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Topic 9 T Distribution.pptx
- 1. Hypothesis testing t andAnova in Excel, SPSS and PSPP
- 2. What is thet-distribution?
- 10. Hypothesis Testing • LikertScale data • Research Hypothesis & Statistical Hypothesis • Check Normality of Data • Choose Parametric /Non Parametric test • Check p value for Ho or Ha depending on confidence interval
- 11. Hypothesis Testing Nulland Alternative Hypotheses Both Ho and Ha are statements about population parameters, not sample statistics. A decision to retain the null hypothesis implies a lackof support for the alternative hypothesis. A decision to reject the null hypothesis implies supportfor the alternative hypothesis.
- 12. Hypothesis Testing Sample Statistics- Hypothesized Parameter Test Statistic = Standard error of statistic
- 13. Types of Tests ParametricTest The statistical test which makes assumptions about the distribution of population parameters are known as parametric tests. Non Parametric Test The alternative which makes no assumptions about the distribution of population parameters are known as non parametric tests.
- 14. Statistical Techniques Parametric Statistics Non Parametric Statistics Comparative Relationship 2Groups > 2 Groups Covariate 2 Variables > 2 Variables Regression ITT DTT OSTT One Way ANOVA RM- ANOVA Bet-Bet ANOVA Bet-With ANOVA With -With ANOVA ANOVA Simple Correlation Multiple Correlation Partial Correlation Linear Multiple Logistic
- 15. 2 Groups >2 Groups Mann Whitney U test Wilcoxon Rank Test 1 Sample Sign Test Kruskal- Wallis H test Friedman Test Rank Order Correlation Contingency Coefficient Phi Correlation Tetrachoric Correlation Point Biserial Correlation Biserial Correlation Goodness of fit Test for independence Statistical Techniques Parametric Statistics Non Parametric Statistics Comparative Relationship Others Chi Square
- 16. P value • Thelevel in which we are allowed to reject the null hypothesis when it is true or Type 1 Error • A rule of thumb is if p-value < 0.05 (5% level of significance) we reject null hypothesis • if p-value > 0.05 (5% level of significance) we fail to reject null hypothesis.
- 18. Tcal and Ttabto decide Hypothesis • Tcal < Ttab – Fail to Reject Null Hypothesis • Tcal>Ttab – Reject Null Hypothesis Tcal , Zcal ,Fcal will be obtained from formulae Ttab ,Ztab,Ftab will be obtained from Tables All Software give Tcal,Fcal along with p values
- 19. Parametric Test T Test ZTest F Test
- 20. Various types ofT Test One sample T Test Independent sample T Test Dependent sample T Test
- 21. T Test In t-test,independent variable is in nominal scale and dependent variable is in ratio scale.
- 22. One Sample TTest • Null hypothesis: There is no significance differences between the population mean and the sample mean. • In one sample T Test, a sample mean is compared with the known population mean Sample
- 23. Independent Sample TTest • In Independent sample T Test, means of two groups are compared. • Null hypothesis: There is no significant difference in means of two groups
- 24. Dependent Sample TTest • In dependent sample T Test, means of same group is compared before and after the treatment. • Null hypothesis: There is no significant difference in means before and after treatment.
- 25. One Way ANOVA •In Independent sample T Test, means of more than three groups are compared. • Null hypothesis: There is no significance differences in marks of more than two groups
- 26. • One SampleT Tests
- 32. Hypothesis Testing Examples Example: A normal white blood count is assumed to be approximately 8 thousand cells per cc of blood. A random sample of 15 employees of a nuclear plant yielded a mean white count of 7.81 with a standard deviation of 0.872 (in thousands).Is there significant evidence that the mean white count is lower for plant employees using a=0.05? Example : A pill is supposed to contain 20 mg of Phenobarbital. A random sample of 29 pills yielded a mean of 20.5 mg and a standard deviation of 1.5 mg. Test using a=0.10 whether the true mean amount per pill is 20 mg Example: When a process producing ball bearings is operating correctly the weights of the ball bearings have a normal distribution with mean 5 ounces and standard deviation 0.1 ounce .An adjustment has been made to the process and the plant manager suspects that this has raised the mean weight of ball bearings produced leaving the standard deviation unchanged . A random sample of sixteen ball bearings is taken, and their mean weight is found to be 5.038 ounces. Test at significance levels .05 and .10 (that is, at 5% and 10% levels) that the adjustment has not increased the mean weights of the ball bearings
- 33. 6) When aprocess producing ball bearings is operating correctly the weights of the ball bearings have a normal distribution with mean 5 ounces and standard deviation 0.1 ounce .An adjustment has been made to the process and the plant manager suspects that this has raised the mean weight of ball bearings produced leaving the standard deviation unchanged . A random sample of sixteen ball bearings is taken, and their mean weight is found to be 5.038 ounces. Test at significance levels .05 and .10 (that is, at 5% and 10% levels) that the adjustment has not increased the mean weights of the ball bearings
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- 38. Example – Mobilebill for Gender Male Female 431 411 432 412 444 413 432 444 411 424 432 456 422 432 435 435 413 444 415 412 436 418 438 421 445 427 411 428 447 435 448 437 411 440 423 441 427 442 428 437 435 432
- 39. Solution t-Test: Two-Sample AssumingEqual Variances Male Female Mean 429.3333 430.5238 Variance 145.5333 157.7619 Observations 21 21 Pooled Variance 151.6476 Hypothesized Mean Difference 0 df 40 t Stat -0.31325 P(T<=t) one-tail 0.377857 t Critical one-tail 1.683851 P(T<=t) two-tail 0.755715 t Critical two-tail 2.021075
- 40. Paired Sample TTest
- 41. Paired Sample TTest
- 42. Paired Sample TTest Example
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- 44. Example Proble m Systolic BloodPressure Before and After Exercise Null Hypothesis : There is no difference in Systolic Blood Pressure Before and After Exercise Alternative Hypothesis : There is a significance difference in Systolic Blood Pressure Before and After Exercise Statistical Test : Dependent Sample t test /Paired 2 Sample for Means (Excel) Before Exercise After Exercise 116 126 126 132 128 146 132 144 134 148 136 134 138 144 138 146 140 136 142 152 144 150 148 152 150 162 154 156 162 162 170 174
- 45. Solution t-Test: Paired TwoSample for Means Before Exercise After Exercise Mean 141.125 147.75 Variance 185.5833333 152.4666667 Observations 16 16 Pearson Correlation 0.899063955 Hypothesized Mean Difference 0 df 15 t Stat -4.442450112 P(T<=t) one-tail 0.00023741 t Critical one-tail 1.753050356 P(T<=t) two-tail 0.000474821 t Critical two-tail 2.131449546