PSYC*1010 Chapter 5: Z-Scores Flashcards
What is a z-score?
A type of standardized score
What does the sign of a z-score indicate?
- Whether it’s located above or below the mean
- (+) is above the mean
- (-) is below the mean
What does the numerical value of a z-score indicate?
The number of standard deviations between the mean and the score
T or F: The location identified by z-scores are the same for all distributions, regardless of the mean or standard deviation for that distribution.
True
When calculating z-scores, what does the numerator (X-μ) in the equation measure?
- (X-μ) is the deviation score
- Measures the distance in points between the score and the mean
When calculating z-scores, why is the numerator/ deviation score (X-μ) divided by the standard deviation?
So the distance between the mean and the score is in terms of the number of standard deviation units
What is the equation for calculating a z-score in a population?
z= (X-μ)/σ
How can a raw score be determined from a z-score?
By rearranging the z-score equation
What is the equation for transforming a z-score into a raw score from a population?
X= μ + zσ
If every X value is transformed into a z-score, how will the shape of the distribution change?
The distribution of z-scores will have exactly the same shape as the original distribution
If every X value is transformed into a z-score, how will the mean of the distribution change?
The z-score distribution will always have a mean of zero
If every X value is transformed into a z-score, how will the standard deviation of the distribution change?
The z-score distribution will always have a standard deviation of one
What is a standardized distribution?
A distribution composed of scores that have been transformed to create predetermined values for μ and σ
Why does a standardized deviation always have a standard deviation of one?
Because the numerical value of a z-score is exactly the same as the number of standard deviations it is from the mean
Why are two raw scores from different distributions unable to be compared, but two z-scores from different distributions can be?
- Raw scores from two different distributions likely have different means and standard deviations
- All z-scores have the same mean and standard deviation, so they can be compared across distributions
What is a standardized score?
A score that has been transformed into a standard form
What is the procedure for standardizing a distribution to create new values for μ and σ?
- Transform raw scores (X) into z-scores
- Transform z-score back into a raw score/X value using the predetermined μ and σ
What is the difference between the z-score equation for a score from a population and the z-score equation for a score from a sample?
The equation is identical, but the notation is different
What is the equation for calculating a z-score in a sample?
z= (X-M)/s
What is the equation for transforming a z-score into a raw score from a sample?
X= M + zs
T or F: If all scores in a sample are transformed into z-scores, their distribution will have the same properties that exist when all scores in a population are transformed into z-scores.
True
