STATISTICAL ANALYSIS ON DESIGN AND ANALYSIS OF EXPERIMENTS

INTRODUCTION

• Design of experiments is defined as a branch of applied statistics that deals with planning, conducting, analyzing and interpreting controlled tests to evaluate the factors that control the value of a parameter or group of parameters.

• Statistical knowledge has a mysterious quality that inhibits long-term retention.

• Many of the current statistical approaches to designed experiments originate from the work of R.A.Fisher in the early part of the 20th century.

CENTRAL TENDENCY AND VARIABILITY

• Measures of central tendency such as the mean, median, and mode summarize the performance level of a group of scores, and measures of variability describe the spread of scores among participants.

• One provides information on the level of performance, and the other reveals the consistency of that performance.

EXAMPLE OF CENTRAL TENDENCY AND VARIABILITY

Let’s illustrate the two key concepts of central tendency and variability by considering a scenario that is repeated many times. It is the crucial moment in the football game. Your team is losing by four points. Time is running out, it is fourth down with two yards to go, and you need a first down to keep from losing possession of the ball. The quarterback must make a decision: run for two or pass. His report is summarized in given table.

Yards gained or lost by passing and running plays. The mean gain per play, +4 yards, is identical for both running and passing plays.

A frequency distribution shows the number of times each score (in this case, the number of yards) is obtained.

MEASURES OF CENTRAL TENDENCY

Mean

• Two of the most frequently used and most valuable measures of central tendency in psychological research are the mean and median.

• The mean, commonly known as the arithmetic average, consists of the sum of all scores divided by the number of scores.

• Symbolically, this is shown as X. X = in which X is the mean; the sign directs us to sum the values of the variable X.

Median

• The median does not use the value of each score in its determination.

• To find the median, you arrange the values of the variable in order either ascending or descending — and then count down (n + 1) / 2 scores.

• This score is the median. If n is an even number, the median is halfway between the two middle scores.

Mode

• A rarely used measure of central tendency, the mode simply represents the most frequent score in a distribution.

• Thus, the mode for pass plays is 0, and the mode for running plays is 3. • The mode does not consider the values of any scores other than the most frequent score.

• The mode is most useful when summarizing data measured on a nominal scale of measurement.