Bowerman, O'Connell, Aitken Schermer, & Adcock, Business Statistics in Practice, Canadian edition

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1 Bowerman, O'Connell, Aitken Schermer, & Adcock, Business Statistics in Practice, Canadian edition Online Learning Centre Technology Step-by-Step - Excel Microsoft Excel is a spreadsheet software application with built-in statistical functions. The current version is Microsoft Excel 12.0 which is part of the Microsoft Office 2007 software application suite available for the Microsoft Windows XP (32-bit versions) or Vista, and Apple Mac OS X operating systems. Procedures explained utilize Microsoft Excel 11.0 which is a component of the Microsoft Office 2003 application suite. The author s operating system is Windows XP Professional. The described Excel procedures will follow topics in the textbook. Note: Procedures shown are representative, not comprehensive. Refer to the Excel user guide for a more in-depth description of statistical methods. The Microsoft Office 2007 Excel website is Bluman & Mayer, Elementary Statistics, A Step by Step Approach, Canadian Edition Excel Page 1 of 6

2 Excel Excel is a spreadsheet application with basic statistical functions built-in and advanced statistical functionality available through the Data Analysis Add-in. Activate Data Analysis Tool Open Excel. In worksheet menu, click Tools > Add-Ins and select Analysis Toolpak in Add-Ins dialogue box. Click OK. Categorical Frequency Table (Qualitative or Discrete Variable) Type column heading in cell, then input data down column below heading. Input categories in next column with appropriate heading. In next column input heading, such as Count, then move to cell below heading. Click Insert > Function > Statistical category > COUNTIF > OK. Select Range {cells containing data} Criteria {cell containing adjacent category}. Click OK. Move to next cell and repeat for each category listed. Frequency column may be added with the Sum function. Grouped Frequency Distribution Type column heading in cell, then input data down column below heading. Select Tools > Data Analysis > Histogram > OK. Select Input Range {cells containing data} New Worksheet Ply: check Cumulative Percentage > OK. Histogram Repeat Grouped Frequency Distribution procedure and check Chart Output in last step. Optionally, user defined bin ranges, in ascending order, may by typed into worksheet to control histogram output. The bin range should then be selected in Histogram dialogue box. The number of data points between the current bin number and the adjoining higher bin are shown in table and chart. Other Chart Types Input appropriate data in the worksheet. Use the Chart Wizard to construct a bar chart, line chart, pie chart, Pareto chart, or time series plots. Follow the prompts in the displayed dialogue boxes. Descriptive Measures Input data in the worksheet. Move to blank cell. Access the Insert Function Statistical menu to select the desired descriptive measures AVERAGE (mean), MEDIAN, MODE, STDEV (standard deviation), and VAR (variance). Select data range in dialogue box. Click OK. Note: Excel functions can be typed manually. Click on cell containing descriptive measure to view function in formula bar. Alternatively, select Tools > Data Analysis. In Descriptive Statistics dialogue in Input Range, identify data range. Select Summary statistics. Click OK. A table of descriptive statistics will be displayed. Measures of Position Input data in the worksheet. Type a single (x) value appropriate to the data set in a cell. Move to blank cell. Access the Insert Function Statistical menu and select the STANDARDIZE function. In the Standardize dialogue, fill in cell locations for X value, data range for Mean and Standard_dev (standard deviation). Click OK. Bluman & Mayer, Elementary Statistics, A Step by Step Approach, Canadian Edition Excel Page 2 of 6

3 Factorials, Permutations, and Combinations Factorial In a blank cell, access Insert > Function > select Math & Trig category > select FACT function. Type value of n. Click OK. Permutation In a blank cell, access Insert > Function > select Statistical category > select PERMUT function. Type value of n in Number box. Type value of r in Number_chosen box. Click OK. Combination In a blank cell, access Insert > Function > select Math & Trig category > select COMBIN function. Type value of n in Number box. Type value of r in Number_chosen box. Click OK. Binomial Probability Distribution and Chart Type column heading (X) in cell, then input data down column below heading. Label 2 nd column P(X). In cell below P(X) heading, using appropriate values, Select Insert > Function > Statistical > BINOMDIST. Fill in dialogue box, Number_s {cell with X value, 0}, Trials {value for n}, Probability_s {value for p}, Cumulative {0 or FALSE}. Click OK. Note: Formula in formula bar can be typed manually in cell. Note: If cumulative probabilities are desired, change Cumulative in dialogue to 1 or TRUE and change heading label to P(X<=x). Use the Chart Wizard to create a graph. Chart type is Column first subtype. Click Next. In Data Range tab Data range: {input range containing P(X) values}. In Series tab, Category (X) axis labels {input range containing X values}. Click Next. Label as desired. Click Next and Finish. Poisson Probability Distribution Type column heading (X) in cell, then input data down column below heading. Label 2 nd column P(X). In cell below P(X) heading, using appropriate values, Select Insert > Function > Statistical > POISSON. Fill in dialogue box X, Mean, Cumulative {0 or FALSE}. Click OK. Copy formula down column to find probabilities of adjacent X values. Note: Formula in formula bar can be typed manually in cell. Note: If cumulative probabilities are desired, change Cumulative in dialogue to 1 or TRUE and change heading label to P(X<=x). Normal Distribution Cumulative area to the left or z-score. In blank cell, select Insert > Function > Statistical NORMSDIST > {type z-score or cell reference containing z-score}. Click OK. Note: For areas between and to the right, type z scores on worksheet, use NORMSDIST function to determine given areas to the left. On worksheet, perform arithmetic (+ or -) calculations to determine required areas. Find z-score given a cumulative area to the left In blank cell, select Insert > Function > Statistical NORMSINV > {type cumulative area to the left or cell reference}. Click OK. Determining Normality - Normal Quantile Plot Input data on worksheet and label column heading. Sort data in ascending order In blank cell adjacent to first data value, select Insert > Function > Statistical NORMSINV > type formula 1/(2*n), where n is number of data values. Repeat procedure to find z scores for each data value changing subsequent formulae to 2/(2*n), then 3/(2*n), and so on. Note: Each z-score represents 1/nth increment of the area under the curve. Bluman & Mayer, Elementary Statistics, A Step by Step Approach, Canadian Edition Excel Page 3 of 6

4 Highlight two columns from above. Open the Chart Wizard > select XY Scatter first Chart sub-type. Label chart appropriately. *Check for linearity to determine normality. Confidence Interval Estimate Normal z Interval (means) Note: The Excel CONFIDENCE function returns the maximum error of estimate (E), not the lower and upper confidence limits. Workaround: Label column heading (i.e. Data) and input data below heading. Label 4 cells (i.e. Mean, E, LCL, UCL). In cell adjacent to mean, input function =AVERAGE(data range). In cell adjacent to E, select Insert > Function > Statistical > CONFIDENCE. In dialogue box, type desired value for Alpha (as decimal); alpha is 1 confidence level. If σ is known, type value. If σ is not known, input function STDEV(data range). In Size box, either type in sample size or input function COUNT(data range). Click OK to display value for E. In cell adjacent to LCL (lower confidence limit) type formula to subtract mean from E. In cell adjacent to UCL (upper confidence limit), type cell references that will add mean to E. t Interval (means) follow procedure for z Interval above for σ is not known. Normal z Interval (proportions) Note: Excel does not include a function for confidence interval estimates for proportions. Workaround: Label cells. (i.e. X, n, phat, CI, z-score, E, LCL, UCL). Type given data in cells adjacent to X and n. For phat, input formula that references data, =X/n. Type confidence level, as decimal, in cell adjacent to CI. For positive z-score, input formula =NORMSINV(1- (1-CI data cell)/2). For error of estimate, E, input formula = z-score data cell*sqrt((phat data cell*(1- phat data cell))/n data cell). In cell adjacent to LCL (lower confidence limit) type formula to subtract phat from E. In cell adjacent to UCL (upper confidence limit), type cell references that will add phat to E. Variance Hypothesis Tests Normal z Test (means) Input data and label heading. Excel will only calculate P-values using the ZTEST function in the Insert > Function > Statistical menu but only for a one-tailed hypothesis test. Input appropriate values in the dialogue box or type the function in a blank cell; =ZTEST(data range, µ 0, σ). For a two-tailed hypothesis test, type the function =2 * MIN(ZTEST(data range, µ 0, σ), 1 - ZTEST(data range, µ 0, σ)). Note: If σ is unknown, leave blank and Excel will calculate s from data. t Test (means) No built-in functions for this procedure. Requires third party add-in or manual workaround. Normal z Test (proportions) No built-in functions for this procedure. Requires third party add-in or manual workaround. Variance No built-in functions for confidence interval estimates for variance. Requires third party addin or manual workaround. Hypothesis Test Difference Between Two Means z Distribution Input 2 data sets and label headings. If variances for two data sets are unknown, in blank cells input =VAR(data range) function for each data set. Select Tools > Data Analysis > z-test: Two Sample for Means. In dialogue box, under Input, Variable 1 Range: select sample 1 data range, Variable 2 Range: select sample 2 data range, Hypothesized Mean Difference: 0, Variable 1 Variance (known): input known or calculated value for data set 1. Variable 2 Variance (known): input known or calculated value for data set 2. Specify desired Alpha: level. Specify output location. Click OK to display results. Bluman & Mayer, Elementary Statistics, A Step by Step Approach, Canadian Edition Excel Page 4 of 6

5 t Distribution (Small Independent Samples) Input 2 data sets and label headings. Select Tools > Data Analysis > t-test: Two Sample for Means. Input Variable 1 and Variable 2 data ranges, Hypothesized Mean Difference: 0, specify Alpha: level and output range. Click OK to display results. t Distribution (Small Dependent Samples) Input 2 data sets and label headings. Select Tools > Data Analysis > t-test: Paired Two Sample for Means. Input Variable 1 and Variable 2 data ranges, Hypothesized Mean Difference: 0, specify Alpha: level and output range. Click OK to display results. Hypothesis Test Difference Between Two Variances Input 2 data sets and label headings. Select Tools > Data Analysis > F-Test: Two Sample for Variances. In dialogue box, under Input, Variable 1 Range: select sample 1 data range, Variable 2 Range: select sample 2 data range, Specify desired Alpha: level. Specify output location. Click OK to display results. Hypothesis Test Difference Between Two Proportions Scatter Plots Input two columns of paired data (x,y) and label headings. Select paired data range. Click Chart Wizard > XY (Scatter) first Chart sub-type > click Next twice > enter titles and axis labels and any desired changes > click Next and Finish to display chart. Correlation Coefficient Input two columns of paired data (x,y) and label headings. Select a blank cell, then select Insert > Function > Statistical > CORREL. In dialogue box, Array 1: select X values and Array 2: Y values. Click OK to display result. Correlation and Regression Input two columns of paired data (x,y) and label headings. For correlation, select Tools > Data Analysis > Correlation. In dialogue box, Input range: select range of both X values and Y values with headings. Grouped by: select Columns (or Rows, if data is in rows). Check box Labels in First Row, if headings are selected with data range. Select desired Output options. Click OK to display resulting correlation. For regression, select Tools > Data Analysis > Regression In dialogue box, under Input, select appropriate Input Y Range: and Input X Range:. Select desired Output option. Click OK to display resulting statistics, including under Coefficients: Intercept and Slope of regression line. Multiple Regression Select Tools > Data Analysis > Regression In dialogue box, under Input, select dependent variable data range in Input Y Range: and data range containing independent variables in Input X Range:. Select desired Output option. Click OK to display resulting statistics, including under Coefficients: Intercept and Slopes for each X Variable of multiple regression line. Chi-square Hypothesis Test Bluman & Mayer, Elementary Statistics, A Step by Step Approach, Canadian Edition Excel Page 5 of 6

6 Χ 2 Goodness-of-Fit Test Input observed frequencies and expected frequencies in 2 columns. Label column headings (i.e. O and E). In blank cell, select Input > Function > Statistical > CHITEST. In Acutal_range, input observed frequency data range. In Expected_range, input expected frequency data range. Click OK. The CHITEST result is the P-value. Χ 2 Independence Test No built-in functions for this procedure. Requires third party add-in or manual workaround. One-Way Analysis of Variance (ANOVA) Input columns of data and label headings. Select Tools > Data Analysis > Anova: Single Factor. In Input Range: select all column data. Grouped by: Columns. In Alpha: type desired significance level. Specify Output option. Click OK to display results including F (test statistic) and P-value. Two-Way Analysis of Variance Input data into columns and rows in contingency table format pairing coded factors with row and column labels. Select Tools > Data Analysis > Anova: Two-Factor With Replication. In dialogue, Input Range: select complete table including labels. Specify an alpha level and output range. Click OK to display results including F (test statistic) and P-value. Sign Test Wilcoxon Mann-Whitney Test Kruskal-Wallis Test Spearman Rank Correlation Coefficient Random Numbers On a new worksheet, select Tools > Data Analysis > Random Number Generation. Click OK. In dialogue box, fill in desired Number of Variables: value for number of different results. Number of Random Numbers: any desired value, Distribution: select Normal, Bernoulli, Binomial, Poisson, or Patterned Discrete. Parameters: input fields will change according to selected Distribution:. Random seed: any number between 1 and 51. Desired Output option. Click OK to display results. Bluman & Mayer, Elementary Statistics, A Step by Step Approach, Canadian Edition Excel Page 6 of 6