Tools to look at Interval or Ratio (Scale) Data

December 31st, 2010

Interval Scale is use when we are measure the differences between observations. Difference between any two successive points is equal. Interval scale numbers that are equally different represent differences of equal magnitude. The zero vale of an interval scale is arbitrary. Often data of this scale are treated as a Ratio scale even if the assumption of equal intervals is incorrect. Some examples of Interval scale data is Calendar time, Voltage and  Temperature.

Ratio Scales is like Interval Scale except it has a true zero point. In other words you can have nothing less than zero, on negative values. Some examples of ratio scale data  is Time, Distance, weight, Speed, ad Frequency.

Of all the measurement scales of data these two give us the most information about the thing we are studying.

So once we have done this data collection how can we look at these data to see better what we found? Well for this scale there several types of statistical tools we can use, but let me tell you about four of the major ones. These are these four are the t-test, F-test, Correlations, and Multiple regressions.

t-test

This test is used to compare and determine differences between the averages or means of two groups of normalized data. It is used for small scale experiments. If you have a large sample you can use want is called a Z test which uses the normal distribution instead of the t distribution. Below is the shape of the normal and two t distributions (sample size =2 and 10) You can see that the t distribution is a good approximation of the normal.

What is done here is you have to calculate an actual “t” value and compare it to a Tabled t value. The Table t values can be found in any statistic book. To calculate the actual ”t” you have to calculate the following formula:

If you have excel and have add the Analysis ToolPak (which is a free download) you can do this comparison using the t-Test: Two Sample Assuming unequal Variances in this add-on.

If the actual is more than the table value then the two means are different.

F test

Where the t test compares the averages or means, the F test is used to compare and determine differences between the variation (distribution spread) of two groups of normalized data.

Like the t test we calculate F and compare it to a tabled value. The formula for calcultating F is:

If you have excel and have add the Analysis ToolPak (which is a free download) you can do this comparison using the F-Test: Two-Sample for Variances in this add-on.

If the actual is more than the table value then the two variances are different.

Correlation

A Scatter plot is one of the most useful correlation tools available. In a scatter plot all you do is plot one factor against another.



In this chart you can see a direct correlation between the time, in days, of fruit on the tree and its weight.


Multiple Regressions

Multiple regression is the term use to describe a study in which we want to learn more about the relationship between several independent or predictor variables and a dependent or criterion variable. An ANOVA is a type of multiple regression. Here is a simple regression on trying to find the key predictors of engine knock.


Regression Analysis: Knock versus Spark, AFR, Intake, Exhaust

The regression equation is

Knock = 23.8 – 0.296 Spark + 3.19 AFR + 0.359 Intake + 0.0134 Exhaust



Predictor      Coef   SE Coef      T      P

Constant     23.815     8.137   2.93  0.019

Spark       -0.2965    0.3072  -0.97  0.363

AFR          3.1918    0.2398  13.31  0.000     A P value less than .05 means it

Intake      0.35870   0.07848   4.57  0.002     is a predictor

Exhaust    0.013376  0.005421   2.47  0.039



S = 0.510560   R-Sq = 98.8%   R-Sq(adj) = 98.2%



Analysis of Variance


Source          DF       SS      MS       F      P

Regression       4  170.245  42.561  163.28  0.000

Residual Error   8    2.085   0.261

Total           12  172.331



Source   DF  Seq SS

Spark     1  84.250

AFR       1  80.029

Intake    1   4.380

Exhaust   1   1.587





Well there you have my thoughts on tools to measure Interval and Ratio Scale Data. If, you have questions or comments please feel free to contact me by leaving a comment below, emailing me, calling me, or leaving a comment on my website.


Bersbach Consulting
Peter Bersbach
Six Sigma Master Black Belt
http://sixsigmatrainingconsulting.com
peter@bersbach.com
1.520.829.0090



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