What is Z score?
In order for you to compare the scores between sampling distributions you will need to standardize the scores. Imagine telling your friend that you have scored 90 for your finance and 60 for you statistics, your friend would naturally think you are a lot stronger in your finance. However, if the average marks in the class are 95 for finance and 56 for statistics, then you are actually better in your statistics.
Overall, standaradization allows:
1) Comparison of scores within a distribution
2) Comparison of scores between distributions
3) Comparison of scores among different scales – metres, milliseconds, grams etc
But it does not
• Fix skewness or kurtosis
There are three ways to standardized distributions:
1. Rescaling Data
a. Multiply or divide all the scores by a constant
b. Shape of distribution remains unchanged
c. Standard deviation has changed by the multiples
2. Shifting Data
a. Add or subtract all scores by a constant
b. Standard deviation remains unchanged
3. Z score (The most popular way)
a. Z Score identify and describe the exact location of every score in a distribution
b. It enables comparison between other normal distributions regardless of whether they are on the same scale or not
– z-scores express how far a score is from the mean in standard deviation units
c. It is given by the formula :
1) Scores on a psychology test have a distribution with a mean = 70 and standard deviation = 12. You score 86 on the exam. What is the z-score? How do you interpret this?
2) Top 5% of the cohort is awarded distinction. The average score in the cohort is 63 and the standard deviation is 10. What marks must you get to be awarded distinction?
3) Continuing the question in 2), what proportion of the students gets more than 70 marks?