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StatTools Guide

Table of Contents

1. Data 2

a) Data Set Manager 2 b) Data Utilities 3

2. Analyses 4

a) Summary Statistics 4 • One-Variable Summary • Correlation and Covariance

b) Summary Graphs 7 • Histogram • Scatterplot • Box-Whisker Plot

c) Statistical Inference 10 • Confidence Interval • Hypothesis Test • Sample Size Selection • One-Way ANOVA • Two-Way ANOVA • Chi-Square Independence Test

d) Normality Tests 13 • Chi-Square Test • Q-Q Normal Plot

e) Time Series and Forecasting 14 • Time Series Graphs • Runs Test for Randomness • Forecast

f) Regression and Classification 15 • Regression • Logistic Regression

g) Quality Control 16 • Pareto Chart • X/R Charts • P, C and U Charts

h) Nonparametric Tests 18 • Sign Test • Wilcoxon Signed-Ranked Test • Mann-Whitney Test

3. Tools 19

a) User Manual 19 b) Example Spreadsheets 19

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The StatTools toolbar is divided into 3 parts:

1. Data Let you define the dataset (i.e. “tell the computer where the data are and what they represent”) a) Data Set Manager

This is the first step you need to take before being able to apply any analysis to the data.

1 3 2

Create a new dataset

Name the dataset or keep the original name

Where are the data?

Optional. If checked your table will look a little nicer.

Are observations given in columns or rows?

Does your table contain a name (title) for each row/column?

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b) Data Utilities

This is an optional step. It is used only if you want to perform any added treatment to your data (i.e. calculate differences, draw random samples, etc.).

Add calculated columns/rows to your table

Select a random sample out of your population

Group values by category, for example MPG by type of car. You will always be able to stack/unstack your data when asking for analysis so you don’t need to decide right now.

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2. Analyses Once you defined your dataset you can apply a number of analyses on it. a) Summary Statistics

Basic statistics for numerical variables.

• One-variable summary

Statistics (mean, variance, etc.) for each numerical variable.

Which summary statistics do you

Which variable(s) do you want to analyze? Stacked by which

If you data are unstacked you will get statistics across all observations (i.e. mean MPG for all cars).

Stacking your data allows you to obtain statistics by category (i.e. mean MPG by type of car)

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Example: One-variable summary for stacked and unstacked variables

Stacked: MPG statistics for all cars Unstacked: MPG statictics for Midsizes and SUVs

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• Correlation and Covariance

Statistics between each pair of numerical variables.

Example: Correlation and Covariance analyses between 3 numerical variables

StatTools (Core Analysis Pack) Analysis: Correlation and Covariance

Performed By: Claire Date: Friday, November 20, 2009

Updating: Live

Age Income Education

Correlation Table Data Set #1 Data Set #1 Data Set #1

Age 1.000 0.084 -0.130 Income 0.084 1.000 -0.111 Education -0.130 -0.111 1.000

Age Income Education

Covariance Table Data Set #1 Data Set #1 Data Set #1

Age 54.822 4.324 -1.921 Income 4.324 48.516 -1.545 Education -1.921 -1.545 4.000

For which pair of variables do you want correlation or covariance?

Correlation or Covariance?

Note: entries above are equal to entries below diagonal (i.e. Cov(A,B)=Cov(B,A))

Note: entries on the diagonal are equal to the variance of each variable (i.e. Cov(A,A)=Var(A))

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b) Summary Graphs

• Histogram

Example: Histogram

Unstacked: one histogram for all data (variable has to be numerical)

Number of bars

Value variable has to be numerical

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• Scatterplot

Example: Scatterplot

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1975 1980 1985 1990 1995 2000 2005 2010 2015

MPG

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ata

Set #

1

Year / Data Set #1

Scatterplot of MPG vs Year of Data Set #1

Both variables must be numerical

Always unstacked

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• Box-Whisker Plot

Description of Plot Elements

Selected variable must be numerical

Includes the following description

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c) Statistical Inference

• Confidence Interval

Confidence interval for mean, standard deviation or proportion

Type of data: one-sample, two-sample or paired-sample

Confidence level

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• Hypothesis Test

• Sample Size Selection

Defines the sample size needed for the confidence level requested.

Confidence interval for mean, standard deviation or proportion

H 0

H a

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• One-Way ANOVA Small p-value means that means are different across populations (H 0 : means are equal) If confidence intervals do not contain 0, means are not equal.

• Two-Way ANOVA Variables must be stacked. Two categories and one numerical variable must be selected

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• Chi-Square Independence Test Tests if attribute in rows and attribute in columns are independent from each other. For example if rows are “gender” and columns are “favorite soft drink”, the Chi-square independence test verifies that favorite soft drink is independent from gender. If the p-value is small the attributes are not independent.

d) Normality Tests

• Chi-square Test Compares histogram of data with the histogram had the data been normally distributed. The smaller the p-value is the closer the data are to a normal distribution.

• Q-Q Normal Plot Compares data quantiles with the quantiles had the data been normally distributed. A straight line at a 45 degrees angle means that the data are normal.

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e) Time Series and Forecasting

• Time Series Graph Displays value of a numerical variable across observations.

• Runs Test for Randomness Variables must be unstacked. Indicates if values of a variable seem random. If number of runs above/below mean is significantly different than E(R) (expected number of runs under randomness) observations are not random.

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• Forecast Allows to forecast future observations using different forecasting methods.

f) Regression and Classification

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• Regression

• Logistic Regression Used when response variables is either 0 or 1 (success or failure). Independent variables can be continuous.

g) Quality Control Indicates whether a process is in statistical control.

Multiple considers all independent variables at once.

Other regression types allow each variable to be considered only for a subset of the observations.

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• Pareto Chart This is a frequency histogram. Example: Pareto Chart

• X/R Charts

Give mean (X) and range (R) for each subset of observations. Two numerical variables need to be selected. • P, C and U Charts

Is the process contained between the upper and lower limits?

Example: C-Chart

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h) Nonparametric Tests Used for hypothesis testing about the median when normal distribution is not assumed.

Both Sign and Wilcoxon Signed-Rank tests can be performed for the median of a single variable (one-sample analysis) or for the median of the differences between pairs of variables (paired-sample analysis).

• Sign Test Is the median positive or negative?

• Wilcoxon Signed-Rank Test Assumes that distribution is symmetric (but not necessarily normal).

• Mann-Whitney Test Can only be performed on two samples. Can be used to test whether two samples are issued from the same probability distribution.

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3. Tools

Useful items can be found under the help menu.

a) User Manual

Detailed description of every StatTools item.

b) Example Spreadsheets Examples and explanations of every StatTools analysis.