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Tests of significance by dr ali2003


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  • 2. Introduction Classification of tests Steps, formulas and exercises Conclusion
  • 3. “Education at home is a friend, abroad an introduction, in solitude a solace, and in society an ornament. It gives once grace and government to genius”  ---Bharthruhari
  • 4.  The term statistical significance is coined by Ronald Fisher(18901962)  Student (William Sealy Gosset) (1876-1937)  Carl Friedrich Gauss (1777-1855)
  • 5.     Range of estimates a characteristic can take (different samples are taken from same population) depends on 1.the mean value 2.the variability of the observations in the original population 3.the size of the sample     Causes of differences observed between two estimates are a) sample variation b) when sample is coming from different population Repeated samples even though from the same population will not yield the same characteristic under observation(esp common among biological observation). This difference between the sample estimates is known as sample variation
  • 6.   The methodologies of statistics which deal with the technique to analyse, how far the difference between the estimates from different samples are due to sampling variation otherwise, is known as testing of hypothesis or Statistical test is a procedure to find the likelihood of a null hypothesis being right on the basis of the given data  Tests of significance is a procedure to test whether or not the observations fall into a specified pattern such as equality of two means or of two proportions   . In statistics, a result is called statistically significant if it is unlikely to have occurred by chance
  • 7.  Should be framed in such a way that it conveys the meaning that differences between the estimates provided by different sample is due to the sampling variance  In other word, the null hypothesis states that the samples are coming out of a common population
  • 8.  The amount of evidence required to accept that an event unlikely to have risen by chance is known as the significance level or critical P-value(probability level)  It fixes the magnitude of risk of making a wrong conclusion of rejecting the null hypothesis  If the value of P is small, it means that the probability of attributing the difference between sample estimates to the sampling variation or chance factor is small--- null hypothesis is rejected  If P value is large then the probability that the difference between the sample estimates caused by sampling variation is large  How small should be this value of P to a reject a null hypothesis depends upon the type of investigation. As a mater of practical convenience a value of less than or equal to0.05 is the usual level which is commonly accepted for rejecting the null hypothesis( it means one would be going wrong in 5 out of 100 cases by rejecting the null hypothesis)  All tests of significance are aimed at finding this value of P
  • 9.  Errors in accepting or rejecting the null hypothesisare  Type1 error – if the null hypothesis is rejected when it is actually true  Type 2 error– if the null hypothesis is accepted when it is false
  • 10. It is the standard deviation of a statistical parameter like mean, proportion, etc. this gives an idea about satatistical parameters obtained from repeated samples from the same population  Standard error is useful for fixing the confidence limits, which gives a range for the statistical parameter, indicating that the true value of the parameter is contained in the range with a certain confidence  It is basic statistical quantity for testing the significance of the difference in estimates between two samples 
  • 11.  Two tailed tests– in testing hypothesis conclusion are made on the basis of tests of significance that the two samples are from the same population or not without considering the direction of the difference between the two sample estimates like mean or proportion  One tailed tests– conclusions are made as to whether one of the sample mean is larger than the other, tests of significance
  • 12. “Among all types of charities such as of good food, water, cows, lands, clothes, gold etc; a charity, donation or grant forth spread of education is superior to all other forms of charities”  ----Manu
  • 13.  Based on specific distribution such as Gaussian    Not based on any particular parameter such as mean Donot require that the means follow a particular distribution such as Gaussian(have less efficiency when underlying distribution is Gaussian Used when the underlying distribution is far from Gaussian (applicable to almost all levels of distribution) and when the sample size is small
  • 14. Student’s t- test(one sample, two sample, and paired)  Proportion test(Gaussian’s z-test)  ANOVA F-test  Sign test(for paired data)  Wilcoxon signed rank test for matched pair  Wilcoxon rank sum test (for unpaired data)  Chi-square test  Many tests based on qualitative data are nonparametric 
  • 15.  Students t- tests--A statistical criterion to test the hypothesis that mean is superficial value, or that specified difference, or no difference exists between two means. It requires Gaussian distribution of the values, but is used when SD is not known  Proportion test---A statistical test of hypothesis based on Gaussian distribution, generelly used to compare two means or two proportions in large samples, particularly when the SD is known   ANOVA F-test--- used when the number of groups compared are three or more and when the objective is to compare the means of a quantative variable
  • 16.  One sample– only one group is studied and an externally determined claim is examined  Two sample– there are two groups to compare  Paired– used when two sets of measurements are available, but they are paired
  • 17. Get up, be awake, resort to the good and acquire knowledge  --- vedas
  • 18.  Find the difference between the actually observed mean and the claimed mean.  Estimate the standard error (SE) of mean by S/n, where s is the standard deviation and n is the number of subjects in the actually studied sample. The SE measures the inter-sample variability  Check the the difference obtained in step 1 is sufficiently large relative to the SE. for this , calculate students t. this is called the test criterion. Rejection or non-rejection of the null depends on the value of this t (this is similar to z-score of mean, but not exactly the same)  Reject the null hypothesis if the t-value so calculated ismore than the critical value corresponding to the pre-fixed alpha level of significance and appropriate df.
  • 19.  Two basic formulas for calculating an uncorrelated t test. Equal sample size x1 – x2 t= √ n sample size Unequal δ21 + δ22 t= √ x1 – x2 ( n1 – 1)δ21 + ( n2 – 1) δ22 n1 + n2 – 2 ∙( ) 1 +1 n1 n2
  • 20.  Obtain the difference for each pair and test the null hypothesis that the mean of these diffrences is zero(this null hypothesis is same as saying that the means before and after are equal)
  • 21.  This is valid only for large n
  • 22.       Situations where it is used are a two sample situation 2. in a paired set-up a repeated measures, when the same subject is measured at different time points such as after 5 minutes, 15 minutes, 30 minutes, 60 minutes etc,. 4.removing the effect of a covariate 5. regression.
  • 23.  Based on signs(positive and negative) of the differences in the levels seen before and after therapy
  • 24.  It is better test than the sign test– assigns rank to the differences of n pairs after ignoring the + or – signs  The lowest difference gets rank 1 and the highest gets rank n  Sum of the only those ranks that are associated with positive difference obtained(Wilcoxon signed rank criteria)  It is similar to Mann-Whitney test
  • 25.  If there are n1 subjects in the first sample andn2inthe second sample, these(n1+n2) values are jointly ranked from 1 to (n1+n2) {the sum of these ranks is obtained for those subjects only who are in smaller group}
  • 26.  Alternative to the test of significance of difference between two proportions
  • 27.  “Never shed tears for errors. Take  lessons from them you will win” ___Panchatantra
  • 28.  A Indrayan and L Satyanarayana- biostatistics, 20006 ed, Printice -Hall of India  MSN Rao, NS Murthy-applied statistics in health sciences, 2nd ed, 2010, jaypee  www. Wikipedia. org
  • 29. µ α Σ δ µ Thank you