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Week 5 Announcement
Great job, you guys on finishing up the 1st month of summer stats! We are still on that learning
curve for both stats & Canvas, so I appreciate everyone’s patience.
The class notes for this week provide for you the basic building blocks for converting raw data to
standardized data so that we can move into inferential statistics & develop measurable
relationships between population data based upon sample data.
When learning about basic probability last week, we stopped prior to normal distribution. This
week, we will cover the normal distribution portion of the text. The material for this week will
end with Chapter 6 in your text. However, we will not be covering Probability & the Binomial
Distribution, so you do not need to intensively study this material covering Binomial
Distribution.
This week we are moving on with the progression of the probability concept. Last week we
worked on basic probability (i.e., coin tosses, die tosses, etc..). Basic probability is a broad
enough category to where it could be a course in & of itself. It serves us also as a foundation for
making broader probabilities with larger data sets.
This week, your written assignment focuses on the normal curve & converting raw scores to
standard scores. We are working from a number of different directions, so I included a lot of
narrative, or steps that are listed in class notes & in your commentary & imbedded them into the
assignment so you can refer straight to the material prior to each set of questions. Your
assignment includes first, using basic formulas for converting raw scores to standard scores &
standard scores back to raw scores, using the Unit Normal Table & then determining the
percentage of chance (probability) of obtaining a certain value given a standard score.
Your SPSS assignment this week involves a simple process of using the software to identify zscores associated with raw scores. Your assignments are due no later than Monday night end of
day. Remember to show your work & utilize the Discussion for any questions.
Below is some helpful commentary on understanding where we have come from, where we are,
& where we are headed next.
A new concept that we will be addressing this week is standardization. Standardization can
be a process in which the value of a potential standard is fixed by a measurement made with
respect to a standard whose value is known; the adoption of generally accepted uniform
procedures, dimensions, materials, or parts that directly affect the outcome; design of a
product or a facility or the process of establishing by common agreement criteria, terms,
principles, practices, materials, items, processes, and parts and components.
So that we can engage in inferential statistics (making statements about a population based
upon sample data), raw data must be conformed to standard data & compared to
measurements based upon a Standardized Distribution; composed of scores that have been
transformed to create predetermined values for a mean and standard deviation. Standardized
distributions are used to make dissimilar distributions comparable.
When raw scores are converted to standard scores, the mean & the standard deviation are
consistent. We covert raw data to standard scores for a couple of reasons:
1) So that we can identify the placement of a particular score within a distribution of
scores. Each standard score has 2 parts: The sign of the z-score (+ or -) signifies whether
the score is above the mean (positive) or below the mean ( - ). The numerical value of the
z-score specifies the distance from the mean by counting the number of standard
deviations b/t X and µ.
2) So that we can compare dissimilar values. Prior to converting raw data to standardized
data, we cannot make legitimate comparisons between dissimilar values (or comparison
between sample & population data) because the values are different & the mean &
standard deviations of the separate data sets are different. Once we convert dissimilar
values to standard scores, all the scores have the same mean & the same standard
deviation & then can be compared based upon each score’s placement on the standard
distribution. For example, people may display intelligence in different ways using
different values. But until you convert these values to standard scores, you cannot make a
valid statement that “one score denotes higher intelligence than another.” Z-scores are
one form of standard scores, but there are other forms of standard scores, one of which
are IQ scores. Raw scores are converted to standard scores using a standard mean of 100
& a standard deviation of 15 so that IQ scores can then be correctly compared &
categorized.
3) Converting raw scores to standard scores helps us to better understand the world of
inferential statistics; where we are using raw values & making inferences about a
population or the lager world around us, based upon the values that we have to work
with.