1. 1995 7888 4320 000 000001 00023 Copyright © 2003 by The McGraw-Hill Companies, Inc. All rights reserved.

2. 1995 7888 4320 000 000001 00023 Copyright © 2003 by The McGraw-Hill Companies, Inc. All rights reserved. CHAPTERCHAPTERCHAPTERCHAPTER 1234 0001 897251 00000 16 Data Analysis: Testing for Significant Differences 16-2

3. 1995 7888 4320 000 000001 00023 Copyright © 2003 by The McGraw-Hill Companies, Inc. All rights reserved. The Value of Testing for Differences in Data  Basic statistical techniques bring “structure” to the raw data which has been captured by the research team.  Every data set needs to be summarized to discern what the entire set of responses mean.  The output from statistical analysis can be displayed graphically, adding a fresh perspective to a decision-maker’s understanding of an information problem, or market opportunity. 16-3

4. 1995 7888 4320 000 000001 00023 Copyright © 2003 by The McGraw-Hill Companies, Inc. All rights reserved. SPSS Applications Database Easy-to-use software like SPSS for Windows has changed the way statistics is being taught and learned:  Class participants no longer have to learn a system of elaborate code to conduct data analysis.  Data is entered, items are chosen from pull-down menus, and options can be “clicked” to create graphs and perform simple or complex analyses.  Generally, SPSS for Windows has improved the quality of life for: 1.Research Teams applying statistics. 2.Teachers teaching statistics. 3.Students learning statistics. 16-4

5. 1995 7888 4320 000 000001 00023 Copyright © 2003 by The McGraw-Hill Companies, Inc. All rights reserved. Bar Charts: An Example 16-5 100 80 60 40 20 0 123456 Importance Frequency

6. 1995 7888 4320 000 000001 00023 Copyright © 2003 by The McGraw-Hill Companies, Inc. All rights reserved. Line Charts: An Example 16-6 12 3 4 5 6 100 80 60 40 20 0

7. 1995 7888 4320 000 000001 00023 Copyright © 2003 by The McGraw-Hill Companies, Inc. All rights reserved. Pie Charts: An Example 16-7 19.7%26.3% 23.4% 17.1% 6.6%

8. 1995 7888 4320 000 000001 00023 Copyright © 2003 by The McGraw-Hill Companies, Inc. All rights reserved. Statistical Analysis Techniques  Descriptive Statistics: Used by researchers to summarize sample data.  Univariate Statistics: Used when a researcher investigates one variable at a time.  Bivariate Statistics: Used when a researcher investigates two variables at a time.  Multivariate Statistics: In a broad sense, multivariate statistics refer to any simultaneous analysis of more than two variables.

9. 1995 7888 4320 000 000001 00023 Copyright © 2003 by The McGraw-Hill Companies, Inc. All rights reserved. Descriptive Statistics  This type of statistics describes sample data and often leads to subsequent analyses.  What is the average income of the sample?  How old is the average employee in Company X?  How different are the employees’ ages in Company X?  How spread out is the income data that have been drawn as a sample of the population?

10. 1995 7888 4320 000 000001 00023 Copyright © 2003 by The McGraw-Hill Companies, Inc. All rights reserved. Descriptive Statistics – cont’d  Three Groups  Central Tendency of the Variable  Mean  Median  Mode  Dispersion  Range  Variation (or Standard Deviation)  Coefficient of Variation  Shape of the Distribution  Skewness  Kurtosis

11. 1995 7888 4320 000 000001 00023 Copyright © 2003 by The McGraw-Hill Companies, Inc. All rights reserved. Measures of Central Tendency  Average: Single value that is typical or representative of a group of numbers.  An average is frequently referred to as a measure of central tendency. The most common known measures of central tendency are the mean, median, and mode. A measure of central tendency describes the center of a distribution.

12. 1995 7888 4320 000 000001 00023 Copyright © 2003 by The McGraw-Hill Companies, Inc. All rights reserved.  Mean: Most commonly used measure of central tendency. The sum of the values in a data set divided by the number of values in the set.  The computation of the mean is based on all values of a set of data.  Median: Value of the middle item when the numbers are arranged in order of magnitude.  A positional average  Not defined algebraically as is the mean  In some cases, cannot be computed exactly as can the mean  Is centrally located Measures of Central Tendency – cont’d

13. 1995 7888 4320 000 000001 00023 Copyright © 2003 by The McGraw-Hill Companies, Inc. All rights reserved.  Mode: The value that occurs most frequently in the set. When there are two or more modes in a set of data, the data are called bimodal or multimodal.  The value with the highest frequency in the set of values.  By definition, is not affected by extreme values.  Is easy to compute with a set of discrete data.  The value of the mode may be greatly affected by the method of designating the class intervals. Measures of Central Tendency – cont’d

14. 1995 7888 4320 000 000001 00023 Copyright © 2003 by The McGraw-Hill Companies, Inc. All rights reserved. Frequency Distribution  Raw Data: The collected data which have not been organized numerically.  Frequency: The number of times a value is repeated.  Frequency Distribution: A distribution of data that summarizes the number of times a certain value of a variable occurs and is expressed in terms of percentage.

15. 1995 7888 4320 000 000001 00023 Copyright © 2003 by The McGraw-Hill Companies, Inc. All rights reserved. Measures of Shapes of Frequency Distributions  In addition to the averages and dispersions, two other measures are used in describing the characteristics of a group of data. These measures are skewness and kurtosis.  Measure of Skewness  Skewness: Indicates the direction of an asymmetrical distribution, either leaning toward higher values or lower values.  Kurtosis: Indicates the relative peakedness according to the frequency distribution.

16. 1995 7888 4320 000 000001 00023 Copyright © 2003 by The McGraw-Hill Companies, Inc. All rights reserved. Figure 16.5 Skewness of a Distribution

17. 1995 7888 4320 000 000001 00023 Copyright © 2003 by The McGraw-Hill Companies, Inc. All rights reserved. Measures of Central Tendency I.The Mean is the arithmetical average of the sample. For example, 5.5 is the mean of the following sample: (1,2,3,4,5,6,7,8,9,10) II.The Median is the middle value of a rank- ordered distribution: For example, 5.5. is the median of the following sample: (1,2,3,4,5,6,7,8,9,10) III.The Mode is the most frequently mentioned response, or number in a data set. There isn’t a mode in the following sample: (1,2,3,4,5,6,7,8,9,10) 16-8

18. 1995 7888 4320 000 000001 00023 Copyright © 2003 by The McGraw-Hill Companies, Inc. All rights reserved. Measures of Dispersion  The Range is the distance between the biggest and smallest values in a data set. For example, 9 is the range for the following data set: (1,2,3,4,5,6,7,8,9,10)  The Variance is the average squared deviation about the mean of a distribution of values. What is the variance for the data set listed above?  The Standard Deviation is the average distance of the distribution values from the mean. What is the standard deviation for the data set listed above? 16-9

19. 1995 7888 4320 000 000001 00023 Copyright © 2003 by The McGraw-Hill Companies, Inc. All rights reserved. What are Univariate Statistics?  Univariate Statistics: Statistics used when a researcher investigates only one variable at a time. More specifically, this type of statistics is used when only one measurement of each element in the sample is taken, or multiple measurements of each element are taken but each variable is analyzed independently.  Univariate statistical techniques can be further broken down according to whether the data is nominal, ordinal, interval, or ratio scaled.

20. 1995 7888 4320 000 000001 00023 Copyright © 2003 by The McGraw-Hill Companies, Inc. All rights reserved. An Overview of Hypothesis Testing  A Statistical Hypothesis: (or simply Hypothesis) An assumption or informed guess made about a population characteristic. It can be defined as an unproven statement or proposition about something under investigation by a researcher.  Before accepting or rejecting any hypothesis, marketing managers test it to determine the likelihood of it being true. It can either be rejected or not rejected.

21. 1995 7888 4320 000 000001 00023 Copyright © 2003 by The McGraw-Hill Companies, Inc. All rights reserved.  Null hypothesis: The hypothesis to be tested for possible acceptance or rejection. A null hypothesis is usually denoted by the symbol H o.  Alternative hypothesis: An assumption believed to be true if the null hypothesis is false. An alternative hypothesis is denoted by H 1. In a given test, there is usually only one null hypothesis, but there may be several alternative hypotheses. An Overview of Hypothesis Testing (cont.)

22. 1995 7888 4320 000 000001 00023 Copyright © 2003 by The McGraw-Hill Companies, Inc. All rights reserved.  Degrees of Freedom: The number of variables that can vary freely in a set of variables under certain conditions.  Statistical Significance: The differences in findings that cannot be caused by chance or sampling error alone. Terminology

23. 1995 7888 4320 000 000001 00023 Copyright © 2003 by The McGraw-Hill Companies, Inc. All rights reserved. Make a decision. Collect relevant data and perform the calculations. State the decision rule. Select the level of significance and critical values. Select a suitable test statistic and its distribution. Steps for Testing Hypotheses State the null and alternative hypotheses.

24. 1995 7888 4320 000 000001 00023 Copyright © 2003 by The McGraw-Hill Companies, Inc. All rights reserved. Figure 16.6 A General Procedure for Hypothesis Testing Formulate H 0 and H 1 Select Appropriate Test Choose Level of Significance, α Collect Data and Calculate Test Statistic Determine Probability Associated with Test Statistic(TS CAL ) Determine Critical Value of Test Statistic TS CR Compare with Level of Significance, α Determine if TS CR falls into (Non) Rejection Region Reject or Do Not Reject H 0 Draw Marketing Research Conclusion Step 1 Step 2 Step 3 Step 4 Step 5 Step 6 Step 7 Step 8 a)b) a)b) Figure 16.6 A General Procedure for Hypothesis Testing

25. 1995 7888 4320 000 000001 00023 Copyright © 2003 by The McGraw-Hill Companies, Inc. All rights reserved. The null hypothesis can be stated as having no difference between the two given values, or the difference is zero. Procedure for Testing Hypotheses Step 1: State the Null and Alternative Hypotheses

26. 1995 7888 4320 000 000001 00023 Copyright © 2003 by The McGraw-Hill Companies, Inc. All rights reserved. To decide on the appropriate test statistic, the researchers should consider the shape and characteristics of the sampling distribution.   Test statistic is calculated from the sample data, whose sampling distribution is used to test whether we may reject the null hypothesis.   Popular test statistics for testing hypotheses are t-test, F-test, and the chi-square goodness of fit test. Step 2: Select a Suitable Test Statistic and Its Distribution

27. 1995 7888 4320 000 000001 00023 Copyright © 2003 by The McGraw-Hill Companies, Inc. All rights reserved. Two Types of Problems, or Errors, Can Result   Type I Error: The researcher rejects a null hypothesis that actually is true.   Type II Error: The researcher accepts a null hypothesis that actually is not true. Step 3: Select the Level of Significance and Critical Values

28. 1995 7888 4320 000 000001 00023 Copyright © 2003 by The McGraw-Hill Companies, Inc. All rights reserved.  Level Of Significance Specifying Type I Error (  ): The maximum probability of making a Type I error specified in a hypothesis test. The level of significance is usually specified before a test is made.  The value of 5% (  = 0.05) or 1% (  = 0.01) is frequently used to set the level of significance, although other values may also be used. Step 3: Select the Level of Significance and Critical Value( cont.)

29. 1995 7888 4320 000 000001 00023 Copyright © 2003 by The McGraw-Hill Companies, Inc. All rights reserved.  Two-Tailed Tests and One-Tailed Tests: The level of significance may be represented by a portion of the area under the normal curve in two ways: 1.The hypothesis tests based on the level of significance represented by both tails under the normal curve are called two-tailed tests or two-sided tests. 2.If the level of significance is represented by only one tail, the tests are called one-tailed tests or one-sided tests. Step 3: Select the Level of Significance and Critical Values (cont.)

30. 1995 7888 4320 000 000001 00023 Copyright © 2003 by The McGraw-Hill Companies, Inc. All rights reserved. Step 4: State the Decision Rule  Specifies the conditions under which the null hypothesis may be rejected, given the sample results. It is based on the level of significance and is stated prior to data collection.  Reject the null hypothesis if the difference between the sample mean and the hypothesized population mean falls into a rejection region. Otherwise, accept the null hypothesis.

31. 1995 7888 4320 000 000001 00023 Copyright © 2003 by The McGraw-Hill Companies, Inc. All rights reserved. Step 5: Collect Relevant Data and Perform the Calculations Collect the relevant information Perform the calculations

32. 1995 7888 4320 000 000001 00023 Copyright © 2003 by The McGraw-Hill Companies, Inc. All rights reserved. Step 6: Make a Decision Refer back to our decision rule (Step 4). We reject the null hypothesis when the computed value falls in the rejection region or accept it when the computed value falls in the acceptance region.

33. 1995 7888 4320 000 000001 00023 Copyright © 2003 by The McGraw-Hill Companies, Inc. All rights reserved. Figure 16.8 Probability of z With a One-Tailed Test Chosen Confidence Level = 95% Chosen Level of Significance, α=.05 z = 1.645 Figure 16.8 Probability of z With a One-Tailed Test Chosen Confidence Level = 95%

34. 1995 7888 4320 000 000001 00023 Copyright © 2003 by The McGraw-Hill Companies, Inc. All rights reserved.  t-Test and t-Distribution: (a.k.a., the Student’s distribution) The t-distribution is a bell-shaped and symmetric distribution that is used for testing small samples (n < 30).  Can be used to test a hypothesis about a sample mean when the population standard deviation (σ) is unknown and the sample size is considered small, usually less than or equal to 30. When a t-distribution is used to test a hypothesis, then the test is called a t-test.  The distribution of the values of t is not normal, but its use and the shape are somewhat analogous to those of the standard normal distribution of z. Selected Hypothesis Tests – cont’d

35. 1995 7888 4320 000 000001 00023 Copyright © 2003 by The McGraw-Hill Companies, Inc. All rights reserved. Developing a Hypothesis The first “stage” in testing a hypothesis is to develop one to be tested!  A hypothesis allows the research team to compare two groups of respondents to see if there are important differences between them.  A hypothesis is developed before any data is collected by the research team.  A hypothesis is developed as part of the overall research plan agreed to by the research team and the client. 16-10

36. 1995 7888 4320 000 000001 00023 Copyright © 2003 by The McGraw-Hill Companies, Inc. All rights reserved. Statistical Significance: Type I Error A Type I error occurs when a research team rejects the null hypothesis when it is true. This is often referred to as the “probability of alpha”. 16-11

37. 1995 7888 4320 000 000001 00023 Copyright © 2003 by The McGraw-Hill Companies, Inc. All rights reserved. Statistical Significance: Type II Error A Type II error occurs when a research team accepts the null hypothesis when the alternative hypothesis is true. This is often referred to as the “probability of beta”. 16-12

38. 1995 7888 4320 000 000001 00023 Copyright © 2003 by The McGraw-Hill Companies, Inc. All rights reserved. Figure 16.7 Type I Error (α) and Type II Error (β )

39. 1995 7888 4320 000 000001 00023 Copyright © 2003 by The McGraw-Hill Companies, Inc. All rights reserved. Univariate Hypothesis Testing: An Example One-Sample Statistics 16-13 NMean Std. Deviation Std. Error Mean X 2 -Competitive Price502.221.15.16 One-Sample Test Test Value = 5.5 95% Confidence Interval of the Difference tdf Sig. (2-tailed) Mean DifferenceLowerUpper X2-Competitive Price-20.20349.000-3.28-3.61-2.95

40. 1995 7888 4320 000 000001 00023 Copyright © 2003 by The McGraw-Hill Companies, Inc. All rights reserved. Bivariate Hypothesis Testing: An Example 16-14a Group Statistics GenderNMean Std. Deviation Std. Error Mean Satisfaction level Male204.351.04.23 Female305.07.78.14

41. 1995 7888 4320 000 000001 00023 Copyright © 2003 by The McGraw-Hill Companies, Inc. All rights reserved. Bivariate Hypothesis Testing: An Example 16-14b Independent Samples Test t-test for Equality of Means FSig.tdf Sig. (2-tailed) Mean Difference Std. Error DifferenceLowerUpper Satisfaction level Equal variances assumed3.415.071-2.77548.008-.72.26-1.24-.20 Equal variances not assumed-2.62433.048.013-.72.27-1.27-.16 Levene’s Test for Equality of Variances 95% Confidence Interval of the Mean

42. 1995 7888 4320 000 000001 00023 Copyright © 2003 by The McGraw-Hill Companies, Inc. All rights reserved. Analysis of Variance: ANOVA In the “language-game” of marketing research, ANOVA stands for the “analysis of variance”. ANOVA is a very sophisticated statistical technique which tells a research team whether three or more means are statistically distinct from one another. 16-15

43. 1995 7888 4320 000 000001 00023 Copyright © 2003 by The McGraw-Hill Companies, Inc. All rights reserved. Analysis of Variance: n-Way ANOVA In the language-game of marketing research, an n-Way ANOVA is another intricate statistical technique which allows the research team to explore several independent variables simultaneously. 16-16

44. 1995 7888 4320 000 000001 00023 Copyright © 2003 by The McGraw-Hill Companies, Inc. All rights reserved. Analysis of Variance: MANOVA In the language-game of marketing research, there’s also something called MANOVA. MANOVA considers the mean differences for a group of dependent measures, exploring a bunch of dependent variables across a bunch of independent variables. 16-17

45. 1995 7888 4320 000 000001 00023 Copyright © 2003 by The McGraw-Hill Companies, Inc. All rights reserved. Summary of Learning Objectives  Understand the mean, median, mode as measures of central tendency.  Understand the range and standard deviation of a frequency distribution as measures of dispersion.  Understand how to graph measures of central tendency.  Understand the difference between independent and related samples.  Explain hypothesis testing and assess potential error in its use.  Understand univariate and bivariate statistical tests.  Apply and interpret the results of the ANOVA and n-way ANOVA statistical methods. 16-18