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3/4/2009
Chia Hui Lai
Claire Bode
EDUC 5394: Understanding
Classroom Research
 Descriptive
statistics: summarize data so they
can easily be comprehended.
 Frequency distribution (f) and percentages are
descriptive statistics.
EDUC 5394: Understanding
Classroom Research
 Inferential
Statistics: help researchers draw
inferences about the effect of sampling errors
on the results that are described with
descriptive statistics.
 Margin of errors: an inferential statistics widely
reported in mass media. For example, the
result of public opinion polls; approval of
President was 45% ±2. ±2 is the margin of
errors.
 Samples= statistics;
population(census)=parameters.
EDUC 5394: Understanding
Classroom Research
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Null Hypothesis:
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Version A: The observed difference was created by
sampling error.
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Version B: There is no true difference between the two
groups.
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True difference is the difference a researcher will find
if there were no sampling errors.
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Version C: The true difference between the two groups
is zero.
EDUC 5394: Understanding
Classroom Research
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Significant tests: determine the probability that the null
hypothesis is true.
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If in a significant test, the probability is less than 5 in
100, the hypothesis will be significant. It would be
stated as p<.05, where p stands for the word
probability.
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If the p number is .05 or less such as .01 or .001, the
research will reject the null hypothesis.
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A researcher has rejected the null hypothesis is to state
that the difference is statistically significant.
EDUC 5394: Understanding
Classroom Research
The Effects of Interactivity on Cross-Channel Communication Effectiveness
H1: Consumers' perceived interactivity has a
positive impact on their trust in the vendor.
H2: Consumers' perceived interactivity
has a positive impact on their
evaluations of products.
H3: Consumer trust mediates the influence of
interactivity on consumer online and offline
purchase intentions.
H4: Consumer product evaluation
mediates the influence of
interactivity on consumer online
and offline purchase intention.
H5: Online purchase intention has a positive
impact on offline purchase intentions.
EDUC 5394: Understanding
Classroom Research
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Nominal level: also called “naming level,” in this case
participants will respond with words not numbers. For
instance: marital status.
Ordinal level: At this level, the measurements place
participants in order from high to low.
Interval level: are scores obtained through the use of
objective instrument such as attitude scales, multiple
choice test.
Ratio level: the highest level, ratio level has absolute
zero point; for instance: weight.
Interval level and ratio level have equal distances
among the scores they yield.
EDUC 5394: Understanding
Classroom Research
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A researcher ask each member of a population of 540
teachers which candidate s/he prefers for a school
board vacancy, and found that 258 preferred Smith and
282 preferred Jones. The 258 and 282 are frequency
and the number of case is 540; usually presented as
N=540.
The numbers of cases can be converted to percentages
(proportions).
EDUC 5394: Understanding
Classroom Research
 Uni-variate
analysis:
the researcher is
analyzing how
participants vary on
only one variable.
 Bivariate analysis:
researcher conducts
a examine on the
relationship between
two nominal
variables.
EDUC 5394: Understanding
Classroom Research
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Chi-Square: the usual test of
the null hypothesis for
differences between
frequencies (number of cases
or n).
Chi-square symbol: X2
df= degrees of freedom.
X2 = 4.00, df = 1; not
descriptive statistics that a
typical consumer of research
should attempt to interpret.
This sample is an uni-variate
analysis
EDUC 5394: Understanding
Classroom Research
X2 = 4.00, df = 1, p<.05
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The Chi-square cal also apply
in a bivariate analysis.
Type I Error: Rejecting the
null hypothesis when it is in
fact a correct hypothesis.
Type II Error: Failing to reject
the null hypothesis when it is
in fact an incorrect
hypothesis.
The odd level can be different
5 in 100 = .05, 1 in 100 = .01, 1
in 1000 = .001.
X2 =7.54, df=2, p<.05
X2 =1.241, df=2, p >.05
EDUC 5394: Understanding
Classroom Research
 Frequency
polygon:
a figure which is
used to present the
data of frequency
distribution.
 The curve is
symmetrical within
the high point in the
middle and dropping
off on the right and
left.
EDUC 5394: Understanding
Classroom Research
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When very large
sample are used, the
curve often takes on an
even smoother shape;
the smooth, bell-shaped
curve is called the
normal curve.
For example, when
researcher measure the
weights of grants of sand
on a beach; the annual
amounts of rainfall in
most area and so on.
EDUC 5394: Understanding
Classroom Research
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Some distribution are
skewed.
Skewed means the
shape has a tail on one
side and not the other.
Positive skewed: is
skewed to the right; for
example: income
Negative skewed: is
skewed to the left; for
example, test
EDUC 5394: Understanding
Classroom Research
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Mean (M): the balance point
in a distribution and the most
frequently used average.
The symbol preferred by
statisticians is:
X, which is pronounced “Xbar.”
The deviation sum has to be
zero or the statistic is not the
mean.
The drawback is that it is
drawn in the direction of
extreme scores.
When the distribution is
highly skewed, research will
use a different average.
EDUC 5394: Understanding
Classroom Research
Scores of Group A: 1, 1, 1, 2, 3, 6, 7, 8, 8,
Mean=4.11
Scores of Group B: 1, 2, 2, 3, 4, 7, 9, 25,
32
Mean=9.44
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Median: the middle of
score. To get an
approximate median,
put the scores in order
from low to high.
An important use of the
median is to describe
the averages of skewed
distributions.
Mode: the most
frequently occurring
score.
The mode can have
more than one value.
EDUC 5394: Understanding
Classroom Research
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Scores of Group A: 1, 1,
1, 2, 3, 6, 7, 8, 8,
Scores of Group B: 1, 2,
2, 3, 4, 7, 9, 25, 32
What is the median in
group A ?
What is the median in
group B ?
What is the mode in
group A ?
What is the mode in
group B ?
Because there is more than one type of average;
therefore, the researchers indicate the specific
type of average being reported with statement
such as the mean is 4.11.
 Average = measures of central tendency.
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EDUC 5394: Understanding
Classroom Research
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Is a margin of error a “descriptive” or an “inferential”
statistic ?
Does the sample error refer to random error or to bias ?
The expression p<.05 stands for what words ?
Which scale of measurement has an absolute zero ?
Which scale of measurement is at the lowest level?
If a researcher found that a chi-square test of a difference
yield a p less than 5 in 100, on the basis of conventional
wisdom, what should the researcher conclude about the null
hypothesis ?
What is the name of the error researchers make when they
reject the null hypothesis when, in fact, it is an incorrect
hypothesis ?
What is the name of the curve that is symmetrical ?
Which average is defined as the most frequently occurring
score?
Which average is defined as the balance point in a
distribution ?
Which average is defined as the middle score ?
EDUC 5394: Understanding
Classroom Research
Mean: Average
Standard
Deviation:
S or SD, s or sd
Describe its variability
Variability:
Amount by which participants vary
or differ from one another.
EDUC 5394: Understanding
Classroom Research
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Median: The middle score in a distribution
 Used when distribution is highly skewed
 Used when data is ordinal
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Range: Highest score minus the lowest score
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Inter quartile range: Range of the middle two quarters
Describes the variability of the
average scores.
EDUC 5394: Understanding
Classroom Research
102, 104 , 105 , 107 , 108, 109, 110, 112, 115, 118, 118
 Median
(middle number) is 109.
 Using the set of numbers to the left of 109, the
median is 105.
 Using the set of numbers to the right of 109, the
median is 115.
 The width of the inter quartile range is 115-105 = 10.
EDUC 5394: Understanding
Classroom Research
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Examines relationship between two quantitative sets of
scores.
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A statistic representing how closely two variables covary; it can vary from -1 (perfect negative correlation)
through 0 (no correlation) to +1.
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Indicates the strength and direction of a linear
relationship between two random variables.
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Could be used to determine relation between
pre-test/post-test
EDUC 5394: Understanding
Classroom Research
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Often used to test null hypothesis regarding observed
differences between two means.
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Assesses whether the means of two groups are
statistically different from each other.
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Only value of interest is p.
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Example: Find the difference between mean scores of
boys and girls on a timed basic facts test.
Analysis of variance called ANOVA
 Only one independent variable is being
considered
 Can compare a number of means
 Indicates whether a set of differences is
significant overall.
 Testing differences between more than two
groups or treatment.
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EDUC 5394: Understanding
Classroom Research
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An extension of the one-way analysis of variance
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Two independent variables
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The investigator can take into account
simultaneously the effects of two factors on an
outcome of interest. (say age, gender, and IQ)
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Additionally, the investigator can test for interaction,
if any, between the two factors.
EDUC 5394: Understanding
Classroom Research
Statistical Significance-Whether a difference is
reliable in light of random errors.
 Practical Significance
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Cost-benefit analysis
Crucial difference
Client acceptability
Public and political acceptability
Ethical and legal implications
EDUC 5394: Understanding
Classroom Research
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Robertniles.Com available from http://www.robertniles.com.stats/stdev.shtml
Answers.com available from http://www.answers.com/topic/interquartile-range
Socialresearchmethosd.net available from
http://www.socialresearchmethods.net/kb/stat_t.php
Childrens-mercy.org available from http://www.childrensmercy.org/stats/definitions/iqr.htm
Mste.uiuc.edu available from
http://www.mste.uiuc.edu/patel/chisquare/keyprobanswer.html
Answers.yahoo.com available from
http://answers,yahoo.com/question/index?qid=200061202052549AAz52s
Jaid.org available from http://www.jiad.org/article60
Roscoe, J. T. (1969). Fundamental Research Statistics. New York, NY: Holt, Rinehart
and Winston, Inc.
Patten, M. L. (2009). Understanding Research Methods. Glendale, CA: Pyrczak
Publishing.
EDUC 5394: Understanding
Classroom Research