Week 4 Flashcards
Describe the two general purposes for transforming X values into z-scores.
- Each z-score shows exactly where each original x value is located in the distribution.
- The z-scores form a standardized distribution that can be directly compared to other distributions that also have been transformed into z-scores.
What is the z-score formula? (Transforms x values into z-scores).
z=X-μ/σ
Deviation divided by standard deviation
What is a z-score and how does it identify a precise location in a distribution?
A metric value that indicates the distance from the mean measured in standard deviations.
Plus or minus signs are used to determine if the score falls above or below the mean.
What is the formula used to transform z-scores into x values?
X=zσ+μ
Z-score times standard deviation plus the mean
How do you find an unknown standard deviation when given a z-score, a score, and the mean?
σ=(X-μ)/z
Score minus mean divided by z-score
How do you find an unknown mean when given a z-score, a score and the standard deviation?
μ=X-zσ
score minus the product of multiplying the z-score the standard deviation
What happens when you standardise a distribution by converting all of the x values in z-scores?
Shape stays the same, mean is always converted to 0, SD is always converted to 1.
This allows dissimilar distributions to be comparable.
Explain how z-scores can help researchers use the data from a sample to draw inferences about populations.
When comparing z-scores, z-scores closer to 0 are representative of the population where as z-scores far away from 0 are significantly different from the other scores in the distribution.
Define “probability”
For a situation where multiple outcomes are possible, the probability is the extent to which an outcome is likely to occur. The outcome is defined as a proportion/fraction/percentage of all possible outcomes.
Define “random sample”
A sample in which each individual in the population have an equal chance of being selected. A sample obtained in this way is called a single random sample.
Define “independent random sample”
Each individual has an equal chance of being selected and the probability of being selected stays the same from one selection to the next. This is sometimes called “equal probability of selection method” or EPSEM.
What is sampling with replacement?
In order to satisfy independent random sampling, the current selection must be returned to the population before the next selection is made to ensure the probability of being selected stays the same.
What is a normal unit table?
A table listing proportions relating to each z-score location in a normal distribution.
What calculation needs to be done to use a normal unit table when given an X value?
z=X-μ/σ
(the z-score formula) this is then used to find z-scores on a normal unit table.
Explain how probability can be used to evaluate a treatment effect by identifying likely and very unlikely outcomes.
Using the probability of obtaining certain scores as criteria for identifying if a treatment has had an effect.
