CH13 Statistical Testing of Differences

Question 1

what are the 3 important concepts applied to the notion of differences?

Answer 1

1. mathematical differences: if numbers are not exactly the same, they are different. this does not, however, mean that the difference is either important or statistically significant
2. statistical significance: a difference that is large enough that is not likely to have occurred because of chance or sampling error
3. managerially important differences: one can argue that a difference is important from a managerial perspective only if results or numbers are sufficiently different
   eg. the difference in consumer responses to 2 different packages in a test market might be statistically significant but so small as to have little practical or managerial significance

Question 2

this chapter covers different approaches to testing whether results are statistically significant. what are the 3 things to keep in mind?

Answer 2

1. random samples are assumed
2. big data does not mean “good” data
3. don’t over rely on significance testing

Question 3

what is a hypothesis in the context of statistical inference?

Answer 3

a hypothesis is an assumption or theory made by a researcher or manager about a characteristic of the population under study

Question 4

what is the purpose of hypothesis testing?

Answer 4

the purpose of hypothesis testing is to determine whether a hypothesis about a population characteristic is valid by calculating the probability of observing a particular result if the stated hypothesis is true

Question 5

what are the 5 steps in hypothesis testing?

Answer 5

1. stating the hypothesis
2. choosing the appropriate statistical test
3. developing a decision rule (decision rule: a rule or standard used to determine whether to reject or fail to reject the null hypothesis)
4. calculating the value of the test statistic
5. stating the conclusion

Question 6

what are the 2 types of errors in hypothesis testing?

Answer 6

the two types of errors in hypothesis testing are type I (α error) and type II (β error):

• a type I error occurs when the null hypothesis is rejected when it is actually true
• a type II error occurs when the null hypothesis is failed to be rejected when the alternative hypothesis is true

Question 7

define independent versus related samples

Answer 7

independent samples are those in which the measurement of a variable in one population has no effect on the measurement of the variable in the other

related samples are samples in which the measurement of a variable in one population may influence the measurement of the variable in the other

Question 8

define the z-value (aka standard score, or standardized value)

Answer 8

the z value is a statistical measure that represents the number of standard deviations an observation or data point is from the mean of distribution

it is calculated by subtracting the mean from the observed value and then dividing the result by the standard deviation

Question 9

what are degrees of freedom?

Answer 9

degrees of freedom are the number of observations in a statistical problem that are free to vary

calculated as n - 1

Question 10

define the chi-square test

Answer 10

the chi-square test is a test of the goodness of fit between the observed distribution and the expected distribution of a variable

Question 11

what is the purpose of a test of goodness of fit?

Answer 11

the purpose of a test of goodness of fit is to determine whether the observed distribution of subjects, objects, or responses in different categories differs significantly from what would be expected by chance

Question 12

what is a t test?

Answer 12

a t test is a hypothesis test used for a single mean if the sample is too small (n > 30) to use the z test

Question 13

what statistical test is commonly used when making inferences about a population mean?

Answer 13

the t test with n − 1 degrees of freedom is commonly used when making inferences about a population mean

Question 14

what statistical test is appropriate for testing differences between responses to the same variable by groups with different characteristics?

Answer 14

the t test is appropriate for testing differences between responses to the same variable by groups with different characteristics

Question 15

define the hypothesis test of proportions

Answer 15

the hypothesis test of proportions is a test to determine whether the difference between proportions is greater than would be expected because of sampling error

Question 16

what is the analysis of variance (ANOVA)?

Answer 16

the analysis of variance (ANOVA) is the test for the differences among the means of 2 or more independent samples

Question 17

what statistical tool is used to test the differences among the means of 3 or more independent samples?

Answer 17

analysis of variance (ANOVA) is the appropriate statistical tool for testing differences among the means of three or more independent samples

Question 18

define the f test

Answer 18

the f test is the test of probability that a particular calculated value could have been due to chance

Question 19

what is the p value

Answer 19

the p value is the exact probability of getting a computed test statistic that is due to chance

the smaller the p value, the smaller the probability that the observed result occurred by chance