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# Week 10 Notes MKT 319

MSU

GPA 3.8

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This 6 page Class Notes was uploaded by Danielle Lynch on Sunday November 22, 2015. The Class Notes belongs to MKT 319 at Michigan State University taught by R. Spreng in Summer 2015. Since its upload, it has received 17 views. For similar materials see Marketing Research in Marketing at Michigan State University.

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Date Created: 11/22/15

Ch 16 Data Analysis Frequency Distribution Hypothesis Testing and CrossTabulation Frequency Distribution Frequency distribution A mathematical distribution with the objective of obtaining a count of the number of responses associated with different values of one variable and to express these counts in percentage terms Conducting Frequency Analysis 0 Calculate the frequency for each value of the variable 0 Calculate the percentage and cumulative percentage for each value adjusting for any missing values 0 Plot the frequency histogram 0 Calculate the descriptive statistics measures of location and variability Statistics Associated with Frequency Distribution Measures of Location A statistic that describes a location within a data set Measures of central tendency describe the center of the distribution 0 Mean The average that value obtained by summing all elements in a set and dividing by the number of elements I Value x Frequency Number of observations without missing values 0 Mode A measure of central tendency given as the value that occurs the most in a sample distribution I Frequency that appears the most 0 Median A measure of central tendency given as the value above which half of the values fall and below which half of the values fall I Midpoint between the two middle values by adding the two middle values and dividing their sum by 2 Asymmetric distribution 0 Mean mode median are equal only when the distribution is symmetric 0 Nominal Mode 0 Ordinal Median o Interval or ratio Mean Measures of Variability Statistics that indicate the distribution s dispersion 0 Range The difference between the smallest and largest values of a distribution 0 Variance and Standard deviation I Deviation from the mean The difference between the mean and the observed value I Variance The mean squared deviation of all the values from the mean I Standard deviation The square root of the variance Introduction to Hypothesis Testing Hypotheses are unproven statements or propositions of interest to the researcher A General Procedure for Hypothesis Testing 1 Formulate the null hypotheses and alternative hypothesis a Null hypothesis A statement of the status quo one of no difference or no effect If the null hypothesis is not rejected no changes will be made i Formulated in a way that its rejection leads to the acceptance of the desired conclusion b Alternative hypothesis Some difference or effect is expected Accepting the alternative hypothesis will lead to changes in opinions or actions c Onetailed test A test of the null hypothesis where the alternative hypothesis is expressed directionally d Twotailed test A test of the null hypothesis where the alternative hypothesis is not expressed directionally 2 Select an appropriate statistical test and the corresponding test statistic a Test statistic Measures how close the sample has come to the null hypothesis It often follows a wellknown distribution such as the normal t or chisquare distribution 3 Choose the level of significance a Type I Error Alpha error occurs when the sample results lead to the rejection of a null hypothesis that is in fact true i Level of significance The probability of making a type I error b Type 11 Error Beta error occurs when the sample results lead to nonrejection of a null hypothesis that is in fact false 4 Determine the sample size and collect the data Calculate the value of the test statistic 5 Determine the probability associated with the test statistic calculated from the sample data under the null hypothesis using the sampling distribution of the test statistic Alternatively determine the critical value associated with the test statistic that divides the rejection and the non rejection region a Pvalue The probability of observing a value of the test statistic as extreme as or more extreme than the value actually observed assuming that the null hypothesis is true 6 Compare the probability associated with the test statistic with the level of significance specified Alternatively determine whether the test statistic calculated form the sample data falls into the rejection or nonrejection rejoin 7 Make the statistical decision to reject or not reject the null hypothesis a Reject the null Calculated or observed lt Level of significance b Reject the null Calculated or observed gt Critical Value 8 Arrive at a conclusion Express the statistical decision in terms of the marketing research problem Cross Tabulation CrossTabulation Describes two or more variables simultaneously and results in tables that re ect the joint distribution of two or more variables that have a limited number of categories or distinct values Contingency table A crosstabulation table It contains a cell for every combination of categories of the two variables Used because 0 Easily interpreted by managers not statistically oriented o Clarity of interpretation provides a stronger link between research results and managerial action 0 Crosstabulation analysis is simple to conduct and more appealing to less sophisticated researchers Bivariate crosstabulation 0 Compute percentages by way of the independent variable Statistics Associated with CrossTabulation Chisquare statistic Test the statistical significance of the observed association in a crosstabulation Assists in determining whether a systematic association exists between the two variables 0 DF r1xc1 Chisquare distribution A skewed distribution whose shape depends solely on the number of degrees of freedom As the number of degrees of freedom increases the chisquare distribution becomes more symmetrical o Goodnessoffit test Determine whether certain models fit the observed data calculating the significance of sample deviations from assumed expected distributions 0 Counts of data 0 Expected frequencies should not be lt5 type I error so recode Phi Coefficient Used to measure the strength of association in the special case of a table with two rows and two columns 2x2 table Contingency Coefficient A measure of the strength of association in a table of any size 0 Used when the null hypothesis was rejected Cramer s V A measure of the strength of associated used in tables larger than 2 x 2 0 lt3 low association 0 3 6 low to moderate o gt6 strong Ch 17 Data Analysis Hypothesis Testing Related to Differences Hypothesis Testing Related to Differences Parametric tests Hypothesistesting procedures that assume the variables of interest are measured on at least an interval scale Ttest A Univariate hypothesis test using the t distribution which is used when the standard deviation is unknown and the sample size is small Tstatistic A statistic that assumes the variable has a symmetric bellshaped distribution and the mean is known or assumed to be known and the population variance is estimated from the sample Tdistribution A symmetric bellshaped distribution that is useful for smallsample nlt30 testing More area in the tails and less in the center than a normal distribution because we must go a larger number of standard deviations Hypothesis Testing Based on the TStatistic 1 2 3 4 6 Formulate Ho and H1 Select Appropriate TTest Choose Level of Significance Collect Data and Calculate Tstatistic a Determine Probability Associated with t Statistic i Compare with Level of Significance b Determine Critical Value of t Statistic i Determine is TScal falls into the Rejection Region If probability larger than the critical value do not reject Ho a If tstatistic is larger than the critical value reject Ho Draw Marketing Research Conclusion OneSample tTest Ztest A Univariate hypothesis test using the standard normal distribution Two Sample ttest Two Independent Samples Independent samples Two samples that are not experimentally related The measurement of one sample has no effect on the values of the other sample Ftest A statistical test of the equality of the variances of two populations F statistic A statistic that is calculated as the ratio of two sample variances with the larger sample variance in the numerator If probability of F gt significance level reject Ho Paired Samples Paired samples The observations are paired so that the two sets of observations relate to the same respondents Paired samples ttest A test for differences in means of paired samples Testing Hypotheses for More Than Two Samples Means with More than two Samples Analysis of Variance ANOVA A statistical technique for examining the differences among means for two or more populations Conducting OneWay ANOVA 1 Identify the Dependent and Independent Variables Decompose the Total Variation Measure the Effects Test Significance Interpret Results 9195 Oneway analysis of variance An ANOVA technique in which there is only one factor Factors Categorical independent variables All the independent variables must be categorical nonmetric to use ANOVA Treatment In ANOVA a particular combination of factor levels or categories Decomposition of the total variation In oneway ANOVA separation of the variation observed in the dependent variable into the variation due to the independent variables plus the variation due to error SSy Total variation in Y SSbetween Also denoted SSX the variation in Y related to the variation in the means of the categories of X The variation between the categories of X or the portion of the sum of squares in Y related to X SSwithin SSerror the variation in Y due to the variation within each of the categories of X This variation is not accounted for by x Etaquot2nquot2 Statistic that measures the strength of the effects of X independent variable or factor on Y dependent variable value ranges between 0 and 1 Mean square The sum of squares divided by the appropriate degrees of freedom Significance of the overall effect A test to determine whether some differences exist between some of the treatment groups

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