Normal Distribution, Z-Scores & Percentiles Flashcards
What is a z-score?
A z score is the number of standard deviations a particular score is from the mean.
The only information we need to convert any raw score to a z score is the mean and standard deviation of the sample or population of interest.
What are the steps for converting a raw score to a standardized score?
Step 1: State appropriate formula (population or sample formula).
Step 2: Subtract the mean from your score.
Step 3: Divide this value by the standard deviation.
What is standardization?
Standardization is the process of converting scores from different distributions to the same distribution.
What are the properties of any normal distribution?
- Its shape is symmetric
- Its distribution has a bump in the middle, with tails going down and out to the left and right.
- The ends of the curve do not touch the abiscca
- It has a theoretical mean of zero (0) and a standard deviation of one (1).
- Proportions follow the Empirical Rule: allows researchers to determine the proportion of values that fall within certain distances from the mean.
Which table is used in z-score calculation?
Table Z:
Column 1 = z-score
Column 2 = Area between the mean and z-score
Column 3 = Area beyond the z-score
To find probability, likelihood or percentage, multiply proportion by 100 to convert to percentage
What is a percentile?
A percentile is a statistical measure that compares a score to the scores of the rest of a group & has a certain percentage of scores below it.
Thepercentile means the percentage group you’re in.
What are the steps for finding percentile?
- Divide percentile by 100 to convert to proportion
- i) If percentile is above the 50th (Proportion – 0.5)
ii)If percentile is below the 50th (0.5 –Proportion) - Find proportion in Column 2 of Table Z
- Determine z-score for this proportion from Column 1. Note: if percentile is below the 50th, the z-score is negative
- Use formula to convert z-score to percentile
x = x + z (s)
