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Understanding Research
Results
Chapter 12
Why do we use statistics
• Statistics are used to describe the data
• When comparing groups in our
experiment, we look for statistically
significant differences between our
conditions. This tells us whether or not our
experimental condition has an effect.
• Statistics are analyzed, and statistical
significance takes into account the number
of subjects when analyzing for differences.
Review of Scales and
Measurement
•
Nominal Scale Variables
– Have no numerical or quantitative properties
– The levels are simply different categories or
groups
– Many independent variables in experiments are
nominal (e.g. gender, marital status, hand
dominance)code or assign a number to the
group (male=1, female=2)
Ordinal Scale Variables
– These variables involve minimal quantitative
distinctionscan rank order levels of the variable
from lowest to highest.
– Rank the stressors in your life from lowest to hightest.
•
•
•
•
•
Exams
Grades
Significant other
Parental approval
Scholarship
– All we know is the order, the strength of the stressor
is not known.
Interval and Ratio Scale Variables
– With interval scale variables, the intervals between the levels
are equal in size
– There is no zero point indicating the absence of
somethingas in there is no absence of mood.
– Ratio scale variables have both equal intervals and a
absolute zero point that indicates the absence of the variable
being measured time, weight, length and other physical
measures are the best examples of ratio scales.
– Interval and ratio data are conceptually different but the
statistical procedures used to analyze the data are exactly
the same.
– With both interval and ratio scales the data can be
summarized using the mean…eg. The average mood of the
group was 6.5.
Analyzing the Results of Research Investigations
•
Comparing group percentages
•
Correlating scores of individuals on two
variables
•
Comparing group means
Comparing Group Percentages
• Type of analysis you can run when you have two
distinct groups or populations you are comparing and
the variable is nominal as in whether or not males vs.
females helped or not (nominal-yes vs. no).
• If you analyzed whether males and females differ in
the way they helped you would count the number of
times females helped, and then the number of times
males helped and get a percentage of each.
• Next we would run statistical analysis on the
differences between the percentages to see if the
groups were significantly different.
Interpreting Statistical Analysis
• For example: In the current study if there were 30 females and
30 males in each condition, and 24 females helped, as opposed
to 21 males,
• We would be able to say that 80% of the females elected to
help as compared to 70% of the males. Next we would run
statistical analysis on 80% vs. 70% using a simple t-test.
• The t-test takes into consideration the number of participants in
the group. Therefore with a t (58)=1.56.
• In order for the difference to be significant with 50 subjects, the
t score, with 60 participants would have to be at least a 2.0,
(according to the tables at the back of the book (p361)
• Therefore, there was no significant difference between males
and females in a helping situation.
Correlating Individual Scores
• Used when you don’t have distinct groups of
subjects.
• Instead, individual subjects are measured on
two variables, and each variable has a range of
numerical values  correlation between
personality types and profession.
• Two variables per subject with the variables
given different numerical values. (could be
something that already has numerical values
test performance and blood pressure)
• Does NOT imply causation, only a relationship.
Comparing Group Means
• Compare the mean of one group to that of a
second group to determine if there are any
differences between the two groups.
• Again, statistical analysis is performed, based on
the number of groups, and the number of
participants to determine if the difference is
statistically significant and therefore conclusions
can be made about treatment and control
groups and whether or not the hypothesis was
supported.
Which Statistics to use
• T-statitistic -statitistical measure for assessing
whether or not there is a difference between
two groups.
• Formuala:
• t=
group difference
within group difference
F-statistic (ANOVA)
• Statistical measure for assessing whether or
not two or more groups are equal.
• Cannot use a t-test with more than two groups.
• Also used to analyze an interaction.
• It is a ratio of two types of variance
• Formula
F= systematic variance (variability b/w groups)
Error Variance (variability within groups)
Degrees of Freedom
• The critical value for both the t and the F-value are
based on degrees of freedom, which are the number of
participants minus the number of conditions.
• N1+N2-number of groups=degrees of freedom
• For example: 30 +30 -2 =58
• The critical value for 58 degrees of freedom can be
looked up in the table. The t or F-value for the
experiment must be higher than the critical value in order
for the experiment to be statistically significant.
• Reporting t(58)=1.67 if the critical value for 58 degrees
of freedom is 2.00, then the t-value is not significant,
which means there is no significant difference between
the treatment and the control group, and therefore the
hypothesis was not supported.
Descriptive Stats
• allows researchers to make precise
statements about the data. Two statistics
are needed to describe the data
•  a single number to describe the central
tendency of the data (usually the mean)
•  a number that describes the Variability ,
or how widely the distribution of scores is
spread.
Central Tendency
•
Mean-appropriate only when the scores are measured on an interval or ratio score.
– Obtained by adding all the scores and dividing by the number of scores.
•
Median-score that divides the group in half—appropriate when using an ordinal scale
as it takes into account only the rank order of the scores. Can also be useful for ratio
and interval scales. (50% above and 50% below the median)  the middle score in
an ordered distribution
– Order your scores from lowest to highest (or vice versa)
– Count down thru the distribution and find the score in the middle of the distribution. This is
the median
– Median gives you more info than the mode, but it doesn’t take into account the magnitude
of the scores above and below the median
– Two distributions can have the same median and yet be very different
– The median is usually used when the mean is not a good choice
•
Mode-most frequent score in the distribution….
– is the only measure that can be used for nominal data.
–
is simple to calculate but the only info it gives is what is the most frequent
score if we gave a test to 15 people and 75 was the score that we saw most often and 6
people got a 75, the mode would be 6does not use the actual value on the scale, it just
indicates the most frequently occurring value
Variability
• Number that shows the amount of spread in the entire
distribution. First calculate the variance of the
individual scores from the mean.
• Variance (s2) –indicates the average deviation of
scores from the mean.
• s2 = (X-X*)2
x = each indiv score
•
n-1
x* = the mean of the distribution
•
n = number of scores
•
Standard Deviation
• To calculate the SD, simply take the
square root of the variance
• Appropriate for only interval and ratio
scores as it uses the actual values of the
scores.
• Tells us something about how the data is
clustered.
Correlating Coefficients
• Is important to know whether a
relationship between variables is relatively
weak or strong.
• Correlation coefficient is a statistic that
describes how strongly variables are
related to one another.
• To do this you must use a measure of
association
The Pearson Product-Moment
Correlation Coefficient
– Pearson r provides an index of the direction and magnitude
of the relationship between two sets of scores
– Generally used when your dependent measures are scaled
on an interval or a ratio scale can be used when numbers
are assigned to variables Meyers Briggs scores and
scores for professions.
– The value of the Pearson r can range from +1 thru 0 to -1
– The sign of the coefficient tells you the direction of the
relationship
– The magnitude of the correlation coefficient tells you the
degree of linear relationship between your two variables
– The sign is unrelated to the magnitude of the relationship
and simply indicates the direction of the relationship
– Relationships do not imply causation.
Factors that affect the Pearson
Correlation Coefficient
• Outliers
• Restricted Range
• E.g., compared IQ and GPA in college
students as opposed to high school
studentsmore homogeneous as IQ must
be above a certain level to be intelligent
enough to get into college.
• Shape of the distribution
Regression Equations and
Predictions
• simple correlation techniques can establish the
direction and degree of relationship between two
variables.
• linear regression can estimate values of a variable
based on knowledge of the values of others
variables.
• Equation Y = a + bX
• Y = predicted score (what we are looking for)
• b = slope of the regression line (weighting value)
• X = known score
• a = constant (y-intercept)
Multiple Correlation
• Used when you want to focus on more than two
variables at a time. (symbolized as R instead of r)
• Used to combine a number of predictor variables to
increase the accuracy of prediction of a given criteria.
• Using multiple predictor variables usually results in
greater accuracy of the prediction than when a single
predictor is considered alone as in the above formula.
• Y =a + b1x1 + b2x2 + b3x3 + b4x4
Frequency distribution
• Indicates the number of individuals that receive
each possible score.
• Graphing
– Pie Charts
– Bar Graphs
– Polygons