3.4 - Measures of Location

Measures of Location

tell us the position of a score within a distribution

• Percentile

• Quartile

• Decile/Sten

Measures of Location (3)

Percentile

divided the ordered observations into 100 equal parts

Quartile

three dividing points

Q1

25th Percentile

Q2

50th Percentile

Q3

75th Percentile

Decile

divide into 10 equal parts

• Skewness

• Kurtosis

Characteristics of DATA DISTRIBUTION (2)

Skewness

measures how asymmetric a distribution is around its mean.

• Positively Skewed

• Negatively Skewed

Skewness (2)

Positively Skewed

more test takers got low scores

• difficult

Positively Skewed

Mean>Median>Mode

Negatively Skewed

more test takers got high scores

• easy

Negatively Skewed

Mode>Median>Mean

mean

To interpret the skewness, look at the tail. The ____ is the nearest to the tail

Kurtosis

refers to the “peakedness” of height of a distribution

• Leptokurtosis

• Platykurtosis

• Mesokurtosis

Types of Kurtosis: (3)

Leptokurtic

tall & narrow peak

Less variation, scores cluster tightly around the mean, heavier tails

Platykurtic

flat & wide peak

Greater dispersion, scores spread out, lighter tails

Mesokurtic

normal bell curve

Moderate peak & spread, standard normal distribution

skewed

A curve is symmetrical if when folded into half, two sides coincide.

• If curve is not symmetrical, curve is ____

Normal Distribution

is a symmetric, bell-shaped distribution where:

• Most scores cluster around the middle

• Few scores are at the extremes

Normal Distribution

Mean = Median = Mode

Normal Distribution

Q1 AND Q3 have EQUAL DISTANCES TO THE Q2 (Median)

Standardized tests

_____ by nature are norm referenced

Norms

are established by administering the instrument to a standardization group and then referencing an individual’s score to the distribution of scores obtained in the standardization sample

Norms

are reference points that allow us to compare an individual’s score to a group

Norms

Establishing ___ (group data characteristics) allows us to compare an individual score with a comparison sample

Developmental Norms

Comparison of an individual’s score to the individual’s grade level or age group

Grade Equivalents

often used on educational achievement tests

to interpret how a student is progressing in terms of grade level

Age Comparisons

Refer to an individual being compared with others in his or her age group

Rank

A person’s ___ or standing within a group is the simplest norm-referenced statistic

• with its interpretation based on the size and composition of the group

Rank

• Used extensively for grades

• Seldom used in describing psychological test results

Standard Scores

Score expressed as a distance

• in standard deviation units, between a raw score and the mean

Standard Scores

A raw score that has been converted from one scale to another scale to make scores more understandable

• statistically significant relative to other test takers

• Z scores

• T Scores

• Deviation IQs

• Stanines

• Standard Error of Measurement (SEM)

Types of Standard Scores: (5)

Z score

Mean of 0 ; SD of 1

• Simplest standard score

Z score

A _____ of 0.05 suggests that the person slightly passes the middle score

Z score

A score that allows us to estimate where a raw score would fall on a normal curve

tests

If you convert raw scores to z scores, you can compare them across different types of ____ easily

Z score

produce both decimals and negative values

Z = X-M/SD

Z Score FORMULA:

X = raw score

M = group mean

SD = standard deviation

T scores

Most common standard score

• used on a number of the most widely used educational and psychological tests

T scores

Mean of 50; SD of 10

• MCCALL’s T of 50 Plus

• Minus 10 Scale

T scores can be called as?

T scores

No Negatives

• Results of many aptitude, interest, and personality measures are profiled in terms of ___ scores

Deviation IQ Scores

Mean = 100 ; SD = 15 (1 standard deviation unit)

• Used for interpreting IQ

Deviation IQ Scores

Standard score on an intelligent test that approximates the SD of Stanford-Binet IQ Distribution

Deviation IQ Scores

Uses statistics to analyze a person’s intelligence relative to their age

Stanines

Based on the term standard nine; divides a data distribution into 9 parts

• Infrequently used

Stanines

_____	Description
1-3	Low
4-6	Average
7-9	High

Sten

divides a distribution into 10 parts

• Mean = 5.5, SD = 2

• Similar to stanines but uses 10 categories instead of 9.

GRE (Graduate Record Exam) / SAT (Scholastic Aptitude Test)

• A Score

Admission to graduate school or college

• Scoring:

  • Mean = 500

  • SD = 100

GRE (Graduate Record Exam) / SAT (Scholastic Aptitude Test)

• A Score

Administered to a large group of students to establish norms

Relationship between Standard Scores:

• Bell shaped / symmetrical

• Mean, Median, Mode EQUAL

• Body and 2 infinite tails

• Asymptotic

QUALITIES OF A NORMAL CURVE OR NORMAL DISTRIBUTION:

Asymptotic

tails (symptote) do not touch the X-Axis or Abscissa

Scatter diagram

is a picture of the relationship between 2 variables

Correlation

we ask whether 2 variables covary. In other words, does Y get larger as X gets larger?

Correlation Coefficient

a mathematical index that describes the direction and magnitude of a relationship

Correlation Coefficient

(r) is a number from -1 to +1 that indicates the strength and direction of a relationship between two variables

1

The nearer to _, the STRONGER the correlation coefficient

• ±1

• 0

• Perfect correlation is __

• weak correlation is near __

• Positive

• Negative

• No Correlation

Correlation (3)

Positive Correlation

High scores on Y go with high scores on X, and low scores on Y go with low scores on X.

• Graph: Upward sloping scatter plot

• Example: Hours studied ↑ → Exam score ↑

Negative Correlation

High scores on Y go with low scores on X, and low scores on Y go with high scores on X.

• Graph: Downward sloping scatter plot

• Example: Hours spent on social media ↑ → Exam score

No Correlation

Variables are not related; knowing X tells nothing about Y

• Graph: Random scatter of points

• Example: Shoe size ↔ IQ

Size of Correlation & Interpretation:

Regression

is a statistical method used to predict scores on one variable (Y) from scores on another variable (X)

• Predictions are based on the regression line

Regression

Related to correlation, but correlation only shows strength and direction, while _____ predicts actual values

Regression Line

best-fitting straight line through a set of points on a scatter diagram/plot

Regression Line

Simple Example

• Variable X = hours studied

• Variable Y = exam score

If a student studies 5 hours, the ______ __ predicts their likely exam score.