Experiments and Variables Help (page 2)
Experiments and Variables
If you want to understand anything about a scientific discipline, you must know the terminology. Statistics is no exception. Here are definitions of some terms used in statistics.
In statistics, an experiment is an act of collecting data with the intent of learning or discovering something. For example, we might conduct an experiment to determine the most popular channels for frequency-modulation (FM) radio broadcast stations whose transmitters are located in American towns having less than 5000 people. Or we might conduct an experiment to determine the lowest barometric pressures inside the eyes of all the Atlantic hurricanes that take place during the next 10 years.
Experiments often, but not always, require specialized instruments to measure quantities. If we conduct an experiment to figure out the average test scores of high-school seniors in Wyoming who take a certain standardized test at the end of this school year, the only things we need are the time, energy, and willingness to collect the data. But a measurement of the minimum pressure inside the eye of a hurricane requires sophisticated hardware in addition to time, energy, and courage.
Variable (in General)
In mathematics, a variable, also called an unknown, is a quantity whose value is not necessarily specified, but that can be determined according to certain rules. Mathematical variables are expressed using italicized letters of the alphabet, usually in lowercase. For example, in the expression x + y + z = 5, the letters x, y, and z are variables that represent numbers.
In statistics, variables are similar to those in mathematics. But there are some subtle distinctions. Perhaps most important is this: In statistics, a variable is always associated with one or more experiments.
In statistics, a discrete variable is a variable that can attain only specific values. The number of possible values is countable. Discrete variables are like the channels of a television set or digital broadcast receiver. It's easy to express the value of a discrete variable, because it can be assumed exact.
When a disc jockey says ''This is radio 97.1,'' it means that the assigned channel center is at a frequency of 97.1 megahertz, where a megahertz (MHz) represents a million cycles per second. The assigned value is exact, even though, in real life, the broadcast engineer can at best get the transmitter output close to 97.1 MHz. The assigned channels in the FM broadcast band are separated by an increment (minimum difference) of 0.2 MHz. The next lower channel from 97.1MHz is at 96.9 MHz, and the next higher one is at 97.3 MHz. There is no ''in between.'' No two channels can be closer together than 0.2MHz in the set of assigned standard FM broadcast channels in the United States. The lowest channel is at 88.1 MHz and the highest is at 107.9 MHz (Fig. 2-1).
Other examples of discrete variables are:
- The number of people voting for each of the various candidates in a political election.
- The scores of students on a standardized test (expressed as a percentage of correct answers).
- The number of car drivers caught speeding every day in a certain town.
- The earned-run averages of pitchers in a baseball league (in runs per 9 innings or 27 outs).
All these quantities can be expressed as exact values. There is no error involved when discrete variables are measured or calculated.
A continuous variable can attain infinitely many values over a certain span or range. Instead of existing as specific values in which there is an increment between any two, a continuous variable can change value to an arbitrarily tiny extent.
Continuous variables are something like the set of radio frequencies to which an analog FM broadcast receiver can be tuned. The radio frequency is adjustable continuously, say from 88MHz to 108MHz for an FM headset receiver with analog tuning (Fig. 2-2). If you move the tuning dial a little, you can make the received radio frequency change by something less than 0.2 MHz, the separation between adjacent assigned transmitter channels. There is no limit to how small the increment can get. If you have a light enough touch, you can adjust the received radio frequency by 0.02 MHz, or 0.002 MHz, or even 0.000002 MHz.
Other examples of continuous variables are:
- Temperature in degrees Celsius.
- Barometric pressure in millibars.
- Brightness of a light source in candela.
- Intensity of the sound from a loudspeaker in decibels with respect to the threshold of hearing.
Such quantities can never be determined exactly. There is always some instrument or observation error, even if that error is so small that it does not have a practical effect on the outcome of an experiment.
Practice problems for these concepts can be found at: Learning the Statistics Jargon Practice Test
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