Design and Statistics
Chapter 4:
OVERVIEW:
If the scores in a distribution are all the same, then there is no variability; if there
are small differences between scores then the variability is small; and if there
are large differences between scores then

Design and Statistics
Chapter 5:
USING Z-SCORES TO STANDARDIZE A DISTRIBUTION:
It is possible to transform every X value in a distribution into a corresponding zscore, the entire distribution of X values is transformed into a distribution of zscores (z-

Design and Statistics
Chapter 5:
OTHER STANDARDIZED DISTRIBUTIONS BASED ON Z-SCORES:
It is common to standardize a distribution by transforming the scores into a new
distribution with a predetermined mean and standard deviation that are whole
round numbe

Design and Statistics
Chapter 5:
INTRODUCTION TO Z-SCORES:
The purpose of z-scores, or standard scores, is to identify and describe the exact
location of every score in a distribution.
A score by itself does not necessarily provide much information abou

Design and Statistics
Chapter 4:
TRANSFORMATIONS OF SCALE:
o Occasionally a set of scores is transformed by adding a constant to each score
or by multiplying each score by a constant value.
o The easiest way to determine the effect of a transformation is

Design and Statistics
Chapter 4:
1. STANDARD DEVIATION (SD)*
The most commonly used and the most important measure of variability.
SD used the mean of the distribution as a reference point and measures
the variability by considering the distance between

Design and Statistics
Chapter 4:
STANDAR DEVIATION AND VARIANCE FOR SAMPLES:
The goal of inferential statistics is to use the limited information from samples to
draw general conclusions about populations.
o The basic assumption of this process is that s

Design and Statistics
Chapter 6
Probability: a fraction or a proportion of all the possible outcomes for a situation
in which several different outcomes are possible.
o If the possible outcomes are identified as A, B, C, D and so on
Probability of A= (nu

Design and Statistics
Chapter 6
PROBABILITY AND THE NORMAL DISTRIBUTION:
Normal distribution is symmetrical, with the highest frequency in the middle and
frequencies tapering off as you move toward either extreme.
Z-scores measure the positions in a dis

Design and Statistics
Chapter 7
Variability and Standard error serves two different purposes:
1. The standard deviation describes the distribution by telling whether the
individual scores are clustered close together or scattered over a wide
range.
2. Th

Design and Statistics
Chapter 7
PROBABILITY AND THE DISTRIBUTION OF SAMPLE MEANS:
The primary use of the distribution of sample means is to find the probability associated
with any specific sample.
o Because the distribution of sample means presents the

Design and Statistics
Chapter 7
Larger populations and larger samples, the number of possible samples will
increase dramatically and it will virtually impossible to actually obtain every
possible random sample.
It is possible to determine exactly what th

Design and Statistics
Chapter 7
SAMPLES AND POPULATIONS:
Sampling error: the natural discrepancy, or amount of error, between a sample
statistic and its corresponding population parameter.
The sample provides an incomplete picture of the population.
Sa

Design and Statistics
Chapter 6
Finding proportions/probabilities for specific z-score values:
o We begin with a specific z-score value and then use the unit normal table
to find probabilities or proportions associated with the z-score.
Finding the z-sco

Design and Statistics
Chapter 6
PROBABILITY AND THE BINOMIAL DISTIRBUTION:
When a variable is measured on a scale consisting of exactly two categories, the
resulting data are called binomial.
The term binomial can be loosely translated as two names, ref