Chapter 17 - Hypothesis testing: Basic concepts and tests of association. In this chapter, the following content will be discussed: Hypothesis testing - basic concepts, hypothesis testing process, basic concepts of hypothesis testing,...
1 Marketing Research Aaker, Kumar, Leone and Day Twelfth Edition Instructor’s Chapter Seventeen Hypothesis Testing: Basic Concepts and Tests of Association Marketing Research 12th Edition Hypothesis Testing: Basic Concepts • • Assumption (hypothesis) made about a population parameter (not sample parameter) Purpose of Hypothesis Testing ▫ • To make a judgment about the difference between two sample statistics or between sample statistic and a hypothesized population parameter Evidence has to be evaluated statistically before arriving at a conclusion regarding the hypothesis ▫ Depends on whether information generated from the sample is with fewer or larger observations Marketing Research 12th Edition Hypothesis Testing • • • The null hypothesis (Ho) is tested against the alternative hypothesis (Ha) At least the null hypothesis is stated Decide upon the criteria to be used in making the decision whether to “reject” or "not reject" the null hypothesis Marketing Research 12th Edition Hypothesis Testing Process Problem Definition Clearly state the null and alternative hypotheses Choose the relevant test and the appropriate probability distribution Determine the significance level Compute relevant test statistic Choose the critical value Determine the degrees of freedom Decide if one-or twotailed test Compare test statistic & critical value Does the test statistic fall in the critical region? No Do not reject null Yes Reject null Marketing Research 12th Edition Basic Concepts of Hypothesis Testing Three Criteria Used To Decide Critical Value (Whether To Accept or Reject Null Hypothesis): • Significance Level • Degrees of Freedom • One or Two Tailed Test Marketing Research 12th Edition Significance Level • • • • • Indicates the percentage of sample means that is outside the cutoff limits (critical value) The higher the significance level ( ) used for testing a hypothesis, the higher the probability of rejecting a null hypothesis when it is true (Type I error) Accepting a null hypothesis when it is false is called a Type II error and its probability is ( ) When choosing a level of significance, there is an inherent tradeoff between these two types of errors A good test of hypothesis should reject a null hypothesis when it is false Marketing Research 12th Edition Relationship between Type I & Type II Errors Marketing Research 12th Edition Relationship between Type I & Type II Errors (Contd.) Marketing Research 12th Edition 10 Relationship between Type I & Type II Errors (Contd.) Marketing Research 12th Edition 14 Basic Concepts of Hypothesis Testing (Contd.) • Select the appropriate probability distribution based on two criteria ▫ Size of the sample ▫ Whether the population standard deviation is known or not Marketing Research 12th Edition 15 Hypothesis Testing Data Analysis Outcome Accept Null Hypothesis Reject Null Hypothesis Null Hypothesis is True Correct Decision Type I Error Null Hypothesis is False Type II Error Correct Decision Marketing Research 12th Edition 16 Crosstabulation and Chi Square In Marketing Applications, Chisquare Statistic is used as: • Test of Independence ▫ Are there associations between two or more variables in a study? • Test of Goodness of Fit ▫ • Statistical Independence ▫ Two variables are statistically independent if a knowledge of one Is there a significant difference between an observed frequency distribution and a theoretical frequency distribution? would offer no information as to the identity of the other Marketing Research 12th Edition 17 The Concept of Statistical Independence If n is equal to 200 and Ei is the number of outcomes expected in cell i, Marketing Research 12th Edition 18 ChiSquare As a Test of Independence Marketing Research 12th Edition 19 ChiSquare As a Test of Independence (Contd.) Null Hypothesis Ho • Two (nominally scaled) variables are statistically independent Alternative Hypothesis Ha • The two variables are not independent Use Chisquare distribution to test Marketing Research 12th Edition 20 Chisquare Distribution • A probability distribution • Total area under the curve is 1.0 • A different chisquare distribution is associated with different degrees of freedom Cutoff points of the chisquare distribution function Marketing Research 12th Edition 21 Chisquare Distribution (Contd.) Degrees of Freedom • Number of degrees of freedom, v = (r 1) * (c 1) r = number of rows in contingency table c = number of columns • Mean of chisquared distribution = Degree of freedom (v) • Variance = 2v Marketing Research 12th Edition 22 Chisquare Statistic ( 2) • Measures of the difference between the actual numbers observed in cell i (Oi), and number expected (Ei) under assumption of statistical independence if the null hypothesis were true 2 n (Oi i Ei ) Ei With (r1)*(c1) degrees of freedom Oi = observed number in cell i Ei = number in cell i expected under independence r = number of rows c = number of columns • Expected frequency in each cell, Ei = pc * pr * n Where pc and pr are proportions for independent variables n is the total number of observations Marketing Research 12th Edition 23 Chisquare StepbyStep Marketing Research 12th Edition 24 Strength of Association • • • • Measured by contingency coefficient 0 = no association (i.e., Variables are statistically independent) Maximum value depends on the size of table Compare only tables of same size Marketing Research 12th Edition 25 Limitations of Chisquare as an Association Measure • It is basically proportional to sample size • Difficult to interpret in absolute sense and compare cross tabs of unequal size It has no upper bound Difficult to obtain a feel for its value Does not indicate how two variables are related Marketing Research 12th Edition 26 Measures of Association for Nominal Variables • Measures based on ChiSquare Phi-squared Cramer’s V Marketing Research 12th Edition 27 Chisquare Goodness of Fit • • Used to investigate how well the observed pattern fits the expected pattern Researcher may determine whether population distribution corresponds to either a normal, Poisson or binomial distribution To determine degrees of freedom: • • Employ (k1) rule Subtract an additional degree of freedom for each population parameter that has to be estimated from the sample data Marketing Research 12th Edition 28 End of Chapter Seventeen Marketing Research 12th Edition ...2 Chapter Seventeen Hypothesis Testing: Basic Concepts and Tests of Association Marketing Research 12th Edition Hypothesis Testing: Basic Concepts • • Assumption (hypothesis) made about a population ... When choosing a level of significance, there is an inherent tradeoff between these two types of errors A good test of hypothesis should reject a null hypothesis when it is false Marketing Research. .. A different chisquare distribution is associated with different degrees of freedom Cutoff points of the chisquare distribution function Marketing Research 12th Edition 21 Chisquare Distribution (Contd.) Degrees of Freedom • Number of degrees of freedom, v = (r 1) * (c 1)