1 Minitab Guide This packet contains: A Friendly Guide to Minitab An introduction to Minitab; including basic Minitab functions, how to create sets of data, and how to create and edit graphs of different types Minitab Step-By-Step A guide to the following subjects: 1. Obtaining a Simple Random Sample 2. Frequency of Relative Frequency Distributions from Raw Data 3. Bar Graphs from Summarized Data 4. Bar Graphs from Raw Data 5. Pie Chart from Raw or Summarized Data 6. Histograms 7. Stem-and-Leaf Plots 8. Dot Plots 9. Determining the Mean and Median 10. Drawing Boxplots Using Technology 11. Determining Quartiles 12. Scatter Diagrams 13. Correlation Coefficient 14. Determining the Least-Squares Regression Line 15. The Coefficient and Determination, R Residual Plots 17. Simulation 18. Computing P(x) as Binomial Probabilities 19. Computing P(X x) as Binomial Probabilities 20. Computing P(x) as a Poisson Probabilities 21. Computing P(X x) as a Poisson Probabilities 22. Finding Areas under the Standard Normal Curve 23. Finding z-scores Corresponding to an Area 24. Finding Areas under the Normal Curve 25. Finding Normal Values Corresponding to an Area 26. Normal Probability Plots 27. Confidence Intervals about µ, Known 28. Confidence Intervals about µ, Unknown 29. Confidence Intervals about p 30. Confidence Intervals about σ 31. Hypothesis Tests Regarding µ, σ Known 32. Hypothesis Tests Regarding µ, σ Unknown 33. Hypothesis Tests Regarding a Population Proportion 34. Hypothesis Tests Regarding a Population Standard Deviation
2 A Friendly Guide to Minitab I. GET TO KNOW MINITAB 1. OPENING MINITAB. When you start Minitab, you begin with new, empty project that can contain three different types of windows: a. Session window b. Worksheet window c. Graph window The session window and worksheet window are default and open up every time the new project is opened. Every command and procedure is recorded in session window. Session window also displays the results of certain commands (like basic statistics). You can copy anything from and into it as well as type any comments. However it doesn t have as many editing options as for example Word. Worksheet is used to enter the data. Its default format is columns. You can change it to rows by clicking on an arrow in the first upper left corner. Columns have 3 formatting settings: Text, Numeric and Date/Time. The normal setting is numeric. If the column has T in its label it is text, if it has D, it s Date/Time. Obviously any calculations in Minitab can be done only with numeric data. Sometimes students copy data from different source. The Minitab may stubbornly copy it as text even if you try to change the column s format. 2. EDITING: Anything from the Minitab can be copied and passed to Word and then edited as desired. 3. PRINTING: Because of 3 different windows, when printing, make sure that the window you want to print is active. 4. NOTE 1: You can minimize any window in Minitab; also if you have multiple windows open, the inactive windows can be hidden behind active windows. So if something disappears from the screen, minimize your windows and you should be able to find it eventually.
3 5. NOTE2: Sometimes students have played with Minitab for a while and have checked or unchecked one of the options in whatever they were doing. If they cannot undo that and now the histogram, box-and-whiskers display, scatterplot, etc. comes up messy every time, the best thing to do is to save everything, close Minitab and open it again. It should come back to normal again. 6. HINT: Books for Data Analysis have a Technology Step-By-Step guide at the end of some sections on how to use the technology tools including Minitab. If you are working with a student ask him/ her for a book to look up the proper procedure(s). The book for Engineering Statistics ( ) has no guide to Minitab except for occasional printouts used in examples. Students taking Probability and Statistics for Engineers ( ) are not required to complete Minitab projects. Also some of the statistics books contain the tables and formulas with explanation of notations either on the inside covers of the book or in one of the appendixes. So even if you are not familiar with a particular symbol you may know very well the concept behind it. When you work with a student on his/her project leave any interpretation up to the student.
4 II. WORKING IN MINITAB 1. CREATING A SET OF DATA IN MINITAB a. From previously created set: (Example: rolling a fair six-sided die) i. Create the set to sample from: Calc > Make Patterned Data > Simple Set of Numbers Store it in C1, from first value (choose a number) to last value (choose a number) in steps of 1 ii. Sample from (created) set: Calc > Random Data > Sample From Columns Number of rows:. (whatever number of data pieces you need) From sample C1 Store data in C2 (do it again with C1 and see what happens). If the data set that you need is larger than your original set that you are sampling from, make sure to check the with replacement box). You can experiment with different types of data (check how much you remember from statistics). iii. Rank sort data: To sort data: Data > Sort To rank date: Data> Rank b. Or you can always type the collected set of data into Minitab. (Make sure that the data is in numeric format) 2. FREQUENCY DISTRIBUTION Stat > Tables > Tally Individual Variables. Select the appropriate column into the Variables: box. Choose one of the options from the results that can be displayed. Counts- (i.e. frequency), -Percents- (i.e. relative frequency) > OK Minitab does not have any option to create a grouped data frequency table. The closest thing to it is a histogram.
5 3. DESCRIPTIVE STATISTICS a. To be displayed in a session window: Stat> Basic Statistics> Display Descriptive Statistics> check columns to calculate the descriptive statistics from>statistics> check whatever measures are needed. b. All required statistics to be shown as single entries in cells of a worksheet: Stat> Basic Statistics> Store Descriptive Statistics> check columns to calculate the descriptive statistics from>statistics> check whatever measures are needed. c. To graph a histogram, test for normality and display all statistics: Stat> Basic Statistics> Graphical Summary> OK 4. INFERENTIAL STATISTICS a. Confidence Intervals: i. 1-Sample Z: Stat> Basic Statistics> 1-sample Z > check the alpha level in options. ii. 1-Sample t: Stat> Basic Statistics> 1-sample t > check the alpha level in options. b. Hypothesis Testing: i. 1-Sample Z: Stat> Basic Statistics> 1-sample Z > check the alpha level and alternative hypothesis in options ii. 1-Sample t: Stat> Basic Statistics> 1-sample t> check the alpha level and alternative hypothesis in options 5. REGRESSION AND CORRELATION a. Correlation coefficient: Stat > Basic Statistics >Correlation > choose columns - make sure that you choose a different column for each type of data. b. Regression Equation Stat > Regression > Regression. Select output column for the Response and input column for the Predictors > OK. c. Scatter diagram Graph>Scatterplot> choose simple or with regression > OK > Enter the Y-variables and X variables > OK d. Fitted line plot (Scatter diagram with Regression Lin, Equation and Correlation Coefficient displayed) Stat>Regression>Fitted Line Plot Choose columns for x and y according to the scatterplot you have chosen > OK. To get a horizontal graph, select Scale and click Transpose value and category scales > OK
6 6. HOW TO CREATE AND EDIT A GRAPH IN MINITAB a. To graph a histogram from a row data: Graph > Histogram > Simple or Simple with Fit > Graph variable - choose column with the row data > OK b. To graph a histogram from data organized in a frequency table: Graph > Histogram > Simple or Simple with Fit > Graph variable - choose column with grouped data > Data Options > Frequency choose the column with the frequencies > OK c. To graph a cumulative histogram: Graph > Histogram > Simple or Simple with Fit > Graph variable - choose column with the row data > Scale> Y-scale Type - check Accumulate values across bins box > ok d. To edit a histogram: Do not worry about labeling everything appropriately before you create a histogram. You can always do it on the existing histogram by double clicking on the appropriate area or by clicking on the right button. To change the number of intervals: Double click on the histogram (make sure that you are clicking the whole graph (i.e. all bars are highlighted and not just a single bar)> Binning > Select the appropriate midpoint cutpoint, in interval definition enter the midpoint/cutpoint values separated by space. Or Double click on the histogram>binning > Number of intervals type the number of intervals e. To graph and edit a pie chart from a frequency table: Graph > Pie Chart > check the box: Chart values from a table> enter the categorical data, enter the summary variables> OK f. To graph and edit a box-and whiskers-display from a frequency table: Graph > Box plot > Simple> Choose a column for: Graph variables> OK (this is usually graphed from the row data not grouped data)
7 III. TYPES OF GRAPHS 1. To assess relationships between pairs of variables: a. Scatterplot shows relationship between two variables b. Matrix Plot shows the relationships between many pairs of variables at once. c. Marginal Plot Similar to scatterplot, but adds a histogram or boxplot of each variable in the margins of the graph. 2. To assess distributions: a. Histogram displays the shape and central tendency of data. b. Dotplot similar to a histogram but more useful with small amounts of data. c. Steam-and-Leaf - displays actual data values in binned format. d. Probability Plot Displays how well your data follow a specific distribution. e. Empirical CDF similar to probability plot but its scales are always linear. f. Boxplot (Box-And-Whiskers display) compares sample distribution characteristics such as median, range and symmetry, and identifies outliers. 3. To compare summaries or individual values of a variable a. Boxplot (Box-And-Whiskers display) compares sample distribution characteristics and screens outliers. b. Interval Plot compares means and confidence intervals. c. Individual Value Plot assesses and compares individual data values. d. Bar Chart compares a summary statistic, such as the mean, across grouping levels. e. Pie Chart compares the proportion of each group relative to the whole. 4. To assess distributions of counts: a. Bar Chart compares the distribution of counts. b. Pie Chart compares the proportion of each group relative to the whole. 5. To plot a series of data over time: a. Time Series Plot- for data that was collected in equally spaced time intervals and is in chronological order. b. Area Graph shows how the compositions of the sum changes over time with stacked data. c. Scatterplot for data that is collected at irregular intervals or not in chronological order in the worksheet.
8 MINITAB STEP BY STEP A guide to the following subjects: 35. Obtaining a Simple Random Sample 36. Frequency of Relative Frequency Distributions from Raw Data 37. Bar Graphs from Summarized Data 38. Bar Graphs from Raw Data 39. Pie Chart from Raw or Summarized Data 40. Histograms 41. Stem-and-Leaf Plots 42. Dot Plots 43. Determining the Mean and Median 44. Drawing Boxplots Using Technology 45. Determining Quartiles 46. Scatter Diagrams 47. Correlation Coefficient 48. Determining the Least-Squares Regression Line 49. The Coefficient and Determination, R Residual Plots 51. Simulation 52. Computing P(x) as Binomial Probabilities 53. Computing P(X x) as Binomial Probabilities 54. Computing P(x) as a Poisson Probabilities 55. Computing P(X x) as a Poisson Probabilities 56. Finding Areas under the Standard Normal Curve 57. Finding z-scores Corresponding to an Area 58. Finding Areas under the Normal Curve 59. Finding Normal Values Corresponding to an Area 60. Normal Probability Plots 61. Confidence Intervals about µ, Known 62. Confidence Intervals about µ, Unknown 63. Confidence Intervals about p 64. Confidence Intervals about σ 65. Hypothesis Tests Regarding µ, σ Known 66. Hypothesis Tests Regarding µ, σ Unknown 67. Hypothesis Tests Regarding a Population Proportion 68. Hypothesis Tests Regarding a Population Standard Deviation 1. Obtaining a Simple Random Sample 1. Select the Calc menu and highlight Set Base Enter any seed number you desire. [Note that it is not necessary to set the seed, because MINITAB uses the time of day in seconds to set the seed.] 3. Select the Calc menu, highlight Random Data, and select Integer Enter a. the number of pieces of data you wish to generate (i.e. the number of rows ) b. which column to place the random data into c. the minimum and maximum data values 5. Click OK
9 2. Frequency of Relative Frequency Distributions from Raw Data 1. Enter the raw data in C1. 2. Select Stat and highlight Tables and select Tally Individual Variables Fill in the window with appropriate values. In the Variables box, enter C1. Check counts for a frequency distribution and/or percents for a relative frequency distribution. Click OK. 3. Bar Graphs from Summarized Data 1. Enter the categories in C1 and the frequency or relative frequency in C2. 2. Select Graph and highlight Bar Chart. 3. In the Bars represent pull-down menu, select Values from a table and highlight Simple. Press OK. 4. Fill in the window with the appropriate values. In the Graph variables box, enter C2. In the Categorical variable box, enter C1. By pressing Labels, you can add a title to the graph. Click OK to obtain the bar graph. 4. Bar Graphs from Raw Data 1. Enter the raw data in C1 2. Select Graph and highlight Bar Chart. From pulldown menu Bar represents choose values from a table. 3. In the Bars represent pull-down menu, select Counts of unique values and highlight Simple. Press OK 4. Fill in the window with the appropriate values. In the Categorical variable box, enter C1. By pressing Labels, you can add a title to the graph. Click Ok to obtain the bar graph. 5. Pie Chart from Raw or Summarized Data 1. If the data are in a summarized table, enter the categories in C1 and the frequency or relative frequency in C2. If the data are raw, enter the data in C1. 2. Select Graph and highlight Pie Chart. 3. Fill in the window with the appropriate values. If the data are summarized, click the Chart values from a table radio button; if the data are raw, click the Chart raw data radio button. For summarized data, enter C1 in the Categorical variable box and C2 in the Summary variable box. If the data are raw, enter C1 in the Categorical variable box. By pressing Labels, you can add a title to the graph. Click OK to obtain the pie chart. 6. Histograms 1. Enter the raw data in C1. 2. Select the Graph menu and highlight Histogram Highlight the simple icon and press OK. 4. Put the cursor in the Graph Variables box. Highlight C1 and press Select. Click SCALE and select the Y-Scale Type tab. For a frequency histogram, click the frequency radio button. For a
10 frequency histogram, click the frequency radio button. For a relative frequency histogram, click the percent radio button. Click OK twice. Note: To adjust the class width and to change the labels on the horizontal axis to the lower class limit, double-click inside one of the bars in the histogram. Select the binning tab in the window that opens. Click the cut point button and the midpoint/cutpoint positions radio button. In the midpoint/cutpoint box, enter the lower class limits of each class. Click OK. 7. Stem-and-Leaf Plots 1. With the raw data entered in C1, select the Graph menu and highlight Stem-and-Leaf. Select the data in C1 and press OK 2. Select the data in C1 and press OK. 8. Dot Plots 1. Enter the raw data in C1. 2. Select the Graph menu and highlight Dotplot. 3. Highlight the simple icon and press OK. 4. Put the cursor in the Graph variables box. Highlight C1 and press Select. Click OK. 9. Determining the Mean and Median (and more) 1. Enter the data in C1. 2. Select the Stat menu, highlight Basic Statistics, and then highlight Display Descriptive Statistics. 3. In the Variables window, enter C1. Click OK 4. Select Statistic if other statistical values are desired. 10. Drawing Boxplots Using Technology 1. Enter the raw data into column C1. 2. Select the Graph menu and highlight Boxplot For a single boxplot, select One Y, simple. For two or more boxplots, select Multiple Y s, simple. 4. Select the data to be graphed. If you want the boxplot to be horizontal rather than vertical, select the Scale button, and then transpose value and category scales. Click OK. 11. Determining Quartiles Follow the same steps given to compute the mean and median from raw data.
11 12. Scatter Diagrams 1. Enter the explanatory variable in C1 and the response variable in C2. You may want to name the variables. 2. Select the Graph menu and highlight Scatterplot Highlight the Simple icon and click OK. 4. With the cursor in the Y column, select the response variable. With the cursor in the X column, select the explanatory variable. Click OK 13. Correlation Coefficient 1. With the explanatory variable in C1 and the response variable in C2, select the Stat menu and highlight Basic Statistics. Highlight Correlation. 2. Select the variables whose correlation you wish to determine and click OK. 14. Determining and Graphing the Least-Squares Regression Line 1. With the explanatory variable in C1 and the response variable in C2, select the Stat menu and highlight Regression. Highlight Fitted Line Plot and check linear 2. Select the explanatory (predictor) variable and response variable and click OK. 3. Look for outputted Regression Analysis located in the session box as well as the outputted graph. 15. The Coefficient and Determination, R 2 This is provided in the printed Regression Analysis (see #14 above) 16. Residual Plots Follow the same steps as those used to obtain the regression output (#14 above). Before selecting OK, click Graphs. In the cell that opens labeled Residuals versus the variables, enter the column name for the explanatory variable. Click OK Two graphs will be displayed. 17. Simulation 1. [Optional see note in #1] Set the seed by selecting the Calc menu and highlighting Set Base... Insert any seed you with into the cell and click OK. 2. Select the Calc menu, highlight Random Data, and then highlight Integer. To simulate rolling a single die 100 times, fill in the windows shown to determine the number of trials (100) and the range of outcomes for each trial (minimum value = 1 and maximum value = 6). 3. Select the Stat menu, highlight Tables, and then highlight Tally... Enter C1 into the variables cell. Make sure that the Counts box is checked and click OK.
12 18. Computing P(x) as Binomial Probabilities 1. Enter the possible values of the random variable X in C1. For example, with n = 15, p = 0.3, enter 0,1,2..., 15 into C1. [Calc>Make Patterned Data>Simple Set of Numbers] 2. Select the CALC menu, highlight Probability Distributions, then highlight Binomial Choose Probability at the top; Number of Trials = n, Event Probability = p, Input Column = C1 from step #1. 4. Specify Optional Storage if you d like the data placed in a column instead of your session page. 5. Click OK. 19. Computing P(X x) [ Cumulative Probability ] as Binomial Probabilities Follow the same steps as those for computing P(x) in #18 above. In the window that comes up after selecting Binomial Distribution, select Cumulative probability instead of Probability. 20. Computing P(x) as a Poisson Probabilities 1. Enter the desired values of the random variable X in C1. 2. Select the CALC menu, highlight Probability Distributions, then highlight Poisson Select Probability, enter the mean, enter the input column as C1, and specify Optional Storage if you d like the data placed in a column instead of your session page. 3. Click OK. 21. Computing P(X x) as a Poisson Probabilities Follow the same steps as those followed for computing the Poisson Probability in #20 above. In the window that comes up after selecting Poisson distribution, select Cumulative probability instead of Probability. 22. Finding Areas under the Standard Normal Curve Note: MINITAB will find an area to the left of a specified z-score. 1. Select the Calc menu, highlight Probability Distributions, and highlight Normal Select Cumulative Probability. Set the mean to 0 and the standard deviation to 1. Select Input Column. Click OK - the area to the left of each data point will be displayed. 3. If you desire to display the area under the curve for just one data point, select Input Constant and enter that one piece of data. Click OK. 23. Finding z-scores Corresponding to an Area Note: MINITAB will find the z-score for an area to the left of an unknown z-score. 1. Select the Calc menu, highlight Probability Distributions, and highlight Normal Select Inverse Cumulative Probability. 3. To display the z-score for just one data point, select Input Constant and enter that one piece of data. Click OK.
13 24. Finding Areas under the Normal Curve 1. Select the Calc menu, highlight Probability Distributions, and highlight Normal Select Cumulative Probability. Enter the mean, µ, and the standard deviation, σ. Select Input Constant, and enter the observation. Click OK. 25. Finding Normal Values Corresponding to an Area 1. Select the Calc menu, highlight Probability Distributions, and highlight Normal Select Inverse Cumulative Probability. Enter the mean, µ, and the standard deviation, σ. Select Input Constant, and enter the area to the left of the unknown normal value. Click OK. 26. Normal Probability Plots 1. Enter the raw data into C1. 2. Select the Graph menu. Highlight Probability Plot... Select Single. Click OK 3. In the Graph variables cell, enter the column that contains the raw data. Make sure Distribution is set to Normal. Click OK. 27. Confidence Intervals about µ, Known 1. If you have raw data, enter them in column C1. 2. Select the Stat menu, highlight Basic Statistics, then click 1-Sample Z If you have raw data, enter C1 in the cell marked One or more samples: each in a column. If you have summarized data, select the Summarized data in the pull-down menu and enter the summarized values. Select Options and enter a confidence level (the alternative hypothesis does not matter for this operation). Click OK. 4. In the cell marked standard deviation, enter the value of σ. Click OK. 28. Confidence Intervals about µ, Unknown 1. If you have raw data, enter them in column C1. 2. Select the Stat menu, highlight Basic Statistics, then highlight 1-Sample t If you have raw data, enter C1 in the cell marked One or more samples: each in a column. If you have summarized data, select the Summarized data in the pull-down menu and enter the summarized values. Select Options and enter a confidence level (the alternative hypothesis does not matter in this case). Click OK twice.
14 29. Confidence Intervals about p 1. If you have raw data, enter the data in column C1. 2. Select the Stat menu, highlight Basic Statistics, then highlight 1 Proportion Enter C1 in the cell marked samples in Columns if you have raw data. If you have summary statistics. Click Summarized data and enter the number of trials, n, and the number of events (successes) x. 4. Click the Options... button. Enter a confidence level, and, from the pull-down menu for Method, Normal Approximation (provided that the assumptions stated are satisfied). [The alternate hypothesis does not matter for this operation.] 5. Click OK twice. 30. Confidence Intervals about σ 1. Enter raw data in column C1 2. Select the Stat menu, highlight Basic Statistics, then highlight Graphical Summary Enter C1 in the cell marked Variables. 4. Enter the confidence level desired. Click OK. The confidence interval for sigma is reported in the output. 31. Hypothesis Tests Regarding µ, σ Known 1. Enter raw data in column C1 if necessary. 2. Select the Stat menu, highlight Basic Statistics, and then highlight 1-Sample Z Click Options. In the cell marked Alternative hypothesis, select the appropriate direction for the alternative hypothesis. Click OK. 4. If you have raw data, enter C1 in the cell marked One or more sample, each in a column: If you have summary statistics, select Summarized Data in the pull-down menu. Enter the value of the sample size and the sample mean. Enter the population standard deviation. 5. Check the box for perform hypothesis test and enter the hypothesized mean (this is the value of the mean stated in the null hypothesis). 6. Click OK. 32. Hypothesis Tests Regarding µ, σ Unknown 1. Enter raw data in column C1. 2. Select the Stat menu, highlight Basic Statistics, then highlight 1-Sample t If you have raw data, enter C1 in the cell marked One or more sample, each in a column: If you have summary statistics, select Summarized Data in the pull-down menu. Enter the value of the sample size, the sample mean, and the sample standard deviation. 4. Check the box for perform hypothesis test and enter the hypothesized mean (this is the value of the mean stated in the null hypothesis). 5. Click OK.
15 33. Hypothesis Tests Regarding a Population Proportion 1. If you have raw data, enter them in C1, using 0 for failure and 1 for success. 2. Select the Stat menu, highlight Basic Statistics, and then highlight 1-Proportion. 3. If you have raw data, select the One or more sample, each in a column from the pull-down menu and enter C1. If you have summarized statistics, select Summarized data and enter the number of trials and the number of events (successes). 4. Click Options. Enter the value of the proportion stated in the null hypothesis. Enter the direction of the alternative hypothesis. 5. Choose exact method unless np 0 (1 p 0 ) 10, in which case choose the method normal approximation. 6. Check the box for perform hypothesis test and enter the hypothesized proportion. 7. Click OK. 34. Hypothesis Tests Regarding a Population Standard Deviation 1. Enter the raw data into column C1 if necessary. Select the Stat menu, highlight Basic Statistics, and then highlight 1 Variance. 2. If you have raw data, select the One or more sample, each in a column from the pull-down menu and enter C1. If you have summarized statistics, select Sample Standard Deviation and enter the sample size and the sample standard deviation. 3. Check Perform Hypothesis Test and from the pull-down menu select Hypothesized Standard Deviation, and enter that value (i.e., the value of the standard deviation in the null hypothesis). 4. Click Options and select the direction of the alternative hypothesis. 5. Click OK twice.
Technology Step-by-Step Using StatCrunch Section 1.3 Simple Random Sampling 1. Select Data, highlight Simulate Data, then highlight Discrete Uniform. 2. Fill in the following window with the appropriate
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
Lean Six Sigma Training/Certification Book: Volume 1 Six Sigma Quality: Concepts & Cases Volume I (Statistical Tools in Six Sigma DMAIC process with MINITAB Applications Chapter 1 Introduction to Six Sigma,
GeoGebra Statistics and Probability Project Maths Development Team 2013 www.projectmaths.ie Page 1 of 24 Index Activity Topic Page 1 Introduction GeoGebra Statistics 3 2 To calculate the Sum, Mean, Count,
Individuals: The objects that are described by a set of data. They may be people, animals, things, etc. (Also referred to as Cases or Records) Variables: The characteristics recorded about each individual.
Using Your TI-NSpire Calculator: Descriptive Statistics Dr. Laura Schultz Statistics I This handout is intended to get you started using your TI-Nspire graphing calculator for statistical applications.
Statistical Analysis Using Gnumeric There are many software packages that will analyse data. For casual analysis, a spreadsheet may be an appropriate tool. Popular spreadsheets include Microsoft Excel,
MTH 140 Statistics Videos Chapter 1 Picturing Distributions with Graphs Individuals and Variables Categorical Variables: Pie Charts and Bar Graphs Categorical Variables: Pie Charts and Bar Graphs Quantitative
Summarizing and Displaying Categorical Data Categorical data can be summarized in a frequency distribution which counts the number of cases, or frequency, that fall into each category, or a relative frequency
SPSS Explore procedure One useful function in SPSS is the Explore procedure, which will produce histograms, boxplots, stem-and-leaf plots and extensive descriptive statistics. To run the Explore procedure,
24 Chapter 2. Describing, Exploring, and Comparing Data Chapter 2. Describing, Exploring, and Comparing Data There are many tools used in Statistics to visualize, summarize, and describe data. This chapter
Data exploration with Microsoft Excel: analysing more than one variable Contents 1 Introduction... 1 2 Comparing different groups or different variables... 2 3 Exploring the association between categorical
Chapter 165 Scatter Plots with Error Bars Introduction The procedure extends the capability of the basic scatter plot by allowing you to plot the variability in Y and X corresponding to each point. Each
Data used in this guide: studentp.sav (http://people.ysu.edu/~gchang/stat/studentp.sav) Organize and Display One Quantitative Variable (Descriptive Statistics, Boxplot & Histogram) 1. Move the mouse pointer
Data Analysis Tools This section of the notes is meant to introduce you to many of the tools that are provided by Excel under the Tools/Data Analysis menu item. If your computer does not have that tool
Data exploration with Microsoft Excel: univariate analysis Contents 1 Introduction... 1 2 Exploring a variable s frequency distribution... 2 3 Calculating measures of central tendency... 16 4 Calculating
Using Excel Jeffrey L. Rummel Emory University Goizueta Business School BBA Seminar Jeffrey L. Rummel BBA Seminar 1 / 54 Excel Calculations of Descriptive Statistics Single Variable Graphs Relationships
Calculate Confidence Intervals Using the TI Graphing Calculator Confidence Interval for Population Proportion p Confidence Interval for Population μ (σ is known 1 Select: STAT / TESTS / 1-PropZInt x: number
Simple Linear Regression in SPSS STAT 314 1. Ten Corvettes between 1 and 6 years old were randomly selected from last year s sales records in Virginia Beach, Virginia. The following data were obtained,
Doing Multiple Regression with SPSS Multiple Regression for Data Already in Data Editor Next we want to specify a multiple regression analysis for these data. The menu bar for SPSS offers several options:
Directions for Frequency Tables, Histograms, and Frequency Bar Charts Frequency Distribution Quantitative Ungrouped Data Dataset: Frequency_Distributions_Graphs-Quantitative.sav 1. Open the dataset containing
Bill Burton Albert Einstein College of Medicine firstname.lastname@example.org April 28, 2014 EERS: Managing the Tension Between Rigor and Resources 1 Calculate counts, means, and standard deviations Produce
SPSS Manual for Introductory Applied Statistics: A Variable Approach John Gabrosek Department of Statistics Grand Valley State University Allendale, MI USA August 2013 2 Copyright 2013 John Gabrosek. All
Chi-Square Tests 15 Chapter Chi-Square Test for Independence Chi-Square Tests for Goodness Uniform Goodness- Poisson Goodness- Goodness Test ECDF Tests (Optional) McGraw-Hill/Irwin Copyright 2009 by The
A Correlation of to the South Carolina Data Analysis and Probability Standards INTRODUCTION This document demonstrates how Stats in Your World 2012 meets the indicators of the South Carolina Academic Standards
Your Name: Section: 36-201 INTRODUCTION TO STATISTICAL REASONING Computer Lab Exercise #5 Analysis of Time of Death Data for Soldiers in Vietnam Objectives: 1. To use exploratory data analysis to investigate
KSTAT MINI-MANUAL Decision Sciences 434 Kellogg Graduate School of Management Kstat is a set of macros added to Excel and it will enable you to do the statistics required for this course very easily. To
How Does My TI-84 Do That A guide to using the TI-84 for statistics Austin Peay State University Clarksville, Tennessee How Does My TI-84 Do That A guide to using the TI-84 for statistics Table of Contents
Appendix 2.1 Tabular and Graphical Methods Using Excel 1 Appendix 2.1 Tabular and Graphical Methods Using Excel The instructions in this section begin by describing the entry of data into an Excel spreadsheet.
Chapter 23. Inferences for Regression Topics covered in this chapter: Simple Linear Regression Simple Linear Regression Example 23.1: Crying and IQ The Problem: Infants who cry easily may be more easily
GeoGebra in 10 lessons Gerrit Stols Acknowledgements GeoGebra is dynamic mathematics open source (free) software for learning and teaching mathematics in schools. It was developed by Markus Hohenwarter
Business Course Text Bowerman, Bruce L., Richard T. O'Connell, J. B. Orris, and Dawn C. Porter. Essentials of Business, 2nd edition, McGraw-Hill/Irwin, 2008, ISBN: 978-0-07-331988-9. Required Computing
SECTION 2-1: OVERVIEW Chapter 2 Describing, Exploring and Comparing Data 19 In this chapter, we will use the capabilities of Excel to help us look more carefully at sets of data. We can do this by re-organizing
USING A TI-83 OR TI-84 SERIES GRAPHING CALCULATOR IN AN INTRODUCTORY STATISTICS CLASS W. SCOTT STREET, IV DEPARTMENT OF STATISTICAL SCIENCES & OPERATIONS RESEARCH VIRGINIA COMMONWEALTH UNIVERSITY Table
Learning objectives Descriptive Statistics F. Farrokhyar, MPhil, PhD, PDoc To recognize different types of variables To learn how to appropriately explore your data How to display data using graphs How
1) Write the following as an algebraic expression using x as the variable: Triple a number subtracted from the number A. 3(x - x) B. x 3 x C. 3x - x D. x - 3x 2) Write the following as an algebraic expression
MINITAB ASSISTANT WHITE PAPER This paper explains the research conducted by Minitab statisticians to develop the methods and data checks used in the Assistant in Minitab 17 Statistical Software. One-Way
Getting started manual XLSTAT Getting started manual Addinsoft 1 Table of Contents Install XLSTAT and register a license key... 4 Install XLSTAT on Windows... 4 Verify that your Microsoft Excel is up-to-date...
1 Commands in JMP and Statcrunch Below are a set of commands in JMP and Statcrunch which facilitate a basic statistical analysis. The first part concerns commands in JMP, the second part is for analysis
SPSS Basics Tutorial 1: SPSS Windows There are six different windows that can be opened when using SPSS. The following will give a description of each of them. The Data Editor The Data Editor is a spreadsheet
MATH 140 Lab 4: Probability and the Standard Normal Distribution Problem 1. Flipping a Coin Problem In this problem, we want to simualte the process of flipping a fair coin 1000 times. Note that the outcomes
business statistics using Excel Glyn Davis & Branko Pecar OXFORD UNIVERSITY PRESS Detailed contents Introduction to Microsoft Excel 2003 Overview Learning Objectives 1.1 Introduction to Microsoft Excel
Summary of Formulas and Concepts Descriptive Statistics (Ch. 1-4) Definitions Population: The complete set of numerical information on a particular quantity in which an investigator is interested. We assume
TIPS FOR DOING STATISTICS IN EXCEL Before you begin, make sure that you have the DATA ANALYSIS pack running on your machine. It comes with Excel. Here s how to check if you have it, and what to do if you
Mathematics Fairfield Public Schools AP Statistics AP Statistics BOE Approved 04/08/2014 1 AP STATISTICS Critical Areas of Focus AP Statistics is a rigorous course that offers advanced students an opportunity
An Introduction to Graphing in Excel This example uses Excel to graph Y vs X. This problem starts as follows: 1.Complete the following table and on graph paper, graph the line for the equation x 2y = Identify
Mathematics Probability and Statistics Curriculum Guide Revised 2010 This page is intentionally left blank. Introduction The Mathematics Curriculum Guide serves as a guide for teachers when planning instruction
MATH BOOK OF PROBLEMS SERIES New from Pearson Custom Publishing! The Math Book of Problems Series is a database of math problems for the following courses: Pre-algebra Algebra Pre-calculus Calculus Statistics
Using Minitab for Regression Analysis: An extended example The following example uses data from another text on fertilizer application and crop yield, and is intended to show how Minitab can be used to
An SPSS companion book to Basic Practice of Statistics SPSS is owned by IBM. 6 th Edition. Basic Practice of Statistics 6 th Edition by David S. Moore, William I. Notz, Michael A. Flinger. Published by
1. Numerical Descriptive Statistics 1.1. Put data in columns: Minitab Directions 01 Descriptive Statistics Note: if your measurement is time, convert all times to seconds or minutes, or whatever is most
Chapter 3: Data Description Numerical Methods Learning Objectives Upon successful completion of Chapter 3, you will be able to: Summarize data using measures of central tendency, such as the mean, median,
Graphing Exercise 1. Create a Pie Graph by Selecting a Data Table This exercise selects the data in an existing data table and creates a pie graph of the data (Figure G1-1). Figure G1-1. Tree species sampled
Entering and Formatting Data Using Microsoft Excel to Plot and Analyze Kinetic Data Open Excel. Set up the spreadsheet page (Sheet 1) so that anyone who reads it will understand the page (Figure 1). Type
Chapter 15 Multiple Choice Questions (The answers are provided after the last question.) 1. What is the median of the following set of scores? 18, 6, 12, 10, 14? a. 10 b. 14 c. 18 d. 12 2. Approximately
EXCEL Tutorial: How to use EXCEL for Graphs and Calculations. Excel is powerful tool and can make your life easier if you are proficient in using it. You will need to use Excel to complete most of your
ETH Zürich Seminar für Statistik Introduction Course in SPSS - Evening 1 Seminar für Statistik, ETH Zürich All data used during the course can be downloaded from the following ftp server: ftp://stat.ethz.ch/u/sfs/spsskurs/
General instructions for the content of all StatTools assignments and the use of StatTools: An important part of Business Management 330 is learning how to conduct statistical analyses and to write text
Curriculum Map Statistics and Probability Honors (348) Saugus High School Saugus Public Schools 2009-2010 Week 1 Week 2 14.0 Students organize and describe distributions of data by using a number of different
Advanced Microsoft Excel 2010 Table of Contents THE PASTE SPECIAL FUNCTION... 2 Paste Special Options... 2 Using the Paste Special Function... 3 ORGANIZING DATA... 4 Multiple-Level Sorting... 4 Subtotaling
Exploratory data analysis (Chapter 2) Fall 2011 Data Examples Example 1: Survey Data 1 Data collected from a Stat 371 class in Fall 2005 2 They answered questions about their: gender, major, year in school,
CHAPTER 5 Probability Distributions CHAPTER OUTLINE 5.1 Probability Distribution of a Discrete Random Variable 5.2 Mean and Standard Deviation of a Probability Distribution 5.3 The Binomial Distribution
How to Use a Data Spreadsheet: Excel One does not necessarily have special statistical software to perform statistical analyses. Microsoft Office Excel can be used to run statistical procedures. Although
Descriptive Statistics Understanding Data: Dataset: Shellfish Contamination Location Year Species Species2 Method Metals Cadmium (mg kg - ) Chromium (mg kg - ) Copper (mg kg - ) Lead (mg kg - ) Mercury
STATISTICS FOR PSYCH MATH REVIEW GUIDE ORDER OF OPERATIONS Although remembering the order of operations as BEDMAS may seem simple, it is definitely worth reviewing in a new context such as statistics formulae.
A Guide for a Selection of SPSS Functions IBM SPSS Statistics 19 Compiled by Beth Gaedy, Math Specialist, Viterbo University - 2012 Using documents prepared by Drs. Sheldon Lee, Marcus Saegrove, Jennifer
Overview A PivotTable report is an interactive table that allows you to quickly group and summarise information from a data source. You can rearrange (or pivot) the table to display different perspectives
Using Excel 2003 with Basic Business Statistics Introduction Use this document if you plan to use Excel 2003 with Basic Business Statistics, 12th edition. Instructions specific to Excel 2003 are needed
AP Statistics: Syllabus 1 Scoring Components SC1 The course provides instruction in exploring data. 4 SC2 The course provides instruction in sampling. 5 SC3 The course provides instruction in experimentation.
FACT SHEET Using Excel for descriptive statistics Introduction Biologists no longer routinely plot graphs by hand or rely on calculators to carry out difficult and tedious statistical calculations. These
Table of Contents TASK 1: DATA ANALYSIS TOOLPAK... 2 TASK 2: HISTOGRAMS... 5 TASK 3: ENTER MIDPOINT FORMULAS... 11 TASK 4: ADD TOTAL LABEL AND FORMULA FOR FREQUENCY... 12 TASK 5: MODIFICATIONS TO THE HISTOGRAM...
LAB 4 INSTRUCTIONS CONFIDENCE INTERVALS AND HYPOTHESIS TESTING In this lab you will explore the concept of a confidence interval and hypothesis testing through a simulation problem in engineering setting.
An introduction to IBM SPSS Statistics Contents 1 Introduction... 1 2 Entering your data... 2 3 Preparing your data for analysis... 10 4 Exploring your data: univariate analysis... 14 5 Generating descriptive
MBA 611 STATISTICS AND QUANTITATIVE METHODS Part I. Review of Basic Statistics (Chapters 1-11) A. Introduction (Chapter 1) Uncertainty: Decisions are often based on incomplete information from uncertain
STAT X400 (2 semester units in Statistics) Business, Technology & Engineering Technology & Information Management Quantitative Analysis & Analytics Course Description This course introduces students to
Overview A PivotTable report is an interactive table that allows you to quickly group and summarise information from a data source. You can rearrange (or pivot) the table to display different perspectives
2014 by Minitab Inc. All rights reserved. Minitab, Quality. Analysis. Results. and the Minitab logo are registered trademarks of Minitab, Inc., in the United States and other countries. Additional trademarks
Basic Pivot Tables Pivot tables summarize data in a quick and easy way. In your job, you could use pivot tables to summarize actual expenses by fund type by object or total amounts. Make sure you do not
Dealing with Data in Excel 2010 Excel provides the ability to do computations and graphing of data. Here we provide the basics and some advanced capabilities available in Excel that are useful for dealing
Using Your TI-NSpire Calculator: Binomial Probability Distributions Dr. Laura Schultz Statistics I This handout describes how to use the binompdf and binomcdf commands to work with binomial probability
Glossary Brase: Understandable Statistics, 10e A B This is the notation used to represent the conditional probability of A given B. A and B This represents the probability that both events A and B occur.
T O P I C 1 2 Techniques and tools for data analysis Preview Introduction In chapter 3 of Statistics In A Day different combinations of numbers and types of variables are presented. We go through these
Contents An introduction to using Microsoft Excel for quantitative data analysis 1 Introduction... 1 2 Why use Excel?... 2 3 Quantitative data analysis tools in Excel... 3 4 Entering your data... 6 5 Preparing
ISS, NEWCASTLE UNIVERSITY IBM SPSS Statistics for Beginners for Windows A Training Manual for Beginners Dr. S. T. Kometa A Training Manual for Beginners Contents 1 Aims and Objectives... 3 1.1 Learning