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# TTU - PSY 2400 - Class Notes - Week 3

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TTU - PSY 2400 - Class Notes - Week 3

This preview shows pages 1 - 3 of a 15 page document. to view the rest of the content PSY 2400 – Statistical Methods 09/13/2016 Ch. 3 Measures of Central Tendency
Likert-type values are NOMINAL
If you are talking about a single item that is measured with a likert-
type response cale (i.e., 1= not at all; 5 = extremely). That is an
ordinal item (ie., there are five, ordered response categories to
choose from).
When taking averages of Likert-type items (as psychologists tend to
do), you form a Likert-type scale score. We can view and use likert-
type scale scores as interval variables (like most in our field do). The
idea is that you are making your measurement scale more reliable
as you combine items (i.e., forming a scale score that is less
‘arbitrary’ than any single item).
The big distinction between an ordinal and interval variable is
whether a mean and standard deviation can be calculated and is
also meaningful to interpret
Defining Central Tendency Central tendency  o A statistical score to define the “center” of a distribution
o Not always easy to find center of distribution with positive or
negative skew o Measures of central tendency use a single number to describe an entire group of scores o Refers to the middle of the group of scores Mean  Median  Mode Purpose: find the single score that is: o Most typical OR o Best represents the entire group  Central Tendency Measures No single concept of central tendency (i.e., mean, median, mode) is
“best” Mean is nonsensical, doesn’t always represent everyone in data Different distribution shapes require different conceptualizations of
“center”
Critically think: which measure of central tendency best represents
a summary of the scores in a specific situation?
Mean The mean is the sum of all the scores divided by the number of
scores in the data
o Population  o Sample Mathematical average of a group of scores o Sum of the scores divided by the number of scores Formula for figuring the mean M = ΣX      X = ΣX           N                       n  o M or  X = mean o ∑ = sum (add up all of the scores)
o X = scores in the distribution of the variable X
o N = number of scores in the distribution (or participants in
your sample).  N X n X M Mean: Three definitions Mathematical definition: sum of the scores divided by the
number of scores in the date
Equity definition: the amount each individual is allocated
when the total is divided equally among all the individuals
in the distribution
Visual definition: the balance point for the distribution “Weighted” Mean        used when combining two sets of scores from two different  groups or samples  Three steps: o Determine the combined sum of all the scores
o Determine the combined number of scores
o Divide the sum of scores by the total number of scores
o Overall mean :
2 1 2 1 n n X X M

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