Marketing Research Chapter 15

skewness

a characteristic of a distribution that assess its symmetry about the mean

contingency table

a cross-tabulation table; contains a cell for every combination of categories of the two variables

F distribution

a frequency distribution that depends upon two sets of degrees of freedom - the degrees of freedom in the numerator and the degrees of freedom in the denominator

binomial test

a goodness-of-fit statistical test for dichotomous variables; tests the goodness of fit of the observed number of observations in each category to the number expected under a specified binomial distribution

frequency distributions

a mathematical distribution whose objective is to obtain a count of the number of responses associated with different values of one variable and to express these counts in percentage terms

median

a measure of central tendency given as the value above which half of the values fall and below which all of the values fall

mode

a measure of central tendency given as the value that occurs the most in a sample distribution

test statistic

a measure of how close the sample has come to the null hypothesis; often follows a well-known distribution, such as the normal, t, or chi-square distribution

asymmetric lambda

a measure of the percentage improvement in predicting the value of the dependent variable, given the value of the independent variable in contingency table analysis; varies between 0 and 1

kurtosis

a measure of the relative peakedness or flatness of the curve defined by the frequency distribution

contingency coefficient (C)

a measure of the strength of association in a table of any size

phi coefficient

a measure of the strength of association in the special case of a table with two rows and two columns (a 2x2 table)

Cramer's V

a measure of the strength of association used in tables larger than 2x2

Kolmogorov-Smirnov (K-S) one-sample test

a one-sample nonparametric goodness-of-fit test that compares the cumulative distribution function for a variable with a specified distribution

chi-square distribution

a skewed distribution whose shape depends solely on the number of degrees of freedom; as the number of degrees of freedom increases, the distribution becomes more symmetrical

null hypothesis

a statement in which no difference or effect is expected; if not rejected, no changes will be made

alternative hypothesis

a statement that some difference or effect is expected; accepting will lead to changes in opinions or actions

t statistic

a statistic that assumes that the variable has a symmetric bell-shaped distribution, the mean is known (or assumed to be known), and the population variance is estimated from the sample

measures of location

a statistic that describes a location within a data set; measures of central tendency describe the center of distribution

measures of variability

a statistic that indicates the distribution's dispersion

cross-tabulation

a statistical technique that describes two or more variables simultaneously and results in tables that reflect the joint distribution of two or more variables that have a limited number of categories or distinct values

Mann-Whitney U test

a statistical test for a variable measured on an ordinal scale, comparing the difference in the location of two populations based on observations from two independent samples

F test

a statistical tests of the equality of the variances of two populations

t distribution

a symmetric bell-shaped distribution that is useful for small sample (n < 30) testing, when the mean is known and the population variance is estimated from the sample

paired samples t test

a test for differences in the means of paired samples

runs test

a test of randomness for a dichotomous variable

one-tailed test

a test of the null hypothesis where the alternative hypothesis is expressed directionally

two-tailed test

a test of the null hypothesis where the alternative hypothesis is not expressed directionally

z test

a univariate hypothesis test using the standard normal distribution

t test

a univariate hypothesis test using the t distribution, which is used when the standard deviation is unknown and the sample size is small

coefficient of variation

a useful expression in sampling theory for the standard deviation as a percentage of the mean

Type I error

alpha error; occurs when the sample results lead to the rejection of a null hypothesis that is in fact true

Type II error

beta error, occurs when the sample results lead to the nonrejection of a null hypothesis that is in fact false

F statistic

computed as the ratio of two sample variances

symmetric lambda

does not make an assumption about which variable is dependent; measures the overall improvement when prediction is done in both direction

nonparametric tests

hypothesis-testing procedures that assume that the variables are measured on a nominal or ordinal scale

parametric tests

hypothesis-testing procedures that assume that the variables of interest are measured on at least an interval scale

paired samples

in hypothesis testing, the observation are paired so that the two sets of observations relate to the same respondents

sign test

nonparametric test for examining differences in the location of two populations, based on paired observations, that compares only the signs of the differences between pairs of variables without taking into account the ranks

Kolmogorov-Smirnov two-sample test

nonparametric test statistic that determines whether two distributions are the same; takes into account any differences in the two distributions, including median, dispersion, and skewness

two-sample median test

nonparametric test statistic that determines whether two groups are drawn from populations with the same median

Wilcoxon matched-pairs signed-ranks test

nonparametric test that analyzes the differences between the paired observations, taking into account the magnitude the differences

gamma

test statistic that measures the association between two ordinal-level variables; does not make an adjustment for ties

tau c

test statistic that measures the association between two ordinal-level variables; makes an adjustment for ties and is most appropriate when the table of variables is not square but a rectangle

tau b

test statistic that measures the association between two ordinal-level variables; makes an adjustment for ties and is most appropriate when the table of variables is square

mean

the average; the value obtained by summing all elements in a set and dividing by the number of elements

range

the difference between the largest and smallest values of a distribution

variance

the mean squared deviation of all the values from the mean

level of significance

the probability of making a Type I error

p value

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

power of a test

the probability of rejecting the null hypothesis when it is in fact false and should be rejected

interquartile range

the range of a distribution encompassing the middle 50 percent of the observations

standard deviation

the square root of the variance

chi-square statistic

the statistic used to test the statistical significance of the observed association in a cross-tabulation; assists in determining whether a systematic association exists between the two variables

independent samples

two samples that are not experimentally related; the measurement of one sample has no effect on the values of the second sample