Download The PsychSim5 Activities - Greenwich Public Schools

Descriptive Statistics 1
PsychSim 5: DESCRIPTIVE STATISTICS
Name:
Section:
Date:
This activity introduces you to the basic statistics that researchers use to summarize their sets of data.
The numbers below represent the scores of a group of students on a math test. Use them to perform
the required calculations.
10, 13, 10, 12, 11, 7, 12, 11, 6, 11, 12, 11, 8, 10, 9
Distribution of Scores
Sort the scores; that is, arrange them in order from lowest to highest.
6, 7, 8, 9, 10, 10, 10, 11, 11, 11, 11, 12, 12, 12, 13
Create a frequency histogram.
Measures of Central Tendency
What is a mode?
The mode is the most frequent score in a distribution and is a measure of the central
tendency.
What is the mode of your distribution? _________11__________
What is a median?
The median is the middle score in a distribution and is the second measure of the central
tendency.
What is the median of your distribution? _________11__________
What is a mean?
The mean is the average of the distribution and the third measure of central tendency.
How is a mean calculated?
The mean is calculated by adding up all the scores and dividing the total by the number of
scores.
Descriptive Statistics 2
What is the mean of your distribution? ______10.2______ Show your calculations.
6
7
8
9
10
10
10
11
Number of scores = 15
153 / 15 = 10.2
11
11
11
12
12
12
13 +
153
Skewed Distributions
Which measure of central tendency would be the best “average” to describe a skewed
distribution? Why?
In a distribution like this, the mean is pulled toward the extreme scores at the high end of the
range. Since the median is not affected by these scores, it is probably a better measure of
central tendency in this case.
Measures of Variability
How is a range calculated?
Range is calculated by subtracting the low score from the high score.
What is the range of your distribution? __________7____________
What is standard deviation?
Standard deviation is a more standard way to measure variation in a distribution. The
standard deviation is the average of the differences between the individual scores and the
mean.
How is standard deviation calculated?
The standard deviation is the average of the differences between the individual scores and
the mean. It’s the average distance, or average deviation, from the mean.
(From PsychSim 5) To calculate the standard deviation, first calculate the difference
between each score and the mean (raw score minus mean score). Next, square each
difference result. After the differences are squared, add them together. Finally, divide that
sum by the number of scores and take the square root.
or (From Hockenbury, Psychology 3/e) To calculate the standard deviation, add all the
scores in a distribution and divide by the number of total scores to get the mean. Then
subtract the mean from each score to get a list of deviations from the mean. Then square
each deviation, add the squared deviations, divide by the total number of cases, and take the
square root.
Everybody’s Doing It! 3
PsychSim 5: CORRELATION
Name:
Section:
Date:
This activity demonstrates the use of scatterplots to visualize positive and negative relationships.
Positive Correlation
What does it mean to say that two variables are positively correlated?
If two variables are positively correlated they go up and down together (their correlation
coefficient is positive).
Negative Correlation
What does it mean to say that two variables are negatively correlated?
Scores that are negatively correlated are associated in such a way that one score falls as the
other rises (as in the relationship between self-esteem and depression); correlation
coefficient is negative.
Uncorrelated Variables
What does it mean to say that two variables are uncorrelated?
If two variables are uncorrelated (or not correlated) the correlation coefficient is near zero.
Look at the example from screen 6 of the exercise: persons with high values on variable 1
are equally likely to have either high or low values on variable 2, and vice versa.
Correlation Coefficient
What is a correlation coefficient?
The correlation coefficient is a statistic (a number) that indicates the strength of the
association between the two variables. It can take values ranging from +1.0 (the strongest
possible positive correlation) through 0.0 (no correlation at all) to -1.0 (the strongest
negative correlation).
Why Use It?
What value or benefit would a researcher gain by calculating a correlation coefficient rather than
simply describing the relationship as a positive correlation or a negative correlation?
The correlation coefficient allows us to talk about the relationship with much more
precision. Instead of saying simply that two variables are correlated or not correlated, we
can say that the two variables have a correlation of 0.85, or 0.12, or -0.59, or whatever the
exact degree of relationship happens to be.
Estimating the Relationship
Look at the scatterplots and try to estimate the direction (positive or negative) and the strength of
the relationship. Write in your guess below.
Scatterplot 1 _.108__
Scatterplot 2 _-.252__
Scatterplot 3 __.816__
Scatterplot 4 _-.628__
Everybody’s Doing It! 4
Scatterplot 5 __.043__
Scatterplot 6 __.594__
Causality and Predictability
The presence of a correlation between two variables doesn’t prove that certain values on one
variable ____cause_______ high or low values on the other. It merely demonstrates that the two
variables are _____associated_____ in some way.
The relationship between two correlated variables has _________predictive value___________.
This means that if a strong correlation exists between variables, then knowing a person’s score on
one variable allows us to predict a person’s score on the other variable.