Educational Research: Data analysis and interpretation 1- Descriptive statistics

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Educational Research Data analysis and
interpretation1- Descriptive statistics
EDU 8603 Educational Research Richard M. Jacobs,
OSA, Ph.D.
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Statistics...

• A set of mathematical procedures for describing,
  synthesizing, analyzing, and interpreting
  quantitative data

the selection of an appropriate statistical
technique is determined by the research design,
hypothesis, and the data collected
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Preparing data for analysis...
Data must be accurately scored and systematically
organized to facilitate data analysis
? scoring assigning a total to each
participants instrument
? tabulating organizing the data in a
systematic manner
? coding assigning numerals (e.g., ID) to data
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• descriptive statistics...

permit the researcher to describe many pieces of
data with a few indices
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• statistics...

indices calculated by the researcher for a
sample drawn from a population
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• parameters...

indices calculated by the researcher for an
entire population
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Types of descriptive statistics
1. graphs
2. measures of central tendency
3. measures of variability
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• graphs...

representations of data enabling the researcher
to see what the distribution of scores look like
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1. Graphs

• frequency polygon

• pie chart

• boxplot

• stem-and-leaf chart

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• measures of central tendency...

indices enabling the researcher to determine the
typical or average score of a group of scores
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2. Measures of central tendency

• mode

• median

• mean

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• mode...

the score attained by more participants than any
other score
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• median...

the point in a distribution above and below
which are 50 of the scores
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• mean...

the arithmetic average of the scores
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• measures of variability...

indices enabling the researcher to indicate how
spread out a group of scores are
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3. Measures of variability

• range

• quartile deviation

• variance

• standard deviation

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• range...

the difference between the highest and lowest
score in a distribution
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• quartile deviation...

one half of the difference between the upper
quartile (the 75ile) and the lower quartile
(the 25ile) in a distribution
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• variance...

a summary statistic indicating the degree of
variability among participants for a given
variable
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• standard deviation...

the square root of variance providing an index
of variability in the distribution of scores
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Normal distributions of data(the normal curve)...
A bell-shaped distribution of scores having four
identifiable properties
50 of the scores fall above the mean and 50 of
the scores fall below the mean
the mean, median, and mode are the same value
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most scores are near the mean and, the farther
from the mean a score is, the fewer the number of
participants who attained that score
the same number, or percentage, of scores is
between the mean and plus one standard deviation
as is between the mean and minus one standard
deviation
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Non-normal distributions of data (skewed
distributions)...
A non-bell-shaped distribution of scores where
mean lt median lt mode (a negatively skewed
distribution)
mean gt median gt mode (a positively skewed
distribution)
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• measures of relative position...

indices enabling the researcher to describe a
participants performance compared to the
performance of all other participants
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4. Measures of relative position

• percentile ranks

• standard scores

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• percentile rank...

indicates the percentage of scores that fall at
or below a given score
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• standard score...

a measure of relative position
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• Types of standard scores...

z score
T score
stanines
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• z score...

a statistic expressing how far a score is from
the mean in terms of standard deviation units
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• T score...

a transformed z score that voids negative
numbers and decimals by multiplying the z score
by 10 and adding 50
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• stanines...

a standard score that divides a distribution
into nine parts
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• measures of relationship...

indices enabling the researcher to indicate the
degree to which two sets of scores are related
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5. Measures of relationship

• Spearman Rho

• Pearson r

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• correlations

determines whether and to what degree a
relationship exists between two or more
quantifiable variables
the degree of the relationship is expressed as a
coefficient of correlation
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the presence of a correlation does not indicate
a cause-effect relationship primarily because of
the possibility of multiple confounding factors
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Correlation coefficient
-1.00
1.00
0.00
strong positive
strong negative
no relationship
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• Spearman Rho...

a measure of correlation used for rank and
ordinal data
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• Pearson r...

a measure of correlation used for data of
interval or ratio scales
assumes that the relationship between the
variables being correlated is linear
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Mini-Quiz

• True and false

the analysis of the data is as important as any
other component of the research process
True
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• True and false

descriptive statistics are normally computed
separately for each group in a research study
True
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• True and false

every instrument administered must always be
scored accurately and consistently, using the
same procedures and criteria
True
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• True and false

tentative scoring procedures must always be
tried out beforehand by administering the
instrument to the study participants
False
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• True and false

a computer should not be used to perform an
analysis that a researcher has never completed by
hand or, at least, studied extensively
True
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• True and false

the first step in data analysis is to describe,
or summarize, the data using descriptive
statistics
True
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• True and false

the number resulting from the computation of a
measure of central tendency represents the
typical score attained by a group of participants
True
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• True and false

the mean is the most precise, stable index of
typical performance that is especially useful in
situations in which there are extreme scores
False
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• True and false

unless a correlation coefficient is used to
compute the reliability of an instrument in a
causal-comparative or experimental study, a
correlation coefficient is only computed in a
correlation study
True
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• True and false

plus and/or minus two standard deviations
includes more the 99 of the scores
False
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• True and false

standard scores are rarely used in research
studies
True
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• True and false

to test a hypothesis adequately, more than
descriptive statistics are normally needed
True
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• True and false

if the extreme scores are at the upper, or
higher, end of the distribution, it is said to be
positively skewed
True
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• True and false

the median of a set of scores corresponds to the
50 percentile
True
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• True and false

a standard score is a measure of relative
position that is appropriate when the data
represent a nominal scale
False
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• True and false

a z score expresses how far a score is from the
mean in terms of standard deviation units
True
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• True and false

the Spearman Rho is the appropriate measure of
correlation when the variables are expressed as
ranks instead of scores
True
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• True and false

the assumption associated with the application
of Pearson r is that the relationship between the
variables being correlated is linear
True
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• Fill in the blank

statistics which permit the researcher to
describe many scores with a small number of
indices
descriptive statistics
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the values calculated for a sample drawn form a
population
statistics
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• Fill in the blank

the values calculated for an entire population
parameters
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• Fill in the blank

a convenient way to describe a set of data with
a single number
measures of central tendency
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• Fill in the blank

the index of central tendency appropriate for
nominal data
mode
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• Fill in the blank

the index of central tendency appropriate for
ordinal data
median
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• Fill in the blank

the index of central tendency appropriate for
interval or ratio data
mean
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• Fill in the blank

the score attained by more participants than any
other score
mode
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• Fill in the blank

the point in a distribution above and below
which are 50 of the scores
median
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• Fill in the blank

the arithmetic average of the scores
mean
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• Fill in the blank

the difference between the highest and lowest
score in a distribution
range
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• Fill in the blank

the measure of variability identifying one half
of the difference between the 75th percentile and
the 25th percentile
quartile deviation
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• Fill in the blank

the measure of variability used for interval and
ratio data
standard deviation
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• Fill in the blank

the only appropriate measure of variability for
nominal data
range
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• Fill in the blank

/- 1.00 standard deviations constitutes ____
of the sample
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extreme scores at the lower end of the
distribution indicates a ______ skewed
distribution
positively
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indices describing where a score is in relation
to all other scores
measures of relative position
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indicates the percentage of scores that fall at
or below a given score
percentile ranks
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if a set of scores is transformed into a set of
z scores, the new distribution has a mean of
____ and a standard deviation of ____
zero one
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• Fill in the blank

a set of standard scores that divide a
distribution into nine parts
stanines
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• Fill in the blank

the most appropriate measure of correlation when
the sets of data to be correlated represent
either interval or ratio scales
Pearson r
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This module has focused on...
descriptive statistics
...the statistical procedures for describing,
synthesizing, analyzing, and interpreting
quantitative data
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The next module will focus on...
inferential statistics
...the statistical procedures for generalizing to
a population of individuals based on information
obtained from a limited number of research
participants