PSYCH 2300 TEST#2 Chapters 5,6,7
Chapter 5: Z-scores
Z-score: procedure to compare scores from different data sets (distributions) with different central tendencies
and dispersions
For Example:
75 70
English 100 Math 100
• Need to know central tendencies and variability of both to decide which you did better on
• English x=75 µ=50 ℺=10
• Math x=70 µ=50 ℺=5
• Z-scores create a common denominator for making comparisons between scores from different
distributions
• Common denominator is the standard deviation
• Z-scores sometimes referred to as procedure for standardizing data/ standard scores
• 2 components
Positive + or negative – refers to above or below the mean
Quantitative value depicting distance between the score and the mean in terms of standard
deviation
Z= x−µ X=µ+Z ℺
• ℺
75−50
• English Z= 10 =2.5
70−50
Z= =4
• Math 5
• Relative to other scores the math score is higher
X=µ+Z ℺
• Solving for X given a Z-score
• Given a distribution of µ=50 and ℺=10
What score has a Z value of 5?
X=50+5(10)
X=100
• Additional characteristics:
Every value in a distribution can be changed into a Z-score
Shape remains exactly the same, scores are simply relabelled in terms of their distance from
the mean
The mean is always 0
Each standard deviation on the Z distribution is 1 unit ℺=1
• Have the disadvantage of having negative values • Often changed to other types of standard scores with pre-established means and standard deviations
(i.e. IQ scores have a mean of 100 and a standard deviation of 15
Chapter 6: Probability
• Relationships between populations and samples is often described in terms of “probability”
• Knowing the make-up of a population allows us to infer the likely characteristics of samples from the
same population (population to sample inference)
• This is backward from what we do in inferential statistics
• In research we are interested in whether the sample values belong to the control group population or
some other population different from the control – determine this using probability statistics
• Probability: number of outcomes classified as ‘A’ divided by total number of possible outcomes
• i.e. probability of picking a queen of spades from a deck of cards is 1/52
• i.e. picking an ace is 4/52
• Random Sampling
For this definition to work we assume our sample is attained by random sampling
There are 2 requirements for random sampling: each individual must have an equal chance of
being selected, if more than one case is selected we must have a constant probability for each
selection (sampling with replacing – putting each selection back into the pool so there is
constant probability)
If you take one card out of a deck the probability of picking a certain card on the second attempt
changes
Requirement for replacement becomes less important as the size of the sample increases
• 6,6,8,9,12,13,13,15
P (probability) of (X>8) = 5/8
P (probability) of (X<9) = 3/8
• Normal Distributions
Symmetrical
Highest frequency in the middle (mode = mean = median)
Frequencies taper off as scores get further from the mean
34.13% (34%) of the data in the distribution is 1 standard devia

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