power of statistical analysis is the power to define, interpret, and understanding numerical data which represents patterns in the real world. Without the ability to measure statistical data, the empirical, hypothetical world of educational models would not be able to be checked by actual performance in the absolute. While statistics has applications in many fields, statistical data is possibly the most powerful when used to identify patterns in personal behavior, and other fields of study which do not exhibit direct patterns across a sampling group. For example, mathematical equations govern how a specific metal will respond to different loads, and different conditions. However, there are no direct mathematical equations which govern the percentage of teenage drivers who will be involved in traffic accidents over a period of time. In order to interpret the influential factors over teen drivers, a statistical measurement of actual experience can be undertaken. Through statistical analysis, patterns and tendencies can be discovered, and decisions can be made based on real life experience rather than theory, and assumption.
For this review of statistical methods, the following data table will be used. This data is a measure of the tar, nicotine, and CO2 which is produces while a given cigarette brand is smoked. The data presented below is taken from Mendenhall and Sincich (1992) and is a subset of the data produced by the Federal Trade Commission. It was submitted by Lauren McIntyre, Department of Statistics, North Carolina State University.
Carbon Monoxide (mg)
Benson & Hedges
Pall Mall Light
Viceroy Rich Light
Statistical data can be categories in the following groups.
Can be Divided into Can be Divided into Nominal Data
Nominal Data is data that can be categorized, but cannot be ranked based in intensity, nor its magnitude. Examples of nominal data include political parties, religions, favorite flavors of ice cream. Ordinal Data is data that can be categorized, and ranked by class, but whose magnitude cannot be measured For example, ordinal data can be rated by a scale such as 'Excellent-Good-Fair-Poor-Bad.' Interval Data is data that can be categorized, ranked, and whose magnitude can be measured. For example, student Grade Point Averages, SAT scores, can be both measures, and ranked according to age, gender, or nationality of the student. Ratio Data is data that can be categorized, ranked, and whose magnitude can be measured, and is such that a score of zero is a valid score, and represents the total absence of the trait being measured. For example, a person's height, or the temperature can be used in ratio data calculations.
Frequency distribution is the measure of the frequency which a particular data presents itself across a given sampling. A chart or table showing how often each value or range of values of a variable appears in a data set is considered a frequency distribution. For example, the number of accidents occurring within the population of teenage driver would create a frequency distribution. Central tendency is a measure of location of the middle or the center of a distribution. The mean or average value is the most commonly used measure of central tendency. Calculated from the cigarette data above, the Mean tar grams for a cigarette is 12.216 milligrams.
A weighted average is a measure which gives additional weight to the occurrence of measured data based on population sampling. Returning to our teenage driver example, an average measure of teen accident per 1000 teen drivers may produce a general figure. A more accurate measurement that could be accurately applied to all teens would be to produce weighted averages which took into account factors such as drugs and alcohol, or number of passengers in the vehicle and how these factors weighted the occurrence of accidents among teen drivers. From a weighted average computation of this type, probability distributions could be plotted regarding the likelihood of a teen accident, based on the additional factors.
Normal distributions for data sets will typically fall within a bell shaped curve. Often just called the bell-curve or bell-shaped curve, which measures the occurrence of most scores…