# UTPA STEM/CBI Courses/Manufacturing Processes/t-statistics

Course Title: Manufacturing Processes Lab
Lecture Topic: Using t-statistics in MS-Excel to find the significant independent variables in an experiment
Instructor: Dr. Rajiv Nambiar
Institution: UTPA

## Backwards Design

Course Objectives
* Primary Objectives- By the next class period students will be able to:
** use t-statistics in MS-Excel to find the significant independent variables in an experiment
* Sub Objectives- The objectives will require that students be able to:
** place the data in MS-Excel so that it can be analyzed by the regression function
** explain the meaning of the regression output
* Difficulties- Students may have difficulty:
** understanding that there is only one dependent variable in the analysis
** knowing that the x-columns must be adjacent to each other
** understanding that it is important to have a label for each column
** understanding that if the t-statistic is large, it is liklely that the indepedent variable affects the dependent variable
** understanding that the magnitude of the coeffiecient is not important
** understanding that a positive t-statistic means a positive corelation and a negative t-statistic means a negative corelation
* Real-World Contexts- There are many ways that students can use this material in the real-world, such as:
** Finding if age, height, weight, gender, or other variables effect GPA
Model of Knowledge
* Concept Map
** Understanding understanding the concept of a dependent and independent variable
** Understanding regression involves only one dependent variable but several independent variables
** Understanding that each independent variable must have at least two values
** Understanding that the set of independent variables must be linearly independent
** Understanding that if the t-statistic is less than 2, there is probably no relationship between the independent and dependent variables
* Content Priorities
** Enduring Understanding
*** t-statistics can be used to find if an independent variable can be used to control a dependent variable
** Important to Do and Know
*** use MS-Excel to conduct a regression analysis
** Worth Being Familiar with
*** regression analysis
Assessment of Learning
* Formative Assessment
** In Class (groups)
*** In class questions about sample data
** Homework (individual)
*** Homework to do regression analysis with generated data
* Summative Assessment
** Report with analysis of the data given to the student

## Legacy Cycle

OBJECTIVE
By the next class period, students will be able to:
* use t-statistics in MS-Excel to find the significant independent variables in an experiment
The objectives will require that students be able to:
* place the data in MS-Excel so that it can be analyzed by the regression function
* explain the meaning of the regression output
THE CHALLENGE
A cavemen is placed in a vehicle that is running on autopilot. The cavemen gets to see a bunch of knobs that can be turned, a few switches and a dial that displays the speed. The challenge for the caveman is to find out which knobs control the speed. As it turns out, one of the knobs is accelerator, another is the brake, another is the radio volume, another is the air conditioning fan, and another is unconnected to any thing.
GENERATE IDEAS
* He can change one knob position forward, and observe what happens, then bring it back to its initial position. He then changes the next, and repeats the process for all five knobs.
* He can change more than one knob at a time, but each to a different level. He will keep changing the one he increases the most so he can identify which of these knobs has a higher effect using a graphical method.
* He can change more than one at a time, but according to a preset plan and then analyze the results statistically, so he can come to the correct conclusion with the minimum number of tries.
MULTIPLE PERSPECTIVES
The students will discuss the advantages of using graphical techniques versus statistical techniques.
RESEARCH & REVISE
The students will be given generated test data to check the method they have used.
TEST YOUR METTLE
The students will be given test data that contains confounding effects of two variables, where a graphical method might show the effects better than the statistical method.
GO PUBLIC
The students will use the t-statistics to analyze their lab experiment data and write a report on this.

## Pre-Lesson Quiz

* What is an independent variable?
* What is a dependent variable?
* Is the x-axis on a graph usually the independent variable or dependent variable?
* When A is plotted versus B, which is the x-axis variable?
* In a linear regression graph, with the equation y = m x + c, what is c?
* In a linear regression graph, with the equation y = m x + c, what is m?
* In a linear regression graph, with the equation y = m x + c, if m zero, what does it mean?
* What does it mean when the standard deviation is large?
* What does it mean when the standard deviation is small?
* What is meant by a normalized Gaussian distribution?

## Test Your Mettle Quiz

* In a linear regression graph, with the equation y = m x + c, if m is large, what does it mean?
* In a regression an analysis, how many dependent variables are you allowed?
* In a regression an analysis, how many independent variables are you allowed?
* If you are doing a statistical analysis, and there are two independent variable, can you vary both at the same time?
* When doing an Excel regression analysis of can you include the header of the column in the data?
* If you include the header in the data for the dependent variable, should you use the header in the dependent variable also?
* If you have two independent variables, in an Excel regression analysis, and one of the dependent variables is in Column A, what must column B contain, the independant variable or the dependant variable?
* What does it mean when the t-statistic for an independent variable is large?
* What does it mean when the t-statistic for an independent variable is small and the coefficient is large?
* What does it mean when the t-statistic for an independent variable is large and the coefficient is small?
Khleeutpa 22:41, 20 November 2009 (UTC)Excellent