Constants, Variables, & a Control                                          Edited 8.11.06 by S. Klein

BOB HAS A PROBLEM

Already constructed houses started having some cement related problems after several years.  Their foundations started to show hairline cracks and some foundations showed early signs of crumbling.  Test blocks poured at the times of each foundation and only tested when the problems showed up, could withstand on average only about 1,800 # of pressure per square inch.  This rating is well below the industry minimum standard.  This was not good for safety or for business. 

BOB HAS A NEW RECIPE

Bob then decided that his “recipe” needed improvements.  He increased the sand to 5 # per 100 # of cement, and added 1 # of  costly Wally’s Wonderful cement hardener per batch.  Test blocks were poured and machine testing showed that the new “recipe” withstood on average 2111 # per square inch before cracking or crumbling.  Bob was then one happy builder. 

                                                        

  

 

        With his new “recipe”, on warm sunny days,
        he could repair houses already built and build
        safer ones for new customers.  (What a good guy!)

 

 

 

 

 

 

BOB MAKES A CLAIM

Bob jumped onto his trusty backhoe (Click on this link now) and loudly exclaimed, “It’s my new cement hardener (a chemical) that has turned my life around.  My houses are saved!”   For a cartoon character, Bob is certainly very dramatic.  Bob recently got married.  Yeh Bob!!  His wife Betty doesn’t trust Wally’s Wonderful cement hardener and still thinks it is a waste of money that could be better spent.  Yeh Betty!!

 

                        Here are some very useful and c o l o r f u l  DEFINITIONS

 

In any experiment, even this real life one, there are often a number of constants and variables. 

 

Constants are those factors or events which could affect an outcome, but which do not change each time the experiment (work) is done. 

 

Variables are those factors or events which do change each time the experiment (work) is done. 

 

Those variables over which the experimenter has some control before the start of the work (the causes) are known as Independent Variables.  They are plotted along the X axis of a graph.  Since they are at the
BEGINning of the experiment and are the INDEPENDENT variable, your teacher jokingly refers to them as the BEGINDEPENDENT VARIABLE. 

 

Those variables over which the experimenter has no control --  data is taken at the end of the experiment -- (the results or effects of the experiment) are known as Dependent Variables.  They are plotted along the Y axis of a graph. 

 

                Link to a standard X,Y graph format with stated variables is at the following site. 

                Please then scroll down to the labeled graph at the bottom of the linked page.   :)

.

                http://www.graphicsserver.com/com_products/choosing_a_graph.aspx

 

Only when there is a single Independent Variables can we draw a valid conclusion to our work.  This rule is often violated with sometimes invalid conclusions. 

 

The portion of the experiment which uses the least amount of the Independent Variable is known as the Control or control trial.  The portion of the experiment in which other greater amounts of the Independent Variable are used are the experimental trials.  . 

 

IDENTIFYING CONSTANTS AND BOTH TYPES OF VARIABLES

 

Answer questions 1,2,3 in print on the separate Web Script before clicking on the link to their answers.

 

1.     Using the definitions above, list all five constants Bob used in his work.  (One is difficult!)

            ___________________________________________________________________

           

2.     Using the definitions above, list all Independent Variables Bob used in his work.  .

           ___________________________________________________________________

 

3.     Using the definitions above, list all three Dependent Variables Bob used in his work. 

        (Hint -- There are several of these!)

            __________________________________________________________________.

 

Click on this link for the answers for questions 1,2,3!

 

WAS BOB’S CLAIM CORRECT?

Can both Bob & Betty be correct about the value of Wall’s Wonderful product?   Could another explanation for the improvements in the blocks be more logical?  To solve this problem, we must reevaluate Bob’s use of his Independent Variables. 

 

4.     How many Independent Variables did Bob use in constructing his (different batches of )
        cement?  _________    (Could you name it/them if asked?)     

 

5.     Is Bob’s claim that Wally’s product made the difference necessarily valid (true)? (y/n)  _____

 

6.     Is Betty’s claim that Wally’s product was a waste necessarily valid (true)?        (y/n)       ______      

 

7.     List 3 different possible reasons why the second cement “recipe” was stronger than the first.

a.                   ______________________________________________________________

b.                  ______________________________________________________________

c.                   ______________________________________________________________

 

We are stuck with multiple (in this case three) different interpretations for the cause of the cement variation because Bob made a fundamental error when he changed his cement “recipe.” 

8.     What was Bob’s fundamental error?  

_________________________________________________________________

 

Link to the answers for Questions 4,5,6,7 & 8

 

 

DIFFERENTIATING BETWEEN VARIABLES, CONSTANTS & THE CONTROLS

For each of the following, the answer is either Constant, Independent Variable, Control or Dependent Variable:  Review the colorful definitions box (in green) above if needed. 

 

9.     This type of variable occurs at the end (effect) of the work.            ________________

10.   You may validly have one or several of this type of variable.          ________________

11.   This set of experiments used only 3 # of sand & no Wally’s.         ________________

12.   This/these remain the same for each experiment.                           .________________

13.   The experimenter regulates this before doing the work.                 .________________

14.   You are permitted to have more than one of these.  (2 possible ans.)  ______________.

 

            Link to answers to questions 9, 10, 11, 12, 13 & 14!

 

 

HOW TO IDENTIFY TYPES OF VARIABLES

Review the colorful definitions box (a green) above if needed. 

 

15.   Is the initial variable the cause or is it the effect in the experiment?             _______________

16.   Is the initial variable the Independent or the Dependent one?                     ______________

17.   Along which axis is the independent variable usually plotted in a graph?     ________

 

18.   Is the second variable known as the Independent or the Dependent one?   ______________

19.   Is the second variable the cause or is it the effect in the experiment?             _____________

 

20.   Along which axis is the dependent variable usually plotted in a graph?                     _______

 

21.   What is the first letter (in order) for each of the six prior answers?       __  __  __  __  __  __

If you memorize this ACRONYM or use each letter in order for a different concept, life will be much easier for you.  A student recently suggested that this acronym really stands for Cylons In X-men Defeated Evil Yesterday.   If you don’t like this acronym sentence, make one of your own on the next line.

22.   (optional)  _________   _________   _________   _________   _________   __________

 

            Link to answers to questions 15, 16, 17, 18, 19, 20, 21, & 22!

 

 

                               

 

STARTING AN EXPERIMENT USING FROGS

 

23.   In a study of how temperature affects activity rate in frogs, the independent variable is ______

 

24.   This Independent Variable often varies through a range of data.  The activity rate of the
        frogs should differ at several different ...  ___________________

 

25.   Temperature is the causal variable because the experimenter has some choice in its values. 
        We could do the experiment by comparing activity rate at 5 versus 15 degrees C, or we
        could do the experiment at 10, 20, 30, & 40 degrees C.  This is known as the
         _____________ variable. 

 

26.   It is a change in the temperature that causes something else (the Dependent Variable) to also

        change.  The initial variations in temperature causes a change in the frogs  ________  ______

 

NOTE -- For many experiments, time is displayed along the X axis as the independent variable, but it is not the cause of something.  There may be several non measurable independent variables that over a period of time have caused some other factor to change.

 

            Link to answers to questions 23, 24, 25 & 26!

 

 

                                                     

 

ANALYZING THIS SAME EXPERIMENT USING FROGS

 

27.   After the experiment is completed, our results should also show some range in variation. 
        (These results also vary and are a SECOND variable.)  These results (or effects) are
        known as the  ____________  variable.   

 

28.   In a study of how temperature affects any of a number of different activity rates in frogs, the
        different dependent variables could be  S _ E _ D,  B _ _ A T _ _ _ G   RATE, food 
        I _ T A _ E    R _ _ _,   S _ I  M _ _ N _   RATE,  or  H _ A _ T    R _ _ _  or many others.
 

NOTE  --  The experimenter has no control over the values for these variables, but merely which type of factor to study.  

 

29.   This dependent variable also often varies through some range of data.  The resulting activity
        rate of frogs (see prior question) may be at a range of  H _ _ S per minute,  B R _ _ T _ _ 
        per minute,  grams of F _ _ _  consumed per day,  D _ S _ A _ C _  swam per minute 
        or  H _ _ _ T  beats per minute.  

 

30.   The above changes in activity rates are several of the  E _ _ E _ _ S  triggered by the original
        change in temperature.  

 

31.   The dependent variable is usually positioned along the  ___ axis.   

 

        Link to answers to questions 27, 28, 29, 30, & 31!

 

 

Examine this graph of 180 years of U.S. Immigration data.

 

                                  

(I'm sorry, but this program (Front Page) does not have a magnifier that is convenient in Word.)

 

    32    The independent variable above is displayed along the ___ axis.

    33.   The independent variable is really due to several factors (political, economic, ecological etc.)
             implied (not really displayed) as ___________ in units of   D _ _ A _ _ S.

    34.   The dependent variable is  P _ _ U _ _ T _ _ N  in units of  M _ _ _ I _ _ S.

    35.   The dependent variable is displayed along the ___ axis.

    36.   In this graph, does the implied independent variable (#33) cause the affect of a range in
            the dependent variable?  (y/n)   ____

 

                 Link to answers to questions 32, 33, 34, 35, & 36!
                                                                                         

 

 

 

 

Examine this graph of Business Activity for Information Systems Management. 
(At least that's what Yahoo & myself think this ISM stands for.)

                             

                    
                           1999  2000  2001   2002   2003  2004  2005   2006

              (I can not increase the resolution of this graphic, so I duplicated them!)
 

37.    The independent variable is displayed along the ______ axis.

38.    The independent variable is displayed (really implied again) as _________

39.    The dependent variable is CHANGES IN THIS PARTICULAR INDEX  in units that vary

         from a low of about ______ units in the year _____ to a high of about ______ units in the

         year _____. 

40.     The dependent variable is displayed along the ____ axis.

41.     In this graph, does the independent variable cause the affect of a range in the dependent

          variable? (y/n)   ____.

 

 

        Link to answers to Questions 37, 38, 39, 40, 41!