Chapter 4: The Normal Curve

distribution of Z

*Appendix A: Table of Areas Under the Normal Curve*--gives information about the amount of area under the normal curve that's located between the mean and any point along the baseline of the curve. *Pages 84-89* 95 % of the area UTNC is located within Z values of +/- 1.96 and 99% of the area UTNC is located withing Z values of +/- 2.58.

Z ratio

a ratio of the difference between a raw score and mean--expressed in standard deviations..

standardized normal curve

a theoretical curve that serves as a basis or model for comparison--point of reference--a standard against which information or data to be judge--*based on an infinite number of cases*. Also referred to as standardized normal distribution and normal curve.

ordinary normal curves

are always tied to empirical or observed--despite endless array of normal distributions each would conform to the same underlying relationship between the mean and standard deviation of the distribution and the shape of the curve.

Z value

in terms of normal curve it is a point along the baseline--because standard deviation is 1 a Z value of 1 on the baseline represents 1 SD away from the mean.

Z score formula

simply directs you to find the difference between raw score and the mean and then divide that difference by the standard deviation.

theoretical curve

standardized normal curve is considered this...based on an *infinite number of cases*--there is never an end to either side of the curve and it NEVER touches the baseline because there is *always more case to consider*.

standardized

two properties that give rise to this term--a mean of 0 (any point along the baseline above the mean as a positive value and below the mean as a negative value) and a standard deviation of 1--and make the standardized normal curve so useful in statistical analysis.

1-2-3 Rule

would always apply--useful due to the fact that you can use it regardless of the underlying scale of measurement--approx 68% +/- 1 standard deviation--approx 95% +/- 2 SD--more than 99% +/- 3 SD *Figure 4-2*