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This post from Advance Innovation Group (http://www.advanceinnovationgroup.com) is document on step by step instruction on how to conduct different hypothesis tests in Minitab. …

This post from Advance Innovation Group (http://www.advanceinnovationgroup.com) is document on step by step instruction on how to conduct different hypothesis tests in Minitab.

It is detail description of Name of the test, When to perform, how to perform & what to conclude from the result, thus making hypothesis testing in Minitab a cake walk exercise.

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- 1. HYPOTHESIS TEST PROCEDURE AIG Confidential & Proprietary 1 Hypothesis Test Procedure Document ID: AIG/P/01 Version: 1.0 Advance Innovation Group A 43, Sector 56, NOIDA, UP, INDIA-201301 Tel. +91.120.4540759 www.advanceinnovationgroup.com
- 2. HYPOTHESIS TEST PROCEDURE AIG Confidential & Proprietary 2 Document Revision History : Date Document Version Document Revision Comments Prepared By Reviewed By Approved By 21 August 2009 1.0 Devendra Singh Pranay kr. Shruti Singh Distribution List: Date Document Version Document Sent To Purpose References: Reference Document Name Description Page No. None Proprietary Notice: This document contains proprietary information that is confidential to Advance Innovation Group. Disclosure of this document in full or in part, may result in material damage to Advance Innovation Group. Written permission must be obtained from Advance Innovation Group prior to the disclosure of this document to a third party..
- 3. HYPOTHESIS TEST PROCEDURE AIG Confidential & Proprietary 3 Contents 1.0 Test for CYCX...........................................................................................................................................5 1.1Regression............................................................................................................................................5 1.2 Scatter Plot..........................................................................................................................................7 2.0 Test for CYDX.........................................................................................................................................10 I Sample T Test........................................................................................................................................10 Sample Z test...........................................................................................................................................12 2 Sample T Test.......................................................................................................................................17 Stacking of Data ......................................................................................................................................19 Test for Equal Variance...........................................................................................................................20 1 Way Anova...........................................................................................................................................23 Turkey’s Family Error Rate (Part of 1 Way Anova)..................................................................................26 2 Way Anova...........................................................................................................................................28 3.0 Test for DYCX: .................................................................................................................................32 3.1 Binary Logistic Regression...........................................................................................................32 4.0 Test for DYDX ..................................................................................................................................34 4.1 1 Proportion Test ........................................................................................................................34 4.2 2 Proportion test:........................................................................................................................36 4.3 Chi Square Test: ...............................................................................................................................38 NON PARAMETRIC TESTS...........................................................................................................................45 1-Sample Sign Test :................................................................................................................................45 Mann Whitney: .......................................................................................................................................47 Moods Median Test:...............................................................................................................................49 Kruskal-Wallis Test..................................................................................................................................51
- 4. HYPOTHESIS TEST PROCEDURE AIG Confidential & Proprietary 4
- 5. HYPOTHESIS TEST PROCEDURE AIG Confidential & Proprietary 5 1 Test for CYCX 1.1Regression This test is conducted to verify relationship between Y and X and to quantify the nature of relationship. When we conduct the regression test the first value that we look at is the P value to accept or reject the Null Hypothesis. Ho: There is no relation between Y and X Ha: There is relation.
- 6. HYPOTHESIS TEST PROCEDURE AIG Confidential & Proprietary 6 In the above example as P<0.05, we will agree to the equation given above in the red box.
- 7. HYPOTHESIS TEST PROCEDURE AIG Confidential & Proprietary 7 1.2 Scatter Plot When is it used? • You have a set of paired data for two continuous variables. • You wish to visually check for evidence of any kind of relationship between the variables.
- 8. HYPOTHESIS TEST PROCEDURE AIG Confidential & Proprietary 8
- 9. HYPOTHESIS TEST PROCEDURE AIG Confidential & Proprietary 9 As depicted from the above diagram, it can be concluded that salt content and water has some relationship.
- 10. HYPOTHESIS TEST PROCEDURE AIG Confidential & Proprietary 10 2.0 Test for CYDX 2.1 1 Sample T Test This test is used when you want to compare the means of two samples. Ho: µ1= µ2 Ha: µ1 is not equal to µ2.
- 11. HYPOTHESIS TEST PROCEDURE AIG Confidential & Proprietary 11 Enter the column which contain data Enter the standard Check the box
- 12. HYPOTHESIS TEST PROCEDURE AIG Confidential & Proprietary 12 Here P is less than 0.05, so reject Ho. 2.2 1 Sample Z test This test is similar to the 1 Sample T, just that the std dev of the process should also be known while one chooses to do this test. Example : Customer for company A has given it a specification that the average length of the fabric has to 150, data as collected, and the company wishes to find if the std of 150 is being met or not.
- 13. HYPOTHESIS TEST PROCEDURE AIG Confidential & Proprietary 13 Input Data
- 14. HYPOTHESIS TEST PROCEDURE AIG Confidential & Proprietary 14 Similar to 1 T Test : Ho - µsample = 150 Ha - µsample not equal to 150 Put Std Dev Put the Std to compare the mean of sample.
- 15. HYPOTHESIS TEST PROCEDURE AIG Confidential & Proprietary 15 As Ha is correct meaning that the sample mean is not equal to 150. Change the Ha to greater than or less than and check the result again.
- 16. HYPOTHESIS TEST PROCEDURE AIG Confidential & Proprietary 16
- 17. HYPOTHESIS TEST PROCEDURE AIG Confidential & Proprietary 17 P value again is coming to 0.000 meaning Ha is correct meaning that the current mean is greater than the previous mean of 150. 2.3 2 Sample T Test This test is done when you want to compare the means of two samples. Ho: μ1=μ2 Ha: μ1 not equal to μ2 Enter the two columns of data
- 18. HYPOTHESIS TEST PROCEDURE AIG Confidential & Proprietary 18 Here, P>0.05, Accept the null hypothesis.
- 19. HYPOTHESIS TEST PROCEDURE AIG Confidential & Proprietary 19 2.4 Stacking of Data This is the step which we do before doing the test of equal variances as the test requires the data to be stacked in one column.
- 20. HYPOTHESIS TEST PROCEDURE AIG Confidential & Proprietary 20 2.5 Test for Equal Variance This is the test which is used to compare the variances of two samples. Ho: σ1 2 = σ2 2 = σ3 2 = …. = σn 2 Ha: Atleast one variance is different
- 21. HYPOTHESIS TEST PROCEDURE AIG Confidential & Proprietary 21
- 22. HYPOTHESIS TEST PROCEDURE AIG Confidential & Proprietary 22 Used for normal data Used for not normal data
- 23. HYPOTHESIS TEST PROCEDURE AIG Confidential & Proprietary 23 2.6 1 Way Anova This test is used for comparing the means of more than two samples. Ho: μ1 = μ2 = μ3 = μ4 =……=μn Ha: Atleast one mean is different OR
- 24. HYPOTHESIS TEST PROCEDURE AIG Confidential & Proprietary 24
- 25. HYPOTHESIS TEST PROCEDURE AIG Confidential & Proprietary 25 Here, P<0.05, Reject the null hypothesis.
- 26. HYPOTHESIS TEST PROCEDURE AIG Confidential & Proprietary 26 2.6.1 Tukey’s Family Error Rate (Part of 1 Way Anova) This is the test within the 1 way Anova test and is used to find out which is/are the means which are different to other means. The output for the same: One-way ANOVA: Gem, Joyride, Starlite, Fantasy, Fun Source DF SS MS F P Factor 4 2715 679 6.14 0.000 Error 52 5751 111 Total 56 8466 S = 10.52 R-Sq = 32.07% R-Sq(adj) = 26.84% Individual 95% CIs For Mean Based on Pooled StDev Level N Mean StDev ------+---------+---------+---------+--- Click Comparison button
- 27. HYPOTHESIS TEST PROCEDURE AIG Confidential & Proprietary 27 Gem 12 44.33 3.40 (-----*-----) Joyride 10 39.99 11.28 (------*------) Starlite 12 29.67 14.98 (-----*-----) Fantasy 11 43.52 8.92 (------*-----) Fun 12 50.02 10.51 (-----*-----) ------+---------+---------+---------+--- 30 40 50 60 Pooled StDev = 10.52 Tukey 95% Simultaneous Confidence Intervals All Pairwise Comparisons Individual confidence level = 99.34% Gem subtracted from: Lower Center Upper ------+---------+---------+---------+--- Joyride -17.08 -4.34 8.39 (------*-----) Starlite -26.81 -14.67 -2.52 (-----*-----) Fantasy -13.23 -0.82 11.60 (------*-----) Fun -6.46 5.68 17.83 (-----*-----) ------+---------+---------+---------+--- -20 0 20 40 Joyride subtracted from: Lower Center Upper ------+---------+---------+---------+--- Starlite -23.06 -10.32 2.41 (------*-----) Fantasy -9.47 3.53 16.52 (------*-----) Fun -2.71 10.03 22.76 (-----*-----) ------+---------+---------+---------+--- -20 0 20 40 Starlite subtracted from: Lower Center Upper ------+---------+---------+---------+--- Fantasy 1.43 13.85 26.27 (-----*-----) Fun 8.21 20.35 32.49 (-----*-----) ------+---------+---------+---------+--- -20 0 20 40 Fantasy subtracted from: Lower Center Upper ------+---------+---------+---------+--- Fun -5.92 6.50 18.92 (-----*-----) ------+---------+---------+---------+--- -20 0 20 40 This range does not include zero, indicating that the difference between these means is significant. If an interval does not contain zero, there is a statistically significant difference between the corresponding means. If the interval does contain zero, the difference between the means is not statistically significant .
- 28. HYPOTHESIS TEST PROCEDURE AIG Confidential & Proprietary 28 2.7 2 Way Anova Use the two-way analysis of variance (ANOVA) procedure to test the equality of population means when there are two fixed factors. This procedure requires that the number of observations for each combination of the factor levels be the same (balanced). S, R2 and adjusted R2 are measures of how well the model fits the data. These values can help you select the model with the best fit. S is measured in the units of the response variable and represents the standard distance data values fall from the fitted values. For a given study, the better the model predicts the response, the lower S is. R2 (R-Sq) describes the amount of variation in the observed response values that is explained by the predictor(s). R2 always increases with additional predictors. For example, the best five- predictor model will always have a higher R2 than the best four-predictor model. Therefore, R2 is most useful when comparing models of the same size. Adjusted R2 is a modified R2 that has been adjusted for the number of terms in the model. If you include unnecessary terms, R2 can be artificially high. Unlike R2 , adjusted R2 may get smaller when you add terms to the model. Use adjusted R2 to compare models with different numbers of predictors.
- 29. HYPOTHESIS TEST PROCEDURE AIG Confidential & Proprietary 29
- 30. HYPOTHESIS TEST PROCEDURE AIG Confidential & Proprietary 30
- 31. HYPOTHESIS TEST PROCEDURE AIG Confidential & Proprietary 31 Temp: Ho: There is no effect of Temp on Time Ha: There is effect of Temp on Time Here, P(temp)<0.05, reject null hypothesis. Catalyst: Ho: There is no effect of Catalyst on Time Ha: There is effect of Catalyst on Time Here, P(catalyst)<0.05, reject null hypothesis. Interaction: Ho: There is no effect of Interaction of temp and catalyst on Time Ha: There is effect of Interaction of temp and catalyst on Time Here P(interaction)>0.05, accept null hypothesis.
- 32. HYPOTHESIS TEST PROCEDURE AIG Confidential & Proprietary 32 3.0 Test for DYCX: 3.1 Binary Logistic Regression Binary logistic regression examines the relationship between one or more predictor variables and a binary response. A binary response variable has two possible outcomes, such as the presence or absence of a disease. Screenshot for the session window only
- 33. HYPOTHESIS TEST PROCEDURE AIG Confidential & Proprietary 33 Here P<0.05, you conclude that there is a significant relationship between the response and at least one of the predictor variables.
- 34. HYPOTHESIS TEST PROCEDURE AIG Confidential & Proprietary 34 4.0 DYDX 4.1 1 Proportion Test Question: A Poll is carried out to find the acceptability of new Cricket coach by the people. 2000 people participated and 482 people supported the new coach. It was decided that if the support rate is less than the bare minimum of 25%, counseling would be done with the coach. Conduct a test to check if the new coach is acceptable with 95% of confidence. Go to STATBASIC STATISTICS1-PROPORTION
- 35. HYPOTHESIS TEST PROCEDURE AIG Confidential & Proprietary 35
- 36. HYPOTHESIS TEST PROCEDURE AIG Confidential & Proprietary 36 Hypothesis: Ho (the null hypothesis): That the population proportion (p) is equal to the reference value Ha (the alternative hypothesis): That the population proportion is not equal to the reference value. Here in this example: Ho: p=0.25 Ha: p not equal to 0.25 As P value for the test is greater than the 0.05, hence accept Ho. 4.2 2 Proportion test: Used to compare two proportions of two different populations such as, % defectives from 2 machines, support rate for two political parties etc. This can be found by testing the difference of two proportions. When you use the two-proportions procedures, you are really trying to decide which of two opposing hypotheses seem to be true, based on your sample data: Ho (the null hypothesis): That the difference between population proportions is equal to the chosen reference value (usually zero) Ha (the alternative hypothesis): That the difference between population proportions is not equal to the chosen reference value. Question1 – On auditing Purchase department, 7 non conformities were found out of 155 check points and hen sales department was audited, 9 non conformities were found out of 200 check points. Find with 95% of confidence if the two proportions are different. Also calculate the confidence interval for difference in non conformities. Hypothesis Ho : p1=p2 Ha: p1 not equal to p2 Go to STATBASIC STATISTICS2-PROPORTIONS
- 37. HYPOTHESIS TEST PROCEDURE AIG Confidential & Proprietary 37
- 38. HYPOTHESIS TEST PROCEDURE AIG Confidential & Proprietary 38 Here in this case P>0.05, than accept Ho. 4.3 Chi Square Test:
- 39. HYPOTHESIS TEST PROCEDURE AIG Confidential & Proprietary 39
- 40. HYPOTHESIS TEST PROCEDURE AIG Confidential & Proprietary 40
- 41. HYPOTHESIS TEST PROCEDURE AIG Confidential & Proprietary 41 Hypothesis: Ho: the variables are not associated. Ha: the variables are associated. Use Chi-Square Test to determine the p-value. Use the p-value to decide whether the variables are associated or not: If the p-value is less than or equal to your chosen a-level then you can conclude that the variables are associated. If the p-value is greater than your chosen a-level then you cannot conclude that the variables are associated. Here, P>0.05, accept Ho.
- 42. HYPOTHESIS TEST PROCEDURE AIG Confidential & Proprietary 42
- 43. HYPOTHESIS TEST PROCEDURE AIG Confidential & Proprietary 43
- 44. HYPOTHESIS TEST PROCEDURE AIG Confidential & Proprietary 44 The chi-square goodness-of-fit test evaluates these hypotheses: Ho: Data follow a multinomial distribution with certain proportions Ha: Data do not follow a multinomial distribution with certain proportions
- 45. HYPOTHESIS TEST PROCEDURE AIG Confidential & Proprietary 45 NON PARAMETRIC TESTS 1-Sample Sign Test :
- 46. HYPOTHESIS TEST PROCEDURE AIG Confidential & Proprietary 46 1 Sign Test is very similar to the One T Test, just that instead of comparing sample mean to standard the 1 Sign test compares median of the sample to a standard. Ho- Median of sample equal to Standard. Ha- Median of sample not equal to standard Here we have taken the Standard of 40
- 47. HYPOTHESIS TEST PROCEDURE AIG Confidential & Proprietary 47 Mann Whitney: Assumptions: Samples are randomly drawn whose distributions have the same shape and whose variances are equal The two random samples are independent The Mann-Whitney test is a nonparametric alternative to the two-sample t test with pooled sample variances. Hypotheses: Ho (null hypothesis) - the two population medians are equal Ha (alternative hypothesis) - the two population medians are not equal.
- 48. HYPOTHESIS TEST PROCEDURE AIG Confidential & Proprietary 48
- 49. HYPOTHESIS TEST PROCEDURE AIG Confidential & Proprietary 49 Moods Median Test: We can use the Mood's median test (also called a median test or sign scores test) to make inferences about the equality of medians for two or more populations based on data from independent, random samples.
- 50. HYPOTHESIS TEST PROCEDURE AIG Confidential & Proprietary 50 Mood's median test is robust against outliers and errors in data and is particularly appropriate in the preliminary stages of analysis. Mood's median test is more robust than is the Kruskal-Wallis test against outliers, but is less powerful for data from many distributions, including the normal. Hypothesis: Ho: The median for all the samples are significantly equal Ha: Atleast one median is significantly different as compared with others. Here, P>0.05, Ho is accepted.
- 51. HYPOTHESIS TEST PROCEDURE AIG Confidential & Proprietary 51 Kruskal-Wallis Test The Kruskal-Wallis test is used to make inferences about the equality of medians for two or more populations based on data from independent, random samples.
- 52. HYPOTHESIS TEST PROCEDURE AIG Confidential & Proprietary 52
- 53. HYPOTHESIS TEST PROCEDURE AIG Confidential & Proprietary 53 N - Number of observations for each level of the factor. Overall - Total number of observations Median - Median of the observations for each level, which provides an estimate of the population medians for each level Ave Rank - Statistic that ranks the levels of data and is used to determine the Kruskal-Wallis statistic The hypotheses are: Ho: No difference exists in the populations medians Ha: A difference exists between at least two population medians Here, P<0.05, Hence reject Ho.

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