPopulations are the group ofinterest –but data analyzed onsamples.
  3. 3. INFERENIAL STATISTICSBased on the laws of probabilityThe larger the difference betweenthe groups ,the lower the probabilityis that the difference occurred bychanceBased on the assumption thatsamples are randomly
  4. 4. INFERENIAL STATISTICSto make judgments of the probability that anobserved difference between groups is adependable one or one that might have happenedby chance in this study.Thus, inferential statistics to make inferences fromour data to more general
  5. 5. PurposesEstimating population parameter from sampledataTesting
  6. 6. Estimating population parametero Sampling error – when the sampledoes not accurately reflect thepopulationo Sampling
  7. 7. Pulse measurements on a population of 20 subjectsAv. pulse rates of agrp.of cardiacpatients66,71,70,67,80,63,65,79,59,70,67,66,70,74,92,80,71,55,83,72Mean pulse rate=71Random sample#1Random sample#2Random sample#3Mean pulse rate ofpopulation=71*Above average forpopulation66,59,70,55,6680,92,83,79,8071,71,70,64,67Mean pulse rate ofRandomsample#3=71Mean=61Mean=83*Mean=71Mean pulse rate ofRandomsample#1Considerably Below
  8. 8. Sampling distributionA theoretical frequency distribution ,basedon an infinite no of samplesBased on mathematical formulas and
  9. 9. Sampling distribution of meanIn normal distribution 68%values lie between+or –1SDand approx 95%lies between +or –2SDie 95%of the values in a normal distribution liebetween +or –1.96SD from the
  10. 10. Confidence intervalsIt is a range of values that with a specified degreeof probability ,is thought to contain the populationvalue.They contain a lower and an upper limit.Theresearcher asserts with some degree of confidencethat the population parameter lies within
  11. 11. A confidence interval (CI) is an interval estimate of apopulation parameterInstead of estimating theparameter by a single value, an interval likely toinclude the parameter is given.Thus, confidence intervals are used to indicate thereliability of an estimate.How likely the interval is to contain the parameter isdetermined by the confidence level or confidencecoefficient.Increasing the desired confidence level will widenthe confidence
  12. 12. Were this procedure to be repeated onmultiple samples, the calculatedconfidence interval (which would differfor each sample) would encompass thetrue population parameter 90% of thetime."Note that this need not be repeatedsampling from the same population, justrepeated
  13. 13. The confidence interval representsvalues for the population parameter forwhich the difference between theparameter and the observed estimate isnot statistically significant at the 10%level―
  14. 14. If the true value of the parameter liesoutside the 90% confidence interval once ithas been calculated, then an event hasoccurred which had a probability of 10% (orless) of happening by
  15. 15. Testing hypothesisThe null hypothesis is subjected to statisticalanalysisStepsState the research hypothesisState the null hypothesis to be testedChoose the appropriate statistical test for the dataDecide on the level of significanceDecide the test –one tailed or two tailed test to beused.Calculate the test statistics using the research dataCompare the value to the critical value to that testReject or fail to reject null hypothesisDetermine support or lack of support for the
  16. 16. Level of significanceProbability of rejecting a null hypothesis when itis true ,and it should not be rejected(alpha)Most common level of significance.. .05The rresearcher Is willing to risk being wrong5%of the time or 5 times out of 100,whenrejecting the null hypothesisMore accurate .01or even at .001Risk
  17. 17. Degree of freedomConcerns the no of values that arefree to vary. df and a
  18. 18. Null hypothesis ---false ---reject—correct decisionNull hypothesis--- true –accept –correct decisionNull hypotheses--- true--- rejected-----type I errorNull hypothesis-- false –accepted---Type II
  19. 19. Type II error –controlled –using alarge
  20. 20. Type I Error No errorNo error Type II ErrorTrue falseNullrejectedNullnotrejectedActual situation in populationNull
  21. 21. Choosing statistical test:1. Are you comparing groups or test scores?Are youcorrelating variables2. What is th helevel of measurement of thevariables (nominal,ordinal,interval/ratio)3. How larg eare the groups?4. How many sets or groups are being considered5. Are the scores or observations dependent orindependent?6. How many observations are available o the eachgroup
  22. 22. Statistical tests used1. T tests2. analysis of variance3.
  23. 23. Thank