# PSY201H1 Lecture Notes - Lecture 4: Lightning, Statistical Inference, Standard Deviation

by OC1939242

Department

PsychologyCourse Code

PSY201H1Professor

Maria IankilevitchLecture

4This

**preview**shows page 1. to view the full**4 pages of the document.**What are z-scores?

• Determining the location of a score

• Transforming distributions into z-scores and other standardized distributions

• Comparing scores of different distributions

Purpose of transforming X values into z-scores:

1. To determine the exact location of a score relative to the distribution

2. To form a standardized distribution that can be directly compared to other distributions

Ex. 78% in this class. Another section of the class had a different mu and different standard

deviation. If you wanted to compare both scores, you need a standardized way to do that. Z-

scores can convert our scores to their scores or vice versa, or we transform them all into z-

soes ad e a see ho they’e all elatie to eah othe.

1. Determining the location of a score in a distribution

Sign indicates whether the score is located above (+) or below (-) the mean

Number indicates the distance between the score and the mean

• Indicates the number of standard deviations a score is from the mean

Z-soe distiutio alays has a ea of . It’s alays eual to the ea. Eah stadad

deviation is equal to 1. When you transform raw scores into z-scores, we transform them so the

mean is 0 and the SD is 1. If you had a skewed distribution, then your z-scores would also be

skewed.

A z-soe of z = +. idiates a positio i a distiutio…

= above the mean by a distance equal to 1 standard deviation

A negative z-score always indicates a location below the mean. (true)

A score close to the mean has a z-score close to 1.00. (false)

Population: Z = (x – μ/σ

Sample: Z = (x – M)/s

What is Maus’s z-score? z = (x – μ/σ = – 7)/0.5 = 1/0.5 = +2

What is Kei’s z-score? z = (x – μ/σ = . – 7)/0.5 = 0.5/0.5 = +1

What is Jaie’s z-score? z= (x- μ/σ = (6.5 – 7)/0.5 = -0.5/0.5 = -1

What is Ai’s z-score? z= (x- μ/σ = (8.2 – 7)0.5 = 1.2/0.5 = +2.4

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