LEARNING OUTCOMES 1.Know what descriptive statistics are and why they are used 2.Create and interpret tabulation tables 3.Use cross-tabulations to display relationships 4.Perform basic data transformations 5.Understand the basics of testing hypotheses using inferential statistics 1. Z test 14–1

The Nature of Descriptive Analysis Descriptive AnalysisDescriptive Analysis  The elementary transformation of raw data in a way that describes the basic characteristics such as central tendency, distribution, and variability. HistogramHistogram  A graphical way of showing a frequency distribution in which the height of a bar corresponds to the observed frequency of the category. 14–2

EXHIBIT 14.1 Levels of Scale Measurement and Suggested Descriptive Statistics 14–3

Cross-Tabulation Cross-TabulationCross-Tabulation Addresses research questions involving relationships among multiple less-than interval variables. Addresses research questions involving relationships among multiple less-than interval variables. Results in a combined frequency table displaying one variable in rows and another variable in columns. Results in a combined frequency table displaying one variable in rows and another variable in columns. Contingency TableContingency Table A data matrix that displays the frequency of some combination of responses to multiple variables. A data matrix that displays the frequency of some combination of responses to multiple variables. MarginalsMarginals Row and column totals in a contingency table, which are shown in its margins. Row and column totals in a contingency table, which are shown in its margins. 20–4

Cross-Tabulation Table Did you watch the movie Into The Woods? Yes NoDid you watch the movie Into The Woods? Yes No What’s your gender? Male FemaleWhat’s your gender? Male Female (Observed distribution) NoYesTotal Male14317 Female Total

Cross-tab: Project Assignment Thirty respondents were asked if they have the access to the 4G network and if they have used mobile banking services.Thirty respondents were asked if they have the access to the 4G network and if they have used mobile banking services. The results showed that 11 people do not have the access to 4G and have not used mobile banking, 4 people have the access to 4G but have not used mobile banking, 12 people have the access to 4G and have used mobile banking, and 3 people do not have the access to 4G but have used mobile banking (using friends’ smartphone).The results showed that 11 people do not have the access to 4G and have not used mobile banking, 4 people have the access to 4G but have not used mobile banking, 12 people have the access to 4G and have used mobile banking, and 3 people do not have the access to 4G but have used mobile banking (using friends’ smartphone). Present the results in a cross-tabulation table in Project Assignment.Present the results in a cross-tabulation table in Project Assignment. 14–6

Cross-Tabulation Table Convert frequency table to percentage table.Convert frequency table to percentage table.  Statistical base – the number of respondents or observations (in a row or column) used as a basis for computing percentages. What was the percentage of males who watched the movie?What was the percentage of males who watched the movie? What was the percentage of moviegoers who were male?What was the percentage of moviegoers who were male? 7

Cross-Tabulation Table % of males watched the movie.% of males watched the movie. % of% ofmoviegoers were male. NoYesTotal (base) Male 3/17= 17.6% Female Total NoYesTotal Male3/20=15% Female Total (base) 8

Cross-Tabulation Table NoYesTotal Male14/29=48%3/20=15% Female15/29=52%17/20=85% Total29/29=100%20/20=100% Percentages are computed in the direction of the “independent” variable, e.g., gender.Percentages are computed in the direction of the “independent” variable, e.g., gender. 9

What would be appropriate “independent” variable and dependent variable?What would be appropriate “independent” variable and dependent variable? Convert the 4G x Mobile Banking cross-tab into a percentage table.Convert the 4G x Mobile Banking cross-tab into a percentage table. 10 Cross-tab: Project Assignment

Data Transformation Data TransformationData Transformation Process of changing the data from their original form to a format suitable for performing a data analysis addressing research objectives. Process of changing the data from their original form to a format suitable for performing a data analysis addressing research objectives. Recoding Recoding Creating summated scales Creating summated scales Collapsing adjacent categories Collapsing adjacent categories Creating index numbers, e.g., consumer price index (CPI) Creating index numbers, e.g., consumer price index (CPI) 20–11

Computer Programs for Analysis Statistical PackagesStatistical Packages  Spreadsheets  Excel  Statistical software:  SPSS (Statistical Package for Social Sciences) –PASW (Predicative Analytics Software)  SAS  MINITAB 14–12

Hypothesis Testing Using Basic Statistics Univariate Statistical AnalysisUnivariate Statistical Analysis  Tests of hypotheses involving only one variable. Bivariate Statistical AnalysisBivariate Statistical Analysis  Tests of hypotheses involving two variables.  E.g., t-test, ANOVA, correlation Multivariate Statistical AnalysisMultivariate Statistical Analysis  Statistical analysis involving three or more variables or sets of variables.  E.g., Multiple regression 14–13

Hypothesis Testing Procedure The specifically stated hypothesis is derived from the research objectives.The specifically stated hypothesis is derived from the research objectives. A sample is obtained and the relevant variable is measured.A sample is obtained and the relevant variable is measured. The measured sample value is compared to the value either stated explicitly or implied in the hypothesis.The measured sample value is compared to the value either stated explicitly or implied in the hypothesis.  If the value is consistent with the hypothesis, the hypothesis is supported.  If the value is not consistent with the hypothesis, the hypothesis is not supported. 14–14

Null Hypothesis vs. Alternative Hypothesis Null hypothesis (H 0 ): A statement about a status quo (asserting that any change from what has been thought to be true will be due entirely to random sampling errors).Null hypothesis (H 0 ): A statement about a status quo (asserting that any change from what has been thought to be true will be due entirely to random sampling errors).  E.g., H 0 : µ = 100 Alternative hypothesis (H 1 ): A statement indicating the opposite of the null hypothesis.Alternative hypothesis (H 1 ): A statement indicating the opposite of the null hypothesis.  E.g., H 1 : µ

Hypothesis Testing (HT) The purpose of HT is to determine which of the two hypotheses is correct.The purpose of HT is to determine which of the two hypotheses is correct. Significant level: The critical probability in choosing between the null and alternative hypotheses.Significant level: The critical probability in choosing between the null and alternative hypotheses. ą (Greek letter alpha) =.05ą (Greek letter alpha) =.05 The probability level that is too low to warrant support of the null hypothesis.The probability level that is too low to warrant support of the null hypothesis. 16

Hypothesis Testing (HT) p-valuep-value  Probability value, or the observed or computed significance level.  p-values are compared to significance levels to test hypotheses.  p <.05, null hypothesis is reject or alternative hypothesis is supported. 14–17

18 Univariate Hypothesis Testing Is the sample mean significantly different from the hypothesized population mean?Is the sample mean significantly different from the hypothesized population mean?  Is the sample a part of the population? Population mean IQ: µ=100Population mean IQ: µ=100 Sample mean (e.g., SJSU) IQ: =105Sample mean (e.g., SJSU) IQ: =105 Is IQ score 105 statistically significantly different from IQ score 100?Is IQ score 105 statistically significantly different from IQ score 100?

“Well, Are They Satisfied or Not?” Suppose Best Buy is interested in if their customers were satisfied with their “Black Friday” shopping in the Best Buy stores.Suppose Best Buy is interested in if their customers were satisfied with their “Black Friday” shopping in the Best Buy stores. Unsatisfied12345 SatisfiedUnsatisfied12345 Satisfied The average score of 225 shoppers is 3.3.The average score of 225 shoppers is 3.3. Is a satisfaction score of 3.3 good or bad?Is a satisfaction score of 3.3 good or bad? Need to compare with other scores.Need to compare with other scores

Step 1*: Stating Hypotheses H 0 : µ=3.0 (customers were neither unsatisfiedH 0 : µ=3.0 (customers were neither unsatisfied nor satisfied.) H 1 : µ≠3.0 (customers were satisfied with their Black Friday shopping.)H 1 : µ≠3.0 (customers were satisfied with their Black Friday shopping.) 20

21 Step 2: Deciding on Region of Rejection Critical Z-scores: Z-distribution The darkly shaded area shows the region of rejection when ą=.025 Raw scores:

HT: Best Buy Example Sample size n=225Sample size n=225 Sample mean =3.3Sample mean =3.3 Sample standard deviation S=1.5Sample standard deviation S=1.5 22

Step 3*: Calculating z-statistic 23 z-statistic: Standard error of mean: The standard deviation of the sampling distribution. (obs=observation; as opposed to expected critical values)

24 Step 4: Comparing Z-Statistic to Critical Value Z-scores:

Step 5*: Making a Decision Z obs =3.0 > Z.05 =1.96Z obs =3.0 > Z.05 =1.96 Therefore, p<.05. This means that the chance we observe µ=3.0 is less than 5%.Therefore, p<.05. This means that the chance we observe µ=3.0 is less than 5%. Reject H 0Reject H 0 This suggests that Best Buy customers were satisfied with their “Black Friday” shopping.This suggests that Best Buy customers were satisfied with their “Black Friday” shopping. 25

Hypothesis Testing Procedure: Z Test 1.State hypotheses.  Null: H 0: µ=  Alternative: H 1: µ≠ 2.Decide on region of rejection, i.e., find the critical value(s) for the significant level p=.05.  Z-distribution: and Calculate the z-statistic 4.Comparing the z-statistic with critical values. 5.Make a decision  If z-statistic falls in [-1.96, 1.96], then fail to reject H 0.  If z-statistic falls out of [-1.96, 1.96], then reject H 0. 26

27 According to the past 5 years of experience, a professor knows that the average hours his students spend on the final project is 15 (standard error of the mean = 0.9). In order to see whether or not the time his students spend on the project has decreased this semester, he randomly sampled 50 of his students and calculated the average hours as State an appropriate null hypothesis and alternative hypothesis. 2.Find the critical values at significant level p=.05 3.Calculate the z-statistic. 4.Compare z-statistic with critical values. 5.Make a decision. Z-test: Project Assignment