educational research: data analysis and interpretation – 1 descriptive statistics edu 8603...
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Educational Research: Educational Research: Data analysis and interpretation – 1Data analysis and interpretation – 1Descriptive statisticsDescriptive statistics
EDU 8603
Educational Research
Richard M. Jacobs, OSA, Ph.D.
Statistics...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
Preparing data for analysis...Preparing data for analysis...
Data must be accurately scored and systematically organized to facilitate data analysis:
tabulatingtabulating: organizing the data in a systematic manner
codingcoding: assigning numerals (e.g., ID) to data
scoringscoring: assigning a total to each participant’s instrument
descriptive statistics...descriptive statistics...…permit the researcher to describe
many pieces of data with a few indices
statistics...statistics...…indices calculated by the researcher
for a sample drawn from a population
parameters...parameters...…indices calculated by the researcher
for an entire population
Types of descriptive statistics…Types of descriptive statistics…
1. graphs2. measures of central tendency
3. measures of variability
graphs...graphs...…representations of data enabling the
researcher to see what the distribution of scores look like
1. Graphs…1. Graphs…
frequency polygon pie chart boxplot stem-and-leaf chart
measures of central tendency...measures of central tendency...…indices enabling the researcher to
determine the typical or average score of a group of scores
2. Measures of central tendency…2. Measures of central tendency…
mode median mean
mode...mode...…the score attained by more
participants than any other score
median...median...…the point in a distribution above and
below which are 50% of the scores
mean...mean...…the arithmetic average of the scores
measures of variability...measures of variability...…indices enabling the researcher to
indicate how spread out a group of scores are
3. Measures of variability…3. Measures of variability…
range quartile deviation variance standard deviation
range...range...…the difference between the highest
and lowest score in a distribution
quartile deviation...quartile deviation...…one half of the difference between
the upper quartile (the 75%’ile) and the lower quartile (the 25%’ile) in a distribution
variance...variance...…a summary statistic indicating the
degree of variability among participants for a given variable
standard deviation...standard deviation...…the square root of variance providing
an index of variability in the distribution of scores
Normal distributions of dataNormal distributions of data(the normal curve)...(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
…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
Non-normal distributions of data Non-normal distributions of data (skewed distributions)...(skewed distributions)...
A non-bell-shaped distribution of scores where…
…mean < median < mode (a “negatively skewed distributionnegatively skewed distribution”)
…mean > median > mode (a “positively skewed distributionpositively skewed distribution”)
measures of relative position...measures of relative position...…indices enabling the researcher to
describe a participant’s performance compared to the performance of all other participants
4. Measures of relative position…4. Measures of relative position…
percentile ranks standard scores
percentile rank...percentile rank...…indicates the percentage of scores
that fall at or below a given score
standard score...standard score...…a measure of relative position
Types of standard scores...Types of standard scores...…z score…T score…stanines
z score...z score...…a statistic expressing how far a score
is from the mean in terms of standard deviation units
T score...T score...…a transformed z score that voids
negative numbers and decimals by multiplying the z score by 10 and adding 50
stanines...stanines...…a standard score that divides a
distribution into nine parts
measures of relationship...measures of relationship...…indices enabling the researcher to
indicate the degree to which two sets of scores are related
5. Measures of relationship…5. Measures of relationship…
Spearman Rho Pearson r
correlationscorrelations…determines whether and to what
degree a relationship exists between two or more quantifiable variablesvariables
…the degree of the relationship is expressed as a coefficient of correlation
…the presence of a correlation does not indicate a cause-effect relationship primarily because of the possibility of multiple confounding factorsconfounding factors
Correlation coefficient…Correlation coefficient…
-1.00 +1.00
strong negative strong positive
0.00
no relationship
Spearman Spearman RhoRho......…a measure of correlation used for
rank and ordinal data
Pearson Pearson rr......…a measure of correlation used for
data of interval or ratio scales
…assumes that the relationship between the variables being correlated is linear
Mini-Quiz…Mini-Quiz…
True and false…
…the analysis of the data is as important as any other component of the research process
True
True and false…
…descriptive statistics are normally computed separately for each group in a research study
True
True and false…
…every instrument administered must always be scored accurately and consistently, using the same procedures and criteria
True
True and false…
…tentative scoring procedures must always be tried out beforehand by administering the instrument to the study participants
False
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
True and false…
…the first step in data analysis is to describe, or summarize, the data using descriptive statistics
True
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
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
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
True and false…
…plus and/or minus two standard deviations includes more the 99% of the scores
False
True and false…
…standard scores are rarely used in research studies
True
True and false…
…to test a hypothesis adequately, more than descriptive statistics are normally needed
True
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
True and false…
…the median of a set of scores corresponds to the 50% percentile
True
True and false…
…a standard score is a measure of relative position that is appropriate when the data represent a nominal scale
False
True and false…
…a z score expresses how far a score is from the mean in terms of standard deviation units
True
True and false…
…the Spearman Rho is the appropriate measure of correlation when the variables are expressed as ranks instead of scores
True
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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…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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…the values calculated for an entire population
parameters
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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…the index of central tendency appropriate for nominal data
mode
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…the index of central tendency appropriate for ordinal data
median
Fill in the blank…
…the index of central tendency appropriate for interval or ratio data
mean
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…the score attained by more participants than any other score
mode
Fill in the blank…
…the point in a distribution above and below which are 50% of the scores
median
Fill in the blank…
…the arithmetic average of the scores
mean
Fill in the blank…
…the difference between the highest and lowest score in a distribution
range
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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…the measure of variability used for interval and ratio data
standard deviation
Fill in the blank…
…the only appropriate measure of variability for nominal data
range
Fill in the blank…
…+/- 1.00 standard deviations constitutes ____ % of the sample
68%
Fill in the blank…
…extreme scores at the lower end of the distribution indicates a ______ skewed distribution
positively
Fill in the blank…
…indices describing where a score is in relation to all other scores
measures of relative position
Fill in the blank…
…indicates the percentage of scores that fall at or below a given score
percentile ranks
Fill in the blank…
…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
Fill in the blank…
…a set of standard scores that divide a distribution into nine parts
stanines
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
This module has focused on...This module has focused on...
descriptive statistics
...the statistical procedures for describing, synthesizing, analyzing, and interpreting quantitative data
The next module will focus on...The next module will focus on...
...the statistical procedures for generalizing to a population of individuals based on information obtained from a limited number of research participants
inferential statistics