Module 16: Transformation Scores and Correlation Coefficients

Question 1

Normal distribution (normal curve)

Answer 1

When plotted as a frequency polygon, a normal distribution forms a symmetrical, bell-shaped pattern often called a normal curve. We say that the pattern approximates a normal distribution because a true normal distribution is a theoretical construct not actually observed in the real world.

Question 2

Kurtosis

Answer 2

Refers to how flat or peaked a normal distribution is

• Positive kurtosos (leptokurtic): distributions with heavier tails than normal distributions; so more extreme score.
• Negative kurtosis (platykurtic): distributions with lighter tails than normal distributions; so even fewer extreme scores than a normal distribution

Question 3

Skewness

Answer 3

Positively/negatively skewed distributions

Positive: leaning toward the left
Negative: leaning toward the right

Question 4

Z-scores

Answer 4

Z-scores are useful for calculating individual information. We may want to know how an individual’s exam score in one class, say psychology, compares with the same person’s exam score in another class, say English. When the z-score is positive it means the person scored higher than the mean of the distribution and when it is negative it means the person scored lower.

Question 5

Conceptual formula z-score

Answer 5

Z-score = (raw score - population mean) / population standard deviation

Question 6

Standard normal distribution

Answer 6

A normal distribution with a mean of 0 and a standard deviation of 1. It’s a theoretical distribution and can’t be achieved perfectly

Question 7

Probability

Answer 7

is defined as the expected relative frequency of a particular outcome, which could be the result of an experiment or any situation in which the result is not known in advance. For example, from the normal curve what is the probability of randomly choosing a score that falls above the mean? The probability is equal to the proportion of scores in that area, or .50.

Question 8

Percentile rank

Answer 8

the percentage of scores equal to or below the given raw score or the percentage of scores the individual’s score is higher than.

Question 9

Correlation coefficients

Answer 9

a statistical measure of the strength of the relationship between the relative movements of two variables. The values range between -1.0 and 1.0. 4 types:

• Pearson’s correlation
• Spearman’s rho
• Point-biserial correlation
• Phi-coefficient

Question 10

Pearson’s correlation

Answer 10

Correlation between two variables with interval or ratio levels of measurement.

E.g. Correlation between size and weight.

Question 11

Spearman’s rho

Answer 11

Correlation between two variables with (at least) ordinal levels of measurement.

E.g. Correlation between stamina (ranging from high to low) and place in a race (ranging from first to last).

Question 12

Point-biserial correlation

Answer 12

Correlation between one nominal variable (with 2 categories) and an interval variable.

E.g. Correlation between gender and body weight.

Question 13

Phi-coefficient

Answer 13

Correlation between two nominal variables (each with 2 categories).

E.g. Correlation between text genre (narrative versus expository) and presence of illustrations (absent versus present).