TOPIC OUTLINE:

1. The Normal Curve

a. Definition/Description

b. Area Under Normal Curve

2. Standard Scores

a. Z-Scores

b. T-Scores

c. Other Standard Scores

NORMAL CURVE

- Karl Friedrich

Gauss:

one of the scientist

that developed the

concept of normal

curve.

Common term:

Laplace-Gaussian

Curve or Gaussian

* Normal Curve

is a continuous

probability distribution

in statistics

Karl Pearson:

first to refer to the

curve as “Normal

Curve”

NORMAL CURVE

- Karl Friedrich

Gauss:

one of the scientist

that developed the

concept of normal

curve.

Common term:

Laplace-Gaussian

Curve or Gaussian

Characteristics:

- Smooth bell shaped curved

- Asymptotic: approaching the x-axis but never touches it

- Symmetric: made up of exactly similar parts facing each other

Characteristics:

- Ranges from negative to positive infinity

- With two tails

A normal curve has two tails.

• The area on the normal curve between 2 and 3 standard deviations above the mean is referred to as a tail.

• The area between -2 and -3 standard deviations below the mean is also referred to as a tail.

AREA UNDER THE NORMAL CURVEThe normal curve can be divided into areas defined in units of

standard deviation.

1. 50% of the scores occur above the mean and 50% of scores occur below the mean

50%(ABOVE)

50%(BELOW)

MEAN

2. Approximately 34% of all scores between the mean and one standard deviation above the mean

3. Approximately 34% of all scores between the mean and one standard deviation bellow the mean

4. Approximately 68% of all scores between the mean and ±1 standard deviation.

5. Approximately 95% of all scores between the mean and ±2 standard deviation.

STANDARD SCORES

-is a raw score that has been converted from one scale to another scale.Raw scores maybe converted to standard scores because standard scores are more easily to understand than raw scores.

Different systems:

Z-scores- called a zero plus or minus one scale- results from the conversion of a raw score into a number indicating how many standard deviation units the raw score is below or above he mean of the distribution. - Scores can be positive and negative

Z-scores

- X - raw score- U - mean- Q - standard deviation

xz

T-Scores

- The scale used in the computation of t-scores can be called a 50 plus or minus ten scale. ( 50 mean set and 10 SD set )

- Composed of scale ranges from 5 SD below the mean to5 SD above the mean.

- One advantage in using T-Scores is that none of the scores is negative.

Page 99

- SD = 15- Mean = 50

Process:

Value = (mean + (number of deviation x 1 standard deviation) )65 = ( 50 + ( 1 X 15 )Value = (mean – (number of deviation x 1 standard deviation) )35 = ( 50 – ( 1 X 15 )

X bar + 1s = 50 + 15 =

X bar - 1s = 50 - 15 =

Stanine: Standard Nine

(STAndard NINE) is a method of scaling test scores on a nine-point standard scale with a

mean of five and a standard deviation of

two.

SUMMARY:

Karl Friedrich Gauss: one of the scientist that developed the concept of normal curve.

Normal Curve is a continuous probability distribution in statistics

Karl Pearson: first to refer to the curve as “Normal Curve”

Asymptotic:approaching the x-axis but never touches it

Symmetric:made up of exactly similar parts facing each other

STANDARD SCORES-is a raw score that has been converted from one scale to another scale.

Z-scorescalled a zero plus or minus one scaleScores can be positive and negative

T-Scoresa none of the scores is negative. It can be called a 50 plus or minus ten scale. ( 50 mean set and 10 SD set )

Stanine: Standard Nine(STAndard NINE) is a method of scaling test scores on a nine-point standard scale with a mean of five and a standard deviation of two.

Reanne MariquitAB PSYCHOLOGY

Rhea MoringAB PSYCHOLOGY

Ace MatilacAB PSYCHOLOGY

UNIVERSITY OF IMMACULATE CONCEPTION Davao City, Philippines © 2015

Reference: Cohen, Swerdilik, & Sturman (2013). Psychological Testing and Assessment: An Introduction to Test and Measurement, Eight h Edition. Philippines: McGrawHill Education.

Reanne MariquitAB PSYCHOLOGY

Rhea MoringAB PSYCHOLOGY

Ace MatilacAB PSYCHOLOGY

UNIVERSITY OF IMMACULATE CONCEPTION Davao City, Philippines © 2015

Reference: Cohen, Swerdilik, & Sturman (2013). Psychological Testing and Assessment: An Introduction to Test and Measurement, Eight h Edition. Philippines: McGrawHill Education.