8. MINITAB COMMANDS WEEK-BY-WEEK

Transcription

1 8. MINITAB COMMANDS WEEK-BY-WEEK In this section of the Study Guide, we give brief information about the Minitab commands that are needed to apply the statistical methods in each week s study. They are numbered by weeks in the same way as the Study Schedule in Chapter 2. Minitab instructions We have not attempted to write a full manual about using Minitab to analyse your data we would need to write a second Study Guide for that! However Minitab has so many different commands in its menus (and sub-menus) and each has so many options that some guidance is necessary to point you in the right direction each week. Instead of writing full notes about the commands for each graphical display and statistical analysis in the course, we have therefore only specified the name of the command (and the menu and sub-menu where it can be found) and a list of the options from the command s dialog box that are relevant to this course. (The dialog boxes often have many other options but, if they are not mentioned here, you are strongly advised to leave them alone!) This guide is not intended for reading on its own. Only use it when you have Minitab running and have opened some worksheet containing variables of the type that are being analysed that week. (Minitab comes with many data sets that can be used or you can type in your own data.) Try out the command that is described, and investigate the various options that we mention. This experimental approach is the best way to learn. We believe that you should be able to pick up enough from this guide (and a bit of common sense) to use Minitab perform all the analyses in this course. However if you find difficulty with any command, Minitab s help system provides a more wordy and extensive description. Remember that you can t hurt Minitab (or your data files if you don t save changes) by experimenting with its commands and options. -93-

2 Shorthand For most statistical methods, we therefore simply specify the menu command, followed by a list of the options that you will need to specify or alter in the resulting dialog box. Occasionally we make a brief comment about the options, but they are usually selfexplanatory. (See Minitab s help if you do not agree!) We use a shorthand to describe the commands and dialog box options. In each case, we assume that you already have the data that you want to analyse in one or more columns of a Minitab worksheet. Select the relevant command from a Minitab menu (or, more often, a sub-menu or sub-sub-menu) and specify the details of the analysis in a dialog box using check boxes, radio buttons or pop-up menus to select options, typing values or variable names in text-edit boxes and clicking buttons. Select a command from a sub-sub-menu Menu Sub-menu Sub-menu Select an option in a dialog box using a radio button Type a value or variable name in a text edit box. You can often double-click variable names on a list elsewhere in the dialog box instead of typing their names. Option Type something : Click a button to display further options. Turn on an option using a check box Option Select an option from a list in a pop-up menu. Pop-up menu : The instructions in the study guide are those for Minitab version

3 Week 1 Introduction Install Minitab on your computer (or make sure that you have access to it). Read the previous chapter to familiarise yourself with the overall structure of Minitab. Exploring Categorical Data: Pie charts and Bar charts Bar charts and pie charts for a single data set can be produced from data in two different formats. The first is a raw data format in which each Minitab row corresponds to a single individual. For example, Individual John Mary Nicole Philip Hair Black Blonde Black The alternative format is a frequency table a summarised form of the raw data. Many data sets are provided in this form. It has the category names in one Minitab column and the frequencies in a second column: Hair Red Frequency Black 53 Blonde 23 Brunette 75 Red 17 Pie Chart... Chart raw data Categorical variables: Name of a variable containing categorical values (e.g. Black, Blonde, Red, ) Chart values from a table Categorical variable: Summary variable: Minitab column containing the distinct category names Minitab column containing the frequencies associated with these category names Investigate the other options in this dialog box -95-

4 Bar chart... Bars represent: One column of values: variables: Categorical variable: Minitab column containing the frequencies Minitab column containing the distinct category names Bars represent: One column of values: variables: Categorical variable: Minitab column containing the frequencies Minitab column containing the distinct category names -96-

5 Week 2 Exploring Univariate Data: Stem-and-leaf Plots Stem-and-Leaf... Variables: specify the Minitab variable name Exploring Univariate Data: Histograms, Transformations & Discrete Data Histogram... Variables: specify the Minitab variable To transform a variable (and put the result in a new variable): Calc Calculator... Store result in variable: Expression: name of new variable to be created use list of variables and list of functions to write the expression Minitab will not produce back-to-back stem and leaf plots or histograms. Exploring Univariate Data: Dot Plots For a dot plot of a single variable, Dotplot... One Y: Variables: Note that Minitab will not draw jittered dot plots. For dot plots to compare two or more groups, there are two ways that the data may be stored. If the groups are in separate Minitab columns, Dotplot... Multiple Y s: Variables: Enter names for the different columns (groups) -97-

6 If the values are stored in a single Minitab columns and a second column distinguishes between the groups, Dotplot... One Y: Variables: By variable: Enter name of single column containing values The variable here should be a Minitab column that distinguishes between the groups (e.g. with values male and female ) Exploratory Univariate Data: Box plot A single box plot can be drawn, but we only recommend box plots for comparing groups. As for dot plots, the method depends on whether the groups are stored as different columns in Minitab. Boxplot... Multiple Y s: variables: Names for the different columns (groups) Or... Boxplot... One Y: variables: Categorical variable: Single column containing values Column distinguishing groups Exploratory Univariate Data: Quartiles and Summary Statistics Stat Basic Statistics Display Descriptive Statistics... Variables: enter the name of a variable Various summary statistics for the variable are output. If there are two or more groups in the data, use the following option in the dialog box: By variable: enter the name of a variable that distinguishes between the groups (e.g. values male and female ) -98-

7 Week 3 Exploring Bivariate Data: Scatterplots Scatterplot... Option Y variable: X variable: variable displayed on vertical axis (response) variable on horizontal axis (explanatory) Exploring Bivariate Data: Least squares and Nonlinear relationshipa Stat Regression Fitted Line Plot... Response [Y]: Predictors [X]: Type of Regression Model Linear Quadratic fits a least squares straight line to the data fits a quadratic curve by least squares the resulting dialog box lets you save residuals and fitted values as new Minitab columns. You can then plot the residuals. Exploring Bivariate Data: Correlation Stat Basic Statistics Correlation... Variables: Display p-values enter the names of 2 or more Minitab variables you can t interpret p-values yet, so don t ask for them! -99-

8 Multivariate data Matrix Plot... Matrix of plots: Variables: if you enter the names of 3 or more variables, a scatterplot matrix will be drawn Editor Brush If you select this option, you can then click on points in graphs (or drag over a group of points) and they will be highlighted in all graphs. Editor Set ID Variables This lets you specify what Minitab column should be used as a name to identify the brushed points on a scatterhplot matrix they are printed on the brushing palette. 3D Scatterplot... Option: Variables: Z Y X This produces a 3-dimensional scatterplot of the three variables. (Rotation is not particularly intuitive though.) -100-

9 Week 4 Exploring Time Series Time Series Plot... Option: variables: Time Scale Index enter the name of a variable the time axis just shows the order number or Calendar: allows you to label the axis with days, months, quarters, etc. the options in the resulting dialog box let you choose the initial date that is displayed on the time axis (see the help button in the dialog box) -101-

10 Relationships between Categorical Variables: Clustered and Stacked Bar Charts For situations where there are two categorical variables (or a categorical variable and two or more groups) there are three different ways in which the data may be stored. Minitab has options for drawing bar charts for each. A. There may be a row for each individual and two Minitab columns with values that distinguish between the categories (or groups). For example, Name Hair Gender John Black Male Mary Blonde Female Angela Black Female Martin Red Male Bar chart... Bars represent: Option: or We don t go into further details for this layout B. The second possible format for this type of data is a condensed form of the above with an extra column containing frequencies for the different combinations of the two categorical variables. For example, Hair Gender Frequency Black Male 53 Blonde Male 23 Brunette Male 75 Red Male 17 Black Female 62 Blonde Female 13 Brunette Female 44 Red Female 29 Bar chart... Bars represent: One column of values: or variables: Column containing frequencies Categorical variable: Enter 2 variable names here. The 2 nd is used to stack/cluster the bars -102-

11 C. Finally, the data can be arranged in a conventional contingency table layout. For example, Hair Male Female Black Blonde Brunette Red Bar chart... Bars represent: Two-way table: or variables: Row labels: Minitab columns containing the frequencies (Male and Female above) Minitab column containing the names of the row categories (Hair above) In A, B and C above, it is possible to draw the bars with heights equal to the proportions within the major clusters (or stacks). Show Y as Percent Within categories at level 1 To produce a frequency table or contingency table (format C. above) from a table of raw data that is laid out as in A. above, Stat Tables Cross Tabulation and Chi-square... For rows: For cols: Minitab columns containing categorical variable Minitab column containing categorical variables If the data are laid out as in B. above, you can produce a table like C. by also specifying the column of frequencies Frequencies are in: Column with frequencies -103-

12 Data Presentation There are no new MINITAB commands for this section of the course. Week 5 About Relationships Again, there are no new MINITAB commands to learn for this section Sample Surveys and Experiments Again, there is nothing new in MINITAB Week 6 Probability and Random Variables Again, there is nothing new in MINITAB -104-

13 Week 7 Variability of Sample Means & Central Limit Theorem Stat Basic Statistics Display Descriptive Statistics... Variables: specify variable name Minitab displays various summary statistics, including SE_MEAN = s n Normal Distributions Calc Probability Distributions Normal... Cumulative probability Mean: for parameter µ St devn: for parameter σ Input constant: Minitab shows P(X x) in the Session Window for constant x Variability of Proportions & Binomial Distribution Calc Probability Distributions Binomial... Probability Number of trials: Probability of success: for parameter n for parameter π Input constant: Minitab shows P(X = x) in the Session Window. for constant x If you choose Cumulative probability, Minitab shows P(X x) instead. Week 8 This is your week to take a break or catch up! -105-

14 Week 9 Inference: Confidence Intervals for the Mean Stat Basic Statistics 1-Sample t... Sample in columns: specify variable name Minitab displays the confidence interval in the Session Window Inference: Confidence Intervals for a Proportion Stat Basic Statistics 1 Proportion... Summarized Data Number of trials: Number of events: for parameter n for observed count, x Use test and interval based on normal dist Minitab displays the confidence interval in the Session Window. It is actually better not to set the checkbox for basing the confidence interval on the normal distribution the normal approximation on which it is based is not valid for small n and Minitab can work out a confidence interval using a more accurate method but the textbook and CAST only describe confidence intervals based on the normal approximation so you will need to set the option in order to get an interval that is the same as you would have calculated by hand

15 Week 10 Inference: Hypothesis Tests about Proportions Stat Basic Statistics 1 Proportion... Summarized Data Number of trials: Number of events: for parameter n for observed count, x Test proportion: Alternative: hypothesised value of π to request a 1- or 2-tailed test Use test and interval based on normal dist As with confidence intervals for a proportion, it is really better not to set the above checkbox when testing a proportion, but the results you get will not be the same as those you obtain by hand unless you do. Inference: Hypothesis Tests about Means Stat Basic Statistics 1-Sample t... Variables: specify variable name Test mean: for the hypothesised value of µ Alternative: to request a 1- or 2-tailed test Minitab displays the t statistic and p-value in the Session Window -107-

16 Week 11 Inference: Comparing Two Means or Proportions To test whether the means of two groups are the same, based on two independent samples, you can use a single Minitab column to hold all values and a second column to hold either 1 or 2 to distinguish between the groups. To do inference on the difference between the two means, Stat Basic Statistics 2-Sample t... Samples in one column Samples: Subscripts: specify variable with the data specify variable distinguishing the groups Alternative: to request a 1- or 2-tailed test Minitab displays a 95% confidence interval and the p-value for testing whether the means are the same. (It is also possible to do the test with the two samples in different Minitab columns and no column of subscripts with the option Samples in different columns.) Stat Basic Statistics 2 Proportions.. Summarized data First: Second: Trials: Events: Minitab gives the p-value for testing whether the population proportions (probabilities) are the same, and a 95% confidence interval for their difference

17 Week 12 Inference: Regression Models and Inference Stat Regression Regression... Response: specify the response variable Predictors: specify one explanatory variable The Minitab output in the Session Window contains information like... The p-values for testing are given in the output. To find 95% confidence intervals, calculate Coef ± t x Stdev, where t is obtained from t-tables. Other useful options in the Regression dialog box are use this to ask for residual plots use this to ask for prediction intervals Prediction intervals for new observations: type the x-values at which you want to predict -109-

18 Week 13 Testing Independence in Contingency Tables To test for independence in a contingency table with r rows and c columns, the counts must first be entered into the first r rows of c Minitab columns (i.e. in format C. that was described in Week 4). Stat Tables Chi-Square Test... Columns containing the table: specify the names of the columns containing the counts. The Minitab output contains the estimated cell counts (assuming independence) and the chi-squared statistic and p-value for the test. Comparing the Means of Several Groups To test whether the means of several groups are the same, all values of the response must be stored in a single Minitab column and a second column should hold a number (1, 2, ) to distinguish between the groups. Stat ANOVA One-way... Response: specify the response variable Factor: specify variable distinguishing the groups The Minitab output in the Session Window contains information like... Analysis of Variance on YIELD Source DF SS MS F p VARIETY Error Total The rightmost p-value is for testing whether the group means are the same. Week 14 Revision You have now learned all you need to know about Minitab for this course. But remember that some computer output will be included in the exam, so you will need to be reasonably familiar with the output that Minitab provides