Data Analysis

1. Educational Research:
Data analysis and interpretation – 1
Descriptive statistics

2. 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

3. Preparing data for analysis...
Data must be accurately scored and
systematically organized to facilitate
data analysis:
 tabulating: organizing the data in a
systematic manner
 coding: assigning numerals (e.g., ID)
to data
 scoring: assigning a total to each
participant’s instrument

4.  descriptive statistics...
…permit the researcher to describe
many pieces of data with a few
indices

5.  statistics...
…indices calculated by the researcher
for a sample drawn from a population

6.  parameters...
…indices calculated by the researcher
for an entire population

7. Types of descriptive statistics…
1. graphs
2. measures of central tendency
3. measures of variability

8.  graphs...
…representations of data enabling the
researcher to see what the
distribution of scores look like

9. 1. Graphs…
 frequency polygon
 pie chart
 boxplot
 stem-and-leaf chart

10.  measures of central tendency...
…indices enabling the researcher to
determine the typical or average
score of a group of scores

11. 2. Measures of central tendency…
 mode
 median
 mean

12.  mode...
…the score attained by more
participants than any other score

13.  median...
…the point in a distribution above and
below which are 50% of the scores

14.  mean...
…the arithmetic average of the scores

15.  measures of variability...
…indices enabling the researcher to
indicate how spread out a group of
scores are

16. 3. Measures of variability…
 range
 quartile deviation
 variance
 standard deviation

17.  range...
…the difference between the highest
and lowest score in a distribution

18.  quartile deviation...
…one half of the difference between
the upper quartile (the 75%’ile) and
the lower quartile (the 25%’ile) in a
distribution

19.  variance...
…a summary statistic indicating the
degree of variability among
participants for a given variable

20.  standard deviation...
…the square root of variance providing
an index of variability in the
distribution of scores

21. 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

22. …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

23. Non-normal distributions of data
(skewed distributions)...
A non-bell-shaped distribution of scores
where…
…mean < median < mode
(a “negatively skewed distribution”)
…mean > median > mode
(a “positively skewed distribution”)

24.  measures of relative position...
…indices enabling the researcher to
describe a participant’s performance
compared to the performance of all
other participants

25. 4. Measures of relative position…
 percentile ranks
 standard scores

26.  percentile rank...
…indicates the percentage of scores
that fall at or below a given score

27.  standard score...
…a measure of relative position

28.  Types of standard scores...
…z score
…T score
…stanines

29.  z score...
…a statistic expressing how far a score
is from the mean in terms of standard
deviation units

30.  T score...
…a transformed z score that voids
negative numbers and decimals by
multiplying the z score by 10 and
adding 50

31.  stanines...
…a standard score that divides a
distribution into nine parts

32.  measures of relationship...
…indices enabling the researcher to
indicate the degree to which two sets
of scores are related

33. 5. Measures of relationship…
 Spearman Rho
 Pearson r

34.  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

35. …the presence of a correlation does
not indicate a cause-effect
relationship primarily because of the
possibility of multiple confounding
factors

36. Correlation coefficient…
-1.00 +1.00
strong negative strong positive
0.00
no
relationship

37.  Spearman Rho...
…a measure of correlation used for
rank and ordinal data

38.  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

40. Mini-Quiz…
 True and false…
…the analysis of the data is as
important as any other component
of the research process
True

41.  True and false…
…descriptive statistics are normally
computed separately for each
group in a research study
True

42.  True and false…
…every instrument administered
must always be scored accurately
and consistently, using the same
procedures and criteria
True

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

44.  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

45.  True and false…
…the first step in data analysis is to
describe, or summarize, the data
using descriptive statistics
True

46.  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

47.  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

48.  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

49.  True and false…
…plus and/or minus two standard
deviations includes more the 99%
of the scores
False

50.  True and false…
…standard scores are rarely used in
research studies
True

51.  True and false…
…to test a hypothesis adequately,
more than descriptive statistics are
normally needed
True

52.  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

53.  True and false…
…the median of a set of scores
corresponds to the 50% percentile
True

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

55.  True and false…
…a z score expresses how far a
score is from the mean in terms of
standard deviation units
True

56.  True and false…
…the Spearman Rho is the
appropriate measure of correlation
when the variables are expressed
as ranks instead of scores
True

57.  True and false…
…the assumption associated with the
application of Pearson r is that the
relationship between the variables
being correlated is linear
True

58.  Fill in the blank…
…statistics which permit the
researcher to describe many scores
with a small number of indices
descriptive statistics

59.  Fill in the blank…
…the values calculated for a sample
drawn form a population
statistics

60.  Fill in the blank…
…the values calculated for an entire
population
parameters

61.  Fill in the blank…
…a convenient way to describe a set of
data with a single number
measures of central tendency

62.  Fill in the blank…
…the index of central tendency
appropriate for nominal data
mode

63.  Fill in the blank…
…the index of central tendency
appropriate for ordinal data
median

64.  Fill in the blank…
…the index of central tendency
appropriate for interval or ratio data
mean

65.  Fill in the blank…
…the score attained by more
participants than any other score
mode

66.  Fill in the blank…
…the point in a distribution above and
below which are 50% of the scores
median

67.  Fill in the blank…
…the arithmetic average of the scores
mean

68.  Fill in the blank…
…the difference between the highest
and lowest score in a distribution
range

69.  Fill in the blank…
…the measure of variability identifying
one half of the difference between
the 75th percentile and the 25th
percentile
quartile deviation

70.  Fill in the blank…
…the measure of variability used for
interval and ratio data
standard deviation

71.  Fill in the blank…
…the only appropriate measure of
variability for nominal data
range

72.  Fill in the blank…
…+/- 1.00 standard deviations
constitutes ____ % of the sample
68%

73.  Fill in the blank…
…extreme scores at the lower end of
the distribution indicates a ______
skewed distribution
positively

74.  Fill in the blank…
…indices describing where a score is
in relation to all other scores
measures of relative position

75.  Fill in the blank…
…indicates the percentage of scores
that fall at or below a given score
percentile ranks

76.  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

77.  Fill in the blank…
…a set of standard scores that divide a
distribution into nine parts
stanines

78.  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

79. This module has focused on...
descriptive statistics
...the statistical procedures for
describing, synthesizing, analyzing,
and interpreting quantitative data

80. 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