Marketing Research  Hypothesis Testing  Hamendra Dangi  [email_address]   9968316938 H  Dangi, FMS
Question  <ul><li>The mean life of sample of 400 fluorescent light bulb produced by a company is found to be 1600 hours wi...
<ul><li>Z= 30/7.5 = 4 </li></ul><ul><li>CV = 1570+2.337x7.5= 1587 </li></ul><ul><li>Since Sample mean > CV null hypotheses...
Question for Discussion  <ul><li>A researcher team tested new battery to see if they lasted significantly lower than compa...
<ul><li>A fertilizer mixing machine is set to give 12 Kg of nitrate for every 100 kg of fertilizer . Ten bags of 100 kg ea...
SPSS Example  H  Dangi, FMS
Nonparametric Tests <ul><li>Nonparametric tests  are used when the independent variables are nonmetric.  Like parametric t...
Question  <ul><li>A Mall  Manager is interested in trying to determine whether footfall  is greater on one day of week on ...
H  Dangi, FMS  Day  O E (o-E)2  (o-E)2/E M 66 60 36 0.60 T 57 60 9 0.15 W 54 60 36 0.60 Th  48 60 144 2.40 F 75 60 225 3.75
<ul><li>Two hundred randomly selected adults were asked whether TV shows as a whole are primarily entertaining,Eduacation ...
H  Dangi, FMS  Gender  Entertaining  Education  Wastage  Total  Female  52 28 30 110 Male  28 12 50 90 Total  80 40 80 200
H  Dangi, FMS  S.No  O E (o-E)2  (o-E)2/E 1 52 44 64 1.454 2 28 22 36 1.636 3 30 44 196 4.455 4 28 36 64 1.777 5 12 18 36 ...
SPSS Example  H  Dangi, FMS
Relationship Among Techniques <ul><li>Analysis of variance (ANOVA)  is used as a test of means for two or more populations...
Relationship Amongst Test, Analysis of Variance, Analysis of Covariance, & Regression H  Dangi, FMS  One Independent One o...
Question for Discussion  <ul><li>Identify appropriate test in the following cases  </li></ul><ul><li>A comparison of mean ...
Effect of Promotion and Clientele on Sales H  Dangi, FMS
Illustrative Applications of One-Way Analysis of Variance <ul><li>EFFECT OF IN-STORE PROMOTION ON SALES </li></ul><ul><li>...
<ul><li>To test the null hypothesis, the various sums of squares are computed as follows: </li></ul><ul><li>  </li></ul><u...
<ul><li>SSx = 10(8.3-6.067) 2  + 10(6.2-6.067) 2  + 10(3.7-6.067) 2 </li></ul><ul><li>= 10(2.233) 2  + 10(0.133) 2  + 10(-...
<ul><li>It can be verified that </li></ul><ul><li>SSy  =  SSx  +  SSerror </li></ul><ul><li>as follows: </li></ul><ul><li>...
<ul><li>From in the Statistical Appendix we see that for 2 and 27 degrees of freedom, the critical value of  F  is 3.35 fo...
One-Way ANOVA: Effect of In-store Promotion on Store Sales H  Dangi, FMS  Cell means Level of   Count Mean Promotion High ...
CLASS ACTIVITY  H  Dangi, FMS
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Mrpt ms10

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Mrpt ms10

  1. 1. Marketing Research Hypothesis Testing Hamendra Dangi [email_address] 9968316938 H Dangi, FMS
  2. 2. Question <ul><li>The mean life of sample of 400 fluorescent light bulb produced by a company is found to be 1600 hours with a S.D of 150 hrs .Test the hypotheses mean life of bulb in general is higher than mean life of 1570 hours at 0.01 level of significance </li></ul>H Dangi, FMS
  3. 3. <ul><li>Z= 30/7.5 = 4 </li></ul><ul><li>CV = 1570+2.337x7.5= 1587 </li></ul><ul><li>Since Sample mean > CV null hypotheses rejected </li></ul>H Dangi, FMS
  4. 4. Question for Discussion <ul><li>A researcher team tested new battery to see if they lasted significantly lower than company's existing battery,tradionally , all experiment have been run on alpha=0.05 .After testing 100 new and 100 old battery ,the mean life of new battery was found to be greater than that of old at alpha =0.05. However a new analyst become greatly excited when it was discussed that difference was significant at alpha =0.01. He commented “This product is much better than we thought , the difference is highly significant </li></ul><ul><li>Is this a correct interpretation of result? </li></ul>H Dangi, FMS
  5. 5. <ul><li>A fertilizer mixing machine is set to give 12 Kg of nitrate for every 100 kg of fertilizer . Ten bags of 100 kg each are examined .The percentage of nitrate so obtained is </li></ul><ul><li>11, 14,13,12,13,,12,13,14,11 and 12 </li></ul><ul><li>Is there any reason to believe that machine is defective </li></ul>H Dangi, FMS
  6. 6. SPSS Example H Dangi, FMS
  7. 7. Nonparametric Tests <ul><li>Nonparametric tests are used when the independent variables are nonmetric. Like parametric tests, nonparametric tests are available for testing variables from one sample, two independent samples, or two related samples. </li></ul>H Dangi, FMS
  8. 8. Question <ul><li>A Mall Manager is interested in trying to determine whether footfall is greater on one day of week on another .His record for the past year show the following sampling distribution </li></ul><ul><li>Day of Week M T W Th F </li></ul><ul><li>No of footfall 66 56 54 48 75 </li></ul><ul><li>Test whether the footfall is uniformly distributed over the week </li></ul><ul><li>Table value =9.49 </li></ul>H Dangi, FMS
  9. 9. H Dangi, FMS Day O E (o-E)2 (o-E)2/E M 66 60 36 0.60 T 57 60 9 0.15 W 54 60 36 0.60 Th 48 60 144 2.40 F 75 60 225 3.75
  10. 10. <ul><li>Two hundred randomly selected adults were asked whether TV shows as a whole are primarily entertaining,Eduacation or Wastage of time ( only one answer chosen ) The respondents were categorized by gender ,There responses are summarized </li></ul><ul><li>( Table Value 5.966) </li></ul>H Dangi, FMS
  11. 11. H Dangi, FMS Gender Entertaining Education Wastage Total Female 52 28 30 110 Male 28 12 50 90 Total 80 40 80 200
  12. 12. H Dangi, FMS S.No O E (o-E)2 (o-E)2/E 1 52 44 64 1.454 2 28 22 36 1.636 3 30 44 196 4.455 4 28 36 64 1.777 5 12 18 36 2.000 6 50 36 196 5.444
  13. 13. SPSS Example H Dangi, FMS
  14. 14. Relationship Among Techniques <ul><li>Analysis of variance (ANOVA) is used as a test of means for two or more populations. The null hypothesis, typically, is that all means are equal. </li></ul><ul><li>Analysis of variance must have a dependent variable that is metric (measured using an interval or ratio scale). </li></ul><ul><li>There must also be one or more independent variables that are all categorical (nonmetric). Categorical independent variables are also called factors . </li></ul>H Dangi, FMS
  15. 15. Relationship Amongst Test, Analysis of Variance, Analysis of Covariance, & Regression H Dangi, FMS One Independent One or More Metric Dependent Variable t Test Binary Variable One-Way Analysis of Variance One Factor N-Way Analysis of Variance More than One Factor Analysis of Variance Categorical: Factorial Analysis of Covariance Categorical and Interval Regression Interval Independent Variables
  16. 16. Question for Discussion <ul><li>Identify appropriate test in the following cases </li></ul><ul><li>A comparison of mean salary of IIT and IIM grads </li></ul><ul><li>A study involving age and drinking habits </li></ul><ul><li>A comparative study performance of commerce , Engineering and Others grads in Semester Exam </li></ul><ul><li>Mobile uses in three age group with disposable income </li></ul>H Dangi, FMS
  17. 17. Effect of Promotion and Clientele on Sales H Dangi, FMS
  18. 18. Illustrative Applications of One-Way Analysis of Variance <ul><li>EFFECT OF IN-STORE PROMOTION ON SALES </li></ul><ul><li>Store Level of In-store Promotion </li></ul><ul><li>No. High Medium Low </li></ul><ul><li>Normalized Sales </li></ul><ul><li>1 10 8 5 </li></ul><ul><li>2 9 8 7 </li></ul><ul><li>3 10 7 6 </li></ul><ul><li>4 8 9 4 </li></ul><ul><li>5 9 6 5 </li></ul><ul><li>6 8 4 2 </li></ul><ul><li>7 9 5 3 </li></ul><ul><li>8 7 5 2 </li></ul><ul><li>9 7 6 1 </li></ul><ul><li>10 6 4 2 </li></ul><ul><li>  </li></ul><ul><li>Column Totals 83 62 37 </li></ul><ul><li>Category means: j 83/10 62/10 37/10 </li></ul><ul><li> = 8.3 = 6.2 = 3.7 </li></ul><ul><li>Grand mean, = (83 + 62 + 37)/30 = 6.067 </li></ul>H Dangi, FMS Y Y
  19. 19. <ul><li>To test the null hypothesis, the various sums of squares are computed as follows: </li></ul><ul><li>  </li></ul><ul><li>SSy = (10-6.067) 2 + (9-6.067) 2 + (10-6.067) 2 + (8-6.067) 2 + (9-6.067) 2 </li></ul><ul><li>+ (8-6.067) 2 + (9-6.067) 2 + (7-6.067) 2 + (7-6.067) 2 + (6-6.067) 2 </li></ul><ul><li>+ (8-6.067) 2 + (8-6.067) 2 + (7-6.067) 2 + (9-6.067) 2 + (6-6.067) 2 </li></ul><ul><li>(4-6.067) 2 + (5-6.067) 2 + (5-6.067) 2 + (6-6.067) 2 + (4-6.067) 2 </li></ul><ul><li>+ (5-6.067) 2 + (7-6.067) 2 + (6-6.067) 2 + (4-6.067) 2 + (5-6.067) 2 </li></ul><ul><li>+ (2-6.067) 2 + (3-6.067) 2 + (2-6.067) 2 + (1-6.067) 2 + (2-6.067) 2 </li></ul><ul><li>=(3.933) 2 + (2.933) 2 + (3.933) 2 + (1.933) 2 + (2.933) 2 </li></ul><ul><li>+ (1.933) 2 + (2.933) 2 + (0.933) 2 + (0.933) 2 + (-0.067) 2 </li></ul><ul><li>+ (1.933) 2 + (1.933) 2 + (0.933) 2 + (2.933) 2 + (-0.067) 2 </li></ul><ul><li>(-2.067) 2 + (-1.067) 2 + (-1.067) 2 + (-0.067) 2 + (-2.067) 2 </li></ul><ul><li>+ (-1.067) 2 + (0.9333) 2 + (-0.067) 2 + (-2.067) 2 + (-1.067) 2 </li></ul><ul><li>+ (-4.067) 2 + (-3.067) 2 + (-4.067) 2 + (-5.067) 2 + (-4.067) 2 </li></ul><ul><li>= 185.867 </li></ul>Illustrative Applications of One-Way Analysis of Variance H Dangi, FMS
  20. 20. <ul><li>SSx = 10(8.3-6.067) 2 + 10(6.2-6.067) 2 + 10(3.7-6.067) 2 </li></ul><ul><li>= 10(2.233) 2 + 10(0.133) 2 + 10(-2.367) 2 </li></ul><ul><li>= 106.067 </li></ul><ul><li>  </li></ul><ul><li>SSerror = (10-8.3) 2 + (9-8.3) 2 + (10-8.3)2 + (8-8.3)2 + (9-8.3)2 </li></ul><ul><li>+ (8-8.3) 2 + (9-8.3)2 + (7-8.3)2 + (7-8.3)2 + (6-8.3)2 </li></ul><ul><li>+ (8-6.2) 2 + (8-6.2)2 + (7-6.2)2 + (9-6.2)2 + (6-6.2)2 </li></ul><ul><li>+ (4-6.2) 2 + (5-6.2)2 + (5-6.2)2 + (6-6.2)2 + (4-6.2)2 </li></ul><ul><li>+ (5-3.7) 2 + (7-3.7)2 + (6-3.7)2 + (4-3.7)2 + (5-3.7)2 </li></ul><ul><li>+ (2-3.7) 2 + (3-3.7)2 + (2-3.7)2 + (1-3.7)2 + (2-3.7)2 </li></ul><ul><li>  </li></ul><ul><li>= (1.7) 2 + (0.7) 2 + (1.7) 2 + (-0.3) 2 + (0.7) 2 </li></ul><ul><li>+ (-0.3) 2 + (0.7) 2 + (-1.3) 2 + (-1.3) 2 + (-2.3) 2 </li></ul><ul><li>+ (1.8) 2 + (1.8) 2 + (0.8) 2 + (2.8) 2 + (-0.2) 2 </li></ul><ul><li>+ (-2.2) 2 + (-1.2) 2 + (-1.2) 2 + (-0.2) 2 + (-2.2) 2 </li></ul><ul><li>+ (1.3) 2 + (3.3) 2 + (2.3) 2 + (0.3) 2 + (1.3) 2 </li></ul><ul><li>+ (-1.7) 2 + (-0.7) 2 + (-1.7) 2 + (-2.7) 2 + (-1.7) 2 </li></ul><ul><li>  = 79.80 </li></ul>Illustrative Applications of One-Way Analysis of Variance H Dangi, FMS
  21. 21. <ul><li>It can be verified that </li></ul><ul><li>SSy = SSx + SSerror </li></ul><ul><li>as follows: </li></ul><ul><li>185.867 = 106.067 +79.80 </li></ul><ul><li>The strength of the effects of X on Y are measured as follows: </li></ul><ul><li>2 = SSx / SSy </li></ul><ul><li>= 106.067/185.867 </li></ul><ul><li>= 0.571 </li></ul><ul><li>  In other words, 57.1% of the variation in sales (Y) is accounted for by in-store promotion (X), indicating a modest effect. The null hypothesis may now be tested. </li></ul><ul><li>  </li></ul><ul><li>  </li></ul><ul><li>  </li></ul><ul><li>= 17.944 </li></ul>Illustrative Applications of One-Way Analysis of Variance H Dangi, FMS  F = S S x / ( c - 1 ) S S e r r o r / ( N - c ) = M S X M S e r r o r F = 106.067/(3-1) 79.800/(30-3)
  22. 22. <ul><li>From in the Statistical Appendix we see that for 2 and 27 degrees of freedom, the critical value of F is 3.35 for . Because the calculated value of F is greater than the critical value, we reject the null hypothesis. </li></ul><ul><li>We now illustrate the analysis of variance procedure using a computer program. The results of conducting the same analysis by computer are presented in Table 16.4. </li></ul>Illustrative Applications of One-Way Analysis of Variance H Dangi, FMS   = 0.05
  23. 23. One-Way ANOVA: Effect of In-store Promotion on Store Sales H Dangi, FMS Cell means Level of Count Mean Promotion High (1) 10 8.300 Medium (2) 10 6.200 Low (3) 10 3.700 TOTAL 30 6.067 Source of Sum of d f Mean F ratio F prob. Variation squares square Between groups 106.067 2 53.033 17.944 0.000 (Promotion) Within groups 79.800 27 2.956 (Error) TOTAL 185.867 29 6.409
  24. 24. CLASS ACTIVITY H Dangi, FMS

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