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• Solutions for Confidence Interval Exercises (last class):  x 95% 90% Problem 1: 4/7 (54.85, 57.14) (55.05, 56.95) (X bar =56, s=4, n = 49) Problem 2: 4/10 (55.2, 56.8) (55.33, 56.66) (X bar =56, s=4, n = 100)
• Look at book page 473: explain Type I/II error
• We do not deal with Goodness of fit!!
• Test whether grade and class are related: Ho: Grade and Class are not related Ha: Grade and Class are related Class Sum 1 2 A 10 (12) 8 (6) 18 (0.12) Grade B 20 (24) 16 (12) 36 (0.24) C 45 (42) 18 (21) 63 (0.42) D 16 (14.66) 6 (7.33) 22 (0.1466) E 9 (7.33) 2 (3.66) 11 (0.0733) Sum: 100 (0.666) 50 (0.333) 150  2 = (10-12) 2 /12 + (8-6) 2 /6 + (20-24) 2 /24 + (16-12) 2/ 12 + (45-42) 2 /42 + (18-21) 2 /21 + (16-14.66) 2 /14.66 + (6-7.33) 2 /7.33 + (9-7.33) 2 /7.33 + (2-3.66) 2 /3.66 = 0.333 + 0.666 + 0.666 + 1.333 + 0.214 + 0.428 + 0.121 + 0.2424 + 0.3787 + 0.752 = 5.136 df = (r-1)*(c-1) = 4*1 = 4  = 0.05 (significance level) Critical value (from table) = 9.49 Since 5.136 &lt; than CV: not reject
• Chi-Square = 14.201 df= 2 (r-1)*(c-1) = (2-1)*(3-1) = 2  = 0.05 CV = 5.991 Reject Ho of independence
• Talk about Z and t distribution
• Population case: therefore z-test Standard error of mean:  x =  /sqrt(n) = 250/10 = 25 z= (4960-5000) / 25 = -1.6 z  /2 = 1.96 if |z calc | &gt; z  /2 then reject Ho since |-1.6| &lt; 1.96 do not reject Ho.
• Softdrink manufacturer plans to introduce new soft drink. 12 supermarkets are selected at random and soft drink is offered in these supermarkets for limited time.Average existing softdrink sales are 1000, new softdrink sales are 1087.1 Sample &lt; 60 therefore t-test Standard error of mean: s x = s /sqrt(n) = 191.6/sqrt(12) = 55.31 t calc = (1087.1-1000) / 55.31 = 1.57 df = 12-1 = 11 t 11 ,  /2 = 3.106 if |t calc | &gt; t  /2 then reject Ho since |1.57| &lt; 3.106 do not reject Ho.
• One sided test Sample &lt; 30 therefore t-test Standard error of mean:  x =  /sqrt(n) = 191.6/sqrt(12) = 55.31 t calc = (1087.1-1000) / 55.31 = 1.57 df = 12-1 = 11 t 11 ,  /2 = 1.796 if t calc &gt; t  then reject Ho since 1.57 &lt; 1.796 do not reject Ho. Rejection rule for opposite directionality: if t calc &lt; -t  then reject Ho
• ### Mkt research

1. 1. Essentials of Marketing Research Kumar, Aaker, Day Instructor’s Presentation Slides Essentials of Marketing Research Kumar, Aaker, Day
2. 2. Chapter Fourteen Fundamentals of Data AnalysisEssentials of Marketing Research Kumar, Aaker, Day
3. 3. Fundamentals of Data Analysis Essentials of Marketing Research Kumar, Aaker, Day
4. 4. Data Analysis3 A set of methods and techniques used to obtain information and insights from data3 Helps avoid erroneous judgements and conclusions3 Can constructively influence the research objectives and the research design Essentials of Marketing Research Kumar, Aaker, Day
5. 5. Preparing the Data for Analysis3 Data editing3 Coding3 Statistically adjusting the data Essentials of Marketing Research Kumar, Aaker, Day
6. 6. Preparing the Data for Analysis (Contd.) Data Editing3 Identifies omissions, ambiguities, and errors in responses3 Conducted in the field by interviewer and field supervisor and by the analyst prior to data analysis Essentials of Marketing Research Kumar, Aaker, Day
7. 7. Preparing the Data for Analysis (Contd.) Problems Identified With Data Editing3 Interviewer Error3 Omissions3 Ambiguity3 Inconsistencies3 Lack of Cooperation3 Ineligible Respondent Essentials of Marketing Research Kumar, Aaker, Day
8. 8. Preparing the Data for Analysis (Contd.) Coding3 Coding closed-ended questions involves specifying how the responses are to be entered3 Open-ended questions are difficult to code x Lengthy list of possible responses is generated Essentials of Marketing Research Kumar, Aaker, Day
9. 9. Preparing the Data for Analysis (Contd.) Statistically Adjusting the Data + Weighting3 Each response is assigned a number according to a pre-specified rule3 Makes sample data more representative of target population on specific characteristics3 Modifies number of cases in the sample that possess certain characteristics3 Adjusts the sample so that greater importance is attached to of Marketing Research with certain characteristics Essentials respondents Kumar, Aaker, Day
10. 10. Preparing the Data for Analysis (Contd.) Statistically Adjusting the Data + Variable Re-specification3 Existing data is modified to create new variables3 Large number of variables collapsed into fewer variables3 Creates variables that are consistent with study objectives3 Dummy variables are used (binary, dichotomous, instrumental, quantitative variables)3 Use (d-1) dummy Research Essentials of Marketing variables to specify (d) levels of Kumar, Aaker, Day
11. 11. Preparing the Data for Analysis (Contd.) Statistically Adjusting the Data + Scale Transformation3 Scale values are manipulated to ensure comparability with other scales3 Standardization allows the researcher to compare variables that have been measured using different types of scales3 Variables are forced to have a mean of zero and a standard deviation of one3 Can be done Marketing on interval or ratioAaker, Day data Essentials of only Research Kumar, scaled
12. 12. Simple Tabulation3 Consists of counting the number of cases that fall into various categories Use of Simple Tabulation3 Determine empirical distribution (frequency distribution) of the variable in question3 Calculate summary statistics, particularly the mean or percentages3 Aid in "data cleaning" aspects Essentials of Marketing Research Kumar, Aaker, Day
13. 13. Frequency Distribution3 Reports the number of responses that each question received3 Organizes data into classes or groups of values3 Shows number of observations that fall into each class3 Can be illustrated simply as a number or as a percentage or histogram3 Response categories may be combined for many questions3 Should result inResearch Essentials of Marketing categories Kumar, Aaker,worthwhile with Day
14. 14. Descriptive Statistics3 Statistics normally associated with a frequency distribution to help summarize information in the frequency table3 Measures of central tendency mean, median and mode3 Measures of dispersion (range, standard deviation, and coefficient of variation)3 Measures of shape (skewness and kurtosis) Essentials of Marketing Research Kumar, Aaker, Day
15. 15. Analysis for Various Population Subgroups3 Differences between means or percentages of two subgroup responses can provide insights3 Difference between means is concerned with the association between two questions3 Question upon which means are based are intervally scaled Essentials of Marketing Research Kumar, Aaker, Day
16. 16. Cross Tabulations3 Statistical analysis technique to study the relationships among and between variables3 Sample is divided to learn how the dependent variable varies from subgroup to subgroup3 Frequency distribution for each subgroup is compared to the frequency distribution for the total sample3 The two variables that are analyzed must be Essentials of Marketing Research Kumar, Aaker, Day
17. 17. Factors Influencing the Choice of Statistical Technique Type of Data x Classification of data involves nominal, ordinal, interval and ratio scales of measurement x Nominal scaling is restricted to the mode as the only measure of central tendency x Both median and mode can be used for ordinal scale x Non-parametric tests can only be run on ordinal data x Mean, median and mode can all be used to measure central tendency for interval and ratio scaled data Essentials of Marketing Research Kumar, Aaker, Day
18. 18. Factors Influencing the Choice of Statistical Technique (Contd.) Research Design x Dependency of observations x Number of observations per object x Number of groups being analyzed x Control exercised over variable of interest Assumptions Underlying the Test Statistic x If assumptions on which a statistical test is based are violated, the test will provide meaningless results Essentials of Marketing Research Kumar, Aaker, Day
19. 19. Overview of Statistical TechniquesUnivariate Techniques x Appropriate when there is a single measurement of each of the n sample objects or there are several measurements of each of the `n observations but each variable is analyzed in isolation x Nonmetric - measured on nominal or ordinal scale x Metric-measured on interval or ratio scale x Determine whether single or multiple samples are involved x For multiple samples, choice of statistical test depends on whether the samples are independent or dependent Essentials of Marketing Research Kumar, Aaker, Day
20. 20. Overview of Statistical Techniques (Contd.) Multivariate Techniques3 A collection of procedures for analyzing association between two or more sets of measurements that have been made on each object in one or more samples of objects3 Dependence or interdependence techniques Essentials of Marketing Research Kumar, Aaker, Day
21. 21. Overview of Statistical Techniques (Contd.) Multivariate Techniques (Contd.) Dependence Techniques3 One or more variables can be identified as dependent variables and the remaining as independent variables3 Choice of dependence technique depends on the number of dependent variables involved in analysis Essentials of Marketing Research Kumar, Aaker, Day
22. 22. Overview of Statistical Techniques (Contd.) Multivariate Techniques (Contd.) Interdependence Techniques3 Whole set of interdependent relationships is examined3 Further classified as having focus on variable or objects Essentials of Marketing Research Kumar, Aaker, Day
23. 23. Overview of Statistical Techniques (Contd.) Why Use Multivariate Analysis?3 To group variables or people or objects3 To improve the ability to predict variables (such as usage)3 To understand relationships between variables (such as advertising and sales) Essentials of Marketing Research Kumar, Aaker, Day
24. 24. Hypothesis Testing: Basic Concepts3 Assumption (hypothesis) made about a population parameter (not sample parameter)3 Purpose of Hypothesis Testing x To make a judgement about the difference between two sample statistics or the sample statistic and a hypothesized population parameter3 Evidence has to be evaluated statistically before arriving at a conclusion regarding the hypothesis. Essentials of Marketing Research Kumar, Aaker, Day
25. 25. Hypothesis Testing3 The null hypothesis (Ho) is tested against the alternative hypothesis (Ha).3 At least the null hypothesis is stated.3 Decide upon the criteria to be used in making the decision whether to “reject” or "not reject" the null hypothesis. Essentials of Marketing Research Kumar, Aaker, Day
26. 26. Significance Level3 Indicates the percentage of sample means that is outside the cut-off limits (critical value)3 The higher the significance level (α) used for testing a hypothesis, the higher the probability of rejecting a null hypothesis when it is true (Type I error)3 Accepting a null hypothesis when it is false is called a Type II error and its probability is (β) Essentials of Marketing Research Kumar, Aaker, Day
27. 27. Hypothesis TestingTests in this class Statistical Test3 Frequency Distributions χ23 Means (one) z (if σ is known) t (if σ is unknown)3 Means (two or more) ANOVA Essentials of Marketing Research Kumar, Aaker, Day
28. 28. Cross-tabulation and Chi SquareIn Marketing Applications, Chi-square Statistic Is Used As Test of Independence3 Are there associations between two or more variables in a study? Test of Goodness of Fit3 Is there a significant difference between an observed frequency distribution and a theoretical frequency distribution? Essentials of Marketing Research Kumar, Aaker, Day
29. 29. Chi-Square As a Test of IndependenceNull Hypothesis Ho3 Two (nominally scaled) variables are statistically independentAlternative Hypothesis Ha3 The two variables are not independent Use Chi-square distribution to test. Essentials of Marketing Research Kumar, Aaker, Day
30. 30. Chi-square Statistic (χ ) 23 Measures of the difference between the actual numbers observed in cell i (Oi), and number expected (Ei) under independence if the null hypothesis were true (Oi − Ei ) n 2 χ =Σ2 i =1 Ei With (r-1)*(c-1) degrees of freedom r = number of rows c = number of columns3 Expected frequency in each cell: Ei = pc * pr * n Where pc and pr are proportions for independent variables and n is the total number of observations Essentials of Marketing Research Kumar, Aaker, Day
31. 31. Chi-square Step-by-Step1) Formulate Hypotheses2) Calculate row and column totals3) Calculate row and column proportions4) Calculate expected frequencies (Ei)5) Calculate χ2 statistic6) Calculate degrees of freedom7) Obtain Critical Value from table8) Make decision regarding the Null-hypothesis Essentials of Marketing Research Kumar, Aaker, Day
32. 32. Example of Chi-square as a Test of Independence Class 1 2 A 10 8Grade B 20 16 C 45 18 This is a ‘Cell’ D 16 6 E 9 2 Essentials of Marketing Research Kumar, Aaker, Day
33. 33. Chi-square As a Test of Independence - ExerciseOwn IncomeExpensive Low Middle HighAutomobileYes 45 34 55No 52 53 27Task: Make a decision whether the two variables are independent! Essentials of Marketing Research Kumar, Aaker, Day
34. 34. Hypothesis Testing About a Single Mean3 Make judgement about a single sample parameter.3 Hypothesis testing depends on whether the population is known on not known ( X − µ) ( X − µ) z= t= σx sx if population variance if population variance is known is not known, or if sample size < 60 Essentials of Marketing Research Kumar, Aaker, Day
35. 35. Hypothesis Testing About a Single Mean - Step-by-Step1) Formulate Hypotheses2) Select appropriate formula3) Select significance level4) Calculate z or t statistic5) Calculate degrees of freedom (for t-test)6) Obtain critical value from table7) Make decision regarding the Null- hypothesis Essentials of Marketing Research Kumar, Aaker, Day
36. 36. Hypothesis Testing About a Single Mean - Example 13 Ho: µ = 5000 (hypothesized value of population)3 Ha: µ ≠ 5000 (alternative hypothesis)3 n = 1003 X = 49603 σ = 2503 α = 0.05Rejection rule: if |zcalc| > zα/2 then reject Ho. Essentials of Marketing Research Kumar, Aaker, Day
37. 37. Hypothesis Testing About a Single Mean - Example 23 Ho: µ = 1000 (hypothesized value of population)3 Ha: µ ≠ 1000 (alternative hypothesis)3 n = 123 X = 1087.13 s = 191.63 α = 0.01Rejection rule: if |tcalc| > tdf, α/2 then reject Ho. Essentials of Marketing Research Kumar, Aaker, Day
38. 38. Hypothesis Testing About a Single Mean - Example 33 Ho: µ ≤ 1000 (hypothesized value of population)3 Ha: µ > 1000 (alternative hypothesis)3 n = 123 X = 1087.13 s = 191.63 α = 0.05Rejection rule: if tcalc > tdf, α then reject Ho. Essentials of Marketing Research Kumar, Aaker, Day
39. 39. Confidence Intervals3 Hypothesis testing and Confidence Intervals are two sides of the same coin. ( X − µ) t= ⇒ X ± ts x = interval sx estimate of µ Essentials of Marketing Research Kumar, Aaker, Day
40. 40. Analysis of Variance (ANOVA)3 Response variable - dependent variable (Y)3 Factor(s) - independent variables (X)3 Treatments - different levels of factors (r1, r2, r3, …) Essentials of Marketing Research Kumar, Aaker, Day
41. 41. Example (Book p.495) Product Sales 1 2 3 4 5 Total Xp 39¢ 8 12 10 9 11 50 10PriceLevel 44 ¢ 7 10 6 8 9 40 8 49 ¢ 4 8 7 9 7 35 7Overall sample mean: X = 8.333Overall sample size: n = 15No. of observations per price level: np = 5 Essentials of Marketing Research Kumar, Aaker, Day
42. 42. Example (Book p.495) Grand MeanEssentials of Marketing Research Kumar, Aaker, Day
43. 43. One - Factor Analysis of Variance3 Studies the effect of r treatments on one response variable3 Determine whether or not there are any statistically significant differences between the treatment means µ1, µ2,... µR3 Ho: All treatments have same effect on mean responses3 H1 : At least 2 of µ1, µ2 ... µr are different Essentials of Marketing Research Kumar, Aaker, Day
44. 44. One - Factor ANOVA - IntuitivelyIf: Between Treatment Variance Within Treatment VarianceWis large then there are differences between treatmentsi is small then there are no differences between treatments3 To Test Hypothesis, Compute the Ratio Between the "Between Treatment" Variance and "Within Treatment" Variance Essentials of Marketing Research Kumar, Aaker, Day
45. 45. One - Factor ANOVA TableSource of Variation Degrees of Mean Sum F-ratioVariation (SS) Freedom of SquaresBetween SSr r-1 MSSr =SSr/r-1 MSSr(price levels) MSSuWithin SSu n-r MSSu=SSu/n-r(price levels)Total SSt n-1 Essentials of Marketing Research Kumar, Aaker, Day
46. 46. One - Factor Analysis of Variance3 Between Treatment Variance r ΣSSr = p=1 np (Xp - X)2 = 23.3 n r3 Within-treatment variance p i=1 p=1SSu = Σ Σ (Xip - Xp)2 = 34WhereSSr = treatment sums of squares r = number of groups size of group ‘p’np = sampleEssentialsin Marketing Research X = meanAaker,group p Kumar, of Day
47. 47. One - Factor Analysis of Variance3 Between variance estimate (MSSr) MSSr = SSr/(r-1) = 23.3/2 = 11.653 Within variance estimate (MSSu) MSSu = SSu/(n-r) = 34/12 = 2.8Wheren = total sample size Research Essentials of Marketing r = Kumar, Aaker, of groups number Day
48. 48. One - Factor Analysis of Variance3 Total variation (SSt): SSt = SSr + SSu = 23.3+34 = 57.33 F-statistic: F = MSSr / MSSu = 11.65/2.8 = 4.163 DF: (r-1), (n-r) = 2, 123 Critical value from table: CV(α, df) = 3.89 Essentials of Marketing Research Kumar, Aaker, Day