Test 2 Study Guide Chapters 5-7

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Kevin Hamilton

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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