Chapter 5  NORMAL DISTRIBUTION AND Z-SCORE

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Chapter 5  NORMAL DISTRIBUTION AND Z-SCORE Understanding Statistics for International Social Work and Other Behavioral Sciences Serge Lee, Maria C Silveira Nunes Dinis, Lois Lowe, and Kelly Anders (2015). Oxford University Press

NORMAL CURVE The sum of the deviations of all observation scores from the mean is balanced at the center point on the number line, which is equal to or very near zero

SKEWED DISTRIBUTION Positively Skewed Distributions Negatively Skewed Distributions Lee. Dinis, Lowe, Anders (2015). Understanding statistics for international social work and other behavioral sciences. Oxford University Press

STANDARD DEVIATION ON PROPORTION OF THE NORMAL CURVE The normal curve is divided into six equal units. The six units collectively reflect the variation that exists within virtually all values of a normally distributed interval or ratio level scale variable. Confidence interval Lee. Dinis, Lowe, Anders (2015). Understanding statistics for international social work and other behavioral sciences. Oxford University Press

DISTANCE BETWEEN THE SAMPLE MEAN AND STANDARD DEVIATION The proportion between the mean and their corresponding standard deviations are divided as below: Distance from the mean and standard deviation 1SD 2SD 3SD Total areas under the normal curve Left side only of the curve between mean and SD (-SD) 34.13 13.59 2.15 49.87 Right side only of the curve between mean and SD (+SD) Both sides under areas of the normal curve 68.26 27.18 4.30 99.74 Confidence interval Lee. Dinis, Lowe, Anders (2015). Understanding statistics for international social work and other behavioral sciences. Oxford University Press

CALCULATE THE Z-SCORE AND CONVERT TO A PERCENTILE Formula: Z = X− X SD Statistics rules for the conversion of the Z-score into percentile ranks: Always round the calculated Z-score to two decimal places. For example, Z = -2.29 If the calculated Z-score is positive (+), add 50% or .50 (if use decimals) to the percentile obtained from the standard normal curve table If the calculated Z-score is negative (-), subtract the percentile obtained from the critical values of the standard normal curve table from 50% or .50 (if use decimals)