Bluman & Mayer, Elementary Statistics, A Step by Step Approach, Canadian Edition

Transcription

1 Bluman & Mayer, Elementary Statistics, A Step by Step Approach, Canadian Edition Online Learning Centre Technology Step-by-Step - Minitab Minitab is a statistical software application originally created to help educators teach statistics but has evolved into a business data analysis tool. "Minitab Inc. is the leading global provider of software and services for quality improvement and statistics education. Our mission is to provide the tools and resources professionals need to analyze complex problems, improve their processes, and train their students." The current version Minitab 15 is available for Microsoft Windows XP (32-bit versions) or Vista. Procedures explained utilize Minitab 14. The author s operating system is Windows XP Professional. The described Minitab procedures will follow topics in the textbook. Note: Procedures shown are representative, not comprehensive. Refer to the Minitab user guide for a more in-depth description of statistical methods. The Minitab application website is Minitab Starting Minitab In Windows XP, click Start > Programs > Minitab 14 > Minitab 14. Opening Screen Session window Column Cell Row Data entry window Bluman & Mayer, Elementary Statisitics, A Step by Step Approach, Canadian Edition Minitab Page 1 of 8

2 Entering Data Input data in the worksheet window in the columns and rows. Column labels may be typed into the cells below the column headings above row 1. Save a Worksheet File and Worksheet Project Click folder. or File > Save Current Worksheet or File > Save Project with file or project name to desired Open a Worksheet File and Worksheet Project Click or File > Open Worksheet or File > Open Project from saved folder. Minitab Commands Menus may be used to access available commands depending on the desired procedure. Procedure shown uses menu commands. Alternatively, commands can be input directly in the Session window, commands are typed at the MTB> prompt, subcommands at the SUBC> prompt and data at the DATA> prompt. Press Enter to execute commands. Note: Command may need to be enabled in menu. Click Editor > Enable Commands. Categorical Frequency Table (Qualitative or Discrete Data) Input data in column and type heading. Select Stat > Tables > Tally Individual Variables. Double-click column with data to display under Variables:, then select Display: Counts Percents Cumulative counts. Click OK. Grouped Frequency Distribution (Quantitative Variable) Input data in column and type heading label. Select Data > Code > Numeric to Text. Double-click column name containing data to display under Code data from columns:. Type new column name under Into columns:. Type class limits separated with a colon under Original values [eg, 1:4 12]:, then type the text category classes, usually separated with a dash, under New:. Continue to type each additional class, then click OK. Click Stat > Tables > Tally Individual Variables, then double-click column with new data (class limits) to display under Variables:, then select Display: Counts Percents Cumulative counts. Click OK. Histogram Enter data with column label on worksheet. Select Graph > Histogram > Simple > OK. In Histogram dialogue, double-click column label containing data to display under Graph variables:. Click Labels > Select Titles/Footnotes {type chart title and subtitle} > OK. Other Chart Types Input appropriate data for the chart type in the worksheet. Pie charts, bar charts, dot plots, stem and leaf plots, and time series plots are accessed in the Graph menu. Pareto charts can be created via the Stat > Quality Tools > Pareto menu. In all cases, the dialogue box will prompt the user for required information. Bluman & Mayer, Elementary Statisitics, A Step by Step Approach, Canadian Edition Minitab Page 2 of 8

3 Descriptive Measures Enter data with column label on worksheet. Click Data > Basic Statistics > Display Descriptive Statistics. Double-click column containing data to display under Variables:. Click Statistics and select desired descriptive measures mean, median, range, standard deviation and variance. Click OK twice to display selected descriptive statistics. Measures of Position Input data in the worksheet. Access Calc > Standardize menu. In the Standardize dialogue, double-click column containing data to display under Input column(s): and identify column to Store results in:. Click OK to convert data to standard (z) scores. Relative Frequency Probabilities Input data for X values and frequencies in two columns in worksheet. Label column headings. Select Calc > Calculator menu. Identify column, or type a new column label, in Store result in variable:. In Expression: window, double-click column with frequency data, then click / (division sign), then under Functions: scroll down and select Sum, then double-click column with frequency data. Expression should be similar to 'f' / SUM('f'). Click OK to display relative frequency probabilities. Contingency Table Input appropriate data in two columns. Label column headings. Select Stat > Tables > Cross Tabulation and Chi-Square. Double-click desired columns under Categorical variables: For rows and For columns:. Select Count Row percents Column percents Total Percents as required. Click OK. Factorials, Permutations, and Combinations Minitab Release 14 does not have built-in functions for Factorials, Permutations, and Combinations and does not handle very large values without an overflow. The solution is with the use of a natural logarithm expression. Select Calc > Calculator. In Store result in variable:, indicate desired column. In Expression, type the following (replace n and r with desired values), then click OK. Factorial EXPO (LNGAMMA(n +1) - LNGAMMA (r +1) - LNGAMMA(n - r +1)) Permutation EXPO (LNGAMMA(n+1) - LNGAMMA(n-x+1)) Combination EXPO (LNGAMMA(n+1) - LNGAMMA(r+1) - LNGAMMA(n-r+1)) Note: In Minitab Release 15 replace above expressions, respectively, with FACTORIAL(n), PERMUTATION(n,r) and COMBINATION(n,r). Binomial Probability Distribution Input data (X values) in column and type heading label. Label 2 nd column for probabilities (i.e. P(X)). Select Calc > Probability Distributions > Binomial. In dialogue box, check Probability, and specify Number of trials: and Probability of success:. Indicate location of Input column: {X values} and Optional storage: {P(X)}. Click OK to display probabilities. Note: If a single binomial probability is desired, type X value in Input constant: instead of using Input column. Bluman & Mayer, Elementary Statisitics, A Step by Step Approach, Canadian Edition Minitab Page 3 of 8

4 Note: If cumulative or inverse cumulative binomial probabilities are desired, check appropriate boxes instead of Probability: in dialogue box. Graph Binomial Distribution Create a binomial probability distribution in worksheet. Select Graph > Scatterplot > Simple. Click Data View > Select Data Display, and check only Project Lines > OK. Click Labels {type an appropriate title and subtitle} > OK. Optional: change Scale > Gridlines > OK twice to display graph. Poisson Probability Distribution Input data (X values) in column and type heading label. Label 2 nd column heading for probabilities (i.e. P(X)). Select Calc > Probability Distributions > Poisson. In dialogue box, check Probability, and specify Mean:. Identify location of Input column: {X values} and Optional storage: {P(X)}. Click OK to display probabilities. Note: If a single binomial probability is desired, type X value in Input constant: instead of using Input column. Note: If a cumulative or inverse cumulative binomial probabilities are desired, check appropriate boxes instead of Probability: in dialogue box. Standard Normal Distribution Select Calc > Probability Distributions > Normal. In dialogue box, check Cumulative Probability, and specify Mean: 0 and Standard Deviation: 1. Select Input constant: {type desired z-score}. Click OK to display area to the left of z-score. Note: To calculate areas to the right of z-score, store probability for area to the left as a variable (i.e. K1) in Optional Storage:. Select Calc > Calculator > {type new variable (i.e. K2) in Store result in variable:}. Type Expression: {i.e. 1 K1}. Click OK. To display areas to the left and right, respectively, select Data > Display Data > select variables {i.e. K1 and K2}. Click OK. Note: To find a z-score given an area, in Normal dialogue box, check Inverse cumulative probability. Specify Mean: 0 and Standard Deviation: 1. Check Input constant: {type desired area to the left}. Click OK to display z-score. Determining Normality Graphical Method Input data in worksheet and label column. Select Stat > Basic Statistics > Graphical Summary. In Variables: double-click column data label. Click OK. *Check for a bell-shaped curve on histogram. Normal Probability Plot Method Input data in worksheet and label column. Select Graph > Probability Plot > select Single. In Graph variables: double-click column data label. Click Distribution > Distribution tab > select Normal. Click OK. Click Labels: and input appropriate title and subtitle. Click OK twice. * Check for linearity of point on graph. Normality Test Method Input data in worksheet and label column. Select Stat > Basic Statistics > Normality Test > In Variable: double-click column data label. Select desired Tests for Normality. Enter Title. Click OK. * Check for linearity of point on graph. Confidence Interval Estimate Bluman & Mayer, Elementary Statisitics, A Step by Step Approach, Canadian Edition Minitab Page 4 of 8

5 Normal z Interval (means) Input data in worksheet and label column. If σ is known, continue to next step*. If σ is not known, select Calc > Column > check Standard deviation > In Input variable: doubleclick column data > In Store results in: type a variable name (i.e. s). Click OK. *Select Stat > Basic Statistics > 1-Sample Z > In Samples in columns: double-click column data label. In Standard deviation: type σ (if known) or variable for standard deviation {i.e. s). > Click Options > In Confidence level: type desired level of confidence. In Alternative: not equal to. Click OK twice to display results. t Interval (means) Input data in worksheet and label column. Select Stat > Basic Statistics > 1-Sample t > In Samples in columns: double-click column data label > Click Options > In Confidence level: type desired level of confidence. In Alternative: not equal to. Click OK twice to display results. Note: If data is not given but summary statistics are known, type values for Sample size:, Mean:, and Standard deviation: in appropriate boxes under Summarized data. Normal z Interval (proportions) No data will be input in worksheet. Select Stat > Basic Statistics > 1 Proportion > Check Summarized data, input appropriate values for Number of trials: and Number of events:.> Click Options > In Confidence level: type desired level of confidence. In Alternative: not equal to. Click OK twice to display results. Variance Minitab Release 14 does not include a confidence interval estimate for variances and standard deviations. This feature will be available in Release 15. Hypothesis Tests Normal z Test (means) Repeat Normal z Interval (means) procedure except in Test mean: type hypothesized mean value > Click Options > In Confidence level: input 1 significance level (α) (i.e. if α = 0.05, 1 α = 0.95, use 95). Change Alternative: to less than or not equal or greater than as required. Click OK twice to display results including z-score and P-value. t Test (means) Repeat t Interval (means) procedure except in Test mean: type hypothesized mean value > Click Options > In Confidence level: input 1 significance level (α) (i.e. if α = 0.01, 1 α = 0.99, use 99). Change Alternative: to less than or not equal or greater than as required. Click OK twice to display results including z-score and P-value. Normal z Test (proportions) Repeat Normal z Interval (proportions) procedure except in Options > Confidence level: input 1 significance level (α) (i.e. if α = 0.10, 1 α = 0.90, use 90). In Test proportion: type value for test. Change Alternative: to less than or not equal or greater than as required. Add check to Use test and interval based on normal distribution. Click OK twice to display results including z-score and P-value. Variance Minitab Release 14 does not include a confidence interval estimate for variances and standard deviations. This feature will be available in Release 15. Hypothesis Test Difference Between Two Means Large Independent Samples Input two columns of data with headings. Select Stat > Basic Statistics > 2-Sample t. Select Samples in different columns. In First: double-click first column data label. In Second: double-click second column data label. Click Options > In Confidence level: input 1 significance level (α) (i.e. if α = 0.05, 1 α = 0.95, use 95). In Test difference: 0.0. In Change Alternative: to less than or not equal or greater than as required. Click OK twice to display results including t-value and P-value. Small Independent Samples with Equal Variances Repeat procedure for Large Independent Samples except in dialogue check Assume equal variances. Bluman & Mayer, Elementary Statisitics, A Step by Step Approach, Canadian Edition Minitab Page 5 of 8

6 Small Dependent Samples Input two columns of data with headings. Select Stat > Basic Statistics > Paired t. Select Samples in columns. In First sample: double-click first column data label. In Second sample: double-click second column data label. Click Options > For Confidence level: input 1 α (as a %), Test mean: 0 and Alternative: less than or not equal or greater than as required. Click OK twice to display results. Hypothesis Test Difference Between Two Variances Input two columns of data with headings. Select Stat > Basic Statistics > 2-Variances. Select Samples in different columns. In First: double-click first column data label. In Second: double-click second column data label. Click Options > In Confidence level: input 1 significance level (α) (i.e. if α = 0.05, 1 α = 0.95, use 95). Type appropriate title. Click OK twice. A graph window is displayed. On the right, under F-Test are displayed the values of the test statistic and P-value for a two-tailed test. Divide P-value by 2 for a one-tailed test. Hypothesis Test Difference Between Proportions No worksheet data is required. Select Stat > Basic Statistics > 2-Proportions. Select Summarized data. In First: and Second: input Trials: and Events: data. Click Options > In Confidence level: 1 α (as a %), Test difference: 0 and Alternative: not equal. Check box Use pooled estimate of p for test. Click OK twice to display results. Scatter Plot Input two columns of paired data (x,y) with headings. Select Graph > Scatterplot > Simple. For Y variables, double-click second column data label. For X variables, double-click first column data label. Click Data View > Data Display > check Data Display Symbols box. Click OK. Click Labels > input appropriate Title and Subtitle in Titles/Footnotes. Click OK twice to display graph. Correlation Coefficient Input two columns of paired data (x,y) with headings. Select Stat > Basic Statistics > Correlation. For Variables, double-click second column data label (Y Variable), then double-click first column data label (X Variable). Check box Display p-values. Click OK to display result. Equation of Regression Line Input two columns of paired data (x,y) with headings. Select Stat > Regression > Regression. For Response:, double-click second column data label (Y Variable) For Predictors: double-click first column data label (X Variable). Click Storage > check boxes Residuals and Fits. Click OK twice to display regression equation. Note: Two columns are added to worksheet containing fitted values and residuals. Multiple Regression Input columns of data with headings. Click Stat > Regression > Regression. In Response: double-click dependent variable column heading. In Predictors: double-click each independent variable column heading. Click Storage > check box for Residuals and Fits. Click OK twice to display statistics including the multiple regression equation, F (test statistic) and P (P-value). Chi-Square Hypothesis Test Bluman & Mayer, Elementary Statisitics, A Step by Step Approach, Canadian Edition Minitab Page 6 of 8

7 Χ 2 Goodness-of-Fit Input observed counts in C1 and expected counts in C2 with headings O and E respectively. Select Calc > Calculator. In Store result in variable:., type 1 st variable name: (i.e. K1). In Expression box, type formula type SUM((O-E)**2/E). Click OK to display result in variable (i.e. K1). Calculate the P-value. Select Calc > Probability Distributions > Chi-square. Select Cumulative probability, type Degrees of Freedom appropriate to data. In Input Constant, double-click saved variable (i.e. K1) from variable list. In Optional Storage, type 2 nd variable name (i.e. K2), which is area to left of test statistic. The P-value is the area to the right. Click OK. Select Calc > Calculator. In Store results in variable: box, type 3 rd variable name (i.e. K3). In expression: box type, 1-{2 nd variable}, (i.e. 1-K2). Click OK. To display the 3 rd variable (i.e. K3) value (P-value), open Window > Project Manager, under Worksheets Constants. Χ 2 Independence Test or Contingency Table Test Input observed frequencies in columns. Label columns but not rows. Select Stat > Tables > Chi-Square Test. Highlight all columns in list. Click Select to move into Columns containing the table box. Click OK to display statistics including Chi- Square test statistic and P-value. One-Way Analysis of Variance (ANOVA) Input columns of data with headings. Select Stat > ANOVA > One-Way (Unstacked). Highlight all columns in list. Click Select to copy list to Responses (in separate columns):. Click OK to display results including F (test statistic) and P (P-value). Two-Way Analysis of Variance Input column data and label headings. Select Stat > ANOVA > Two-Way In Response: double-click dependent variable column label. In Row factor: double-click 1 st independent variable column label. In Column factor: double-click 2 nd independent variable column label. Click OK to display results. To plot data, select Stat > ANOVA > Interactions Plot... In Responses: double-click dependent variable column label. In Row factor: double-click independent variable column labels. OK to display results. The Sign Test Input column data and label headings. Select Stat > Nonparametrics > 1-Sample Sign In Variables: double-click column label. Click on Test median: input hypothesized value. Alternative: select appropriate test. Click OK to display results including P (P-value). The Paired-Sample Test Input two columns of data and label headings (i.e. Before and After). Select Calc > Calculator. In Store result in variable: type variable name (i.e. D for difference). In Expression: double-click 1 st (i.e. Before) column, minus, double-click 2 nd (i.e. After) column. Click OK to display differences in 3 rd or next available column (i.e. column labeled D). Repeat the instruction for the Sign Test on the differences (i.e. D) with hypothesized value of 0. Wilcoxon Rank Sum Test (Mann-Whitney) Input two columns of data and label headings. Select Stat > Nonparametric > Mann-Whitney. In First Sample: double-click 1 st column label. In Second Sample: double-click 2 nd column label. Specify Confidence level: and Alternative:. Click OK to display results. Wilcoxon Signed-Rank Test Bluman & Mayer, Elementary Statisitics, A Step by Step Approach, Canadian Edition Minitab Page 7 of 8

8 Repeat the Paired-Sample Test procedure except in the final step select Stat > Nonparametric > 1-Sample Wilcoxon. In Variables: select C3 (i.e. D), click Test median: input 0. Click OK to display results including P (P-value). Kruskal-Wallis Test Input two columns of data (stacked) with numeric data in one column and associated labels in the second columns. Label column headings. Select Stat > Nonparametric > Kruskal-Wallis. In Response: double-click column with numeric data. In Factor: double-click the column with labels. Click OK to display results. Runs Test for Randomness Input data in column 1 in the same order collected. Label heading. Select Calc > Column Statistics. Check Median: option. In Input Variable: double-click column label. In Store result in: type appropriate name for data. Click OK. Select Stat > Nonparametric > Runs Test. In Variables: double-click column label. Click Above and below, then select name specified in previous step. Click OK to display results including P-value. Random Sample With Replacement Select Calc > Random Data > Integer. Type value in Generate rows of data. In Store in column(s):, type a column name. Type desired Minimum value: and Maximum value:. Click OK to display result on worksheet. Without Replacement Select Calc > Make Patterned Data > Simple Set of Numbers. In Store patterned data in: type column heading. In From first value: and To last value: type desired range (minimum and maximum). Leave In steps of: 1. Click OK to display values in named column. Select Calc > Random Data > Sample from columns. Sample a portion of the range (i.e. If 50 values, sample 10). In Store sample in: type a new column name. Click OK to display results on worksheet. Normal Distribution Select Calc > Random Data > Normal Type value in Generate rows of data. In Store in column(s):, type a column name. Type desired values for Mean: and Standard deviation:. Click OK to display results on worksheet. Note: To display data in session window, select Data > Display data, double-click desired column label. Click OK. Bluman & Mayer, Elementary Statisitics, A Step by Step Approach, Canadian Edition Minitab Page 8 of 8