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Statistics
2nd GRADING by Shai2x
93
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10th Grade
10/19/2015
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Term
Inferential statistics
 Definition
are certain types of procedures
that allow researchers to make inferences about a population based on findings from a sample.
Term
sampling error
 Definition
Samples are not likely to be identical to their parent populations. This difference between
a sample and its population is referred to as
Term
Distribution of sample means
 Definition
Once
sample size reaches 30, however, the _________ is very nearly normal, even if the population is not normally distributed.
Term
sampling distribution
 Definition
a distribution of sample means
Term
mean of the means
 Definition
The mean of a sampling
distribution
Term
standard error of the mean (SEM)
 Definition
The standard deviation of a sampling distribution of
means is called the
Term
SEM= SD
_____
squareroot of n-1
 Definition
equation of SEM
Term
Confidence intervals
 Definition
We now can use the SEM to indicate boundaries, or
limits, within which the population mean lies. Such
boundaries are called
Term
probababilty
 Definition
s
nothing more than predicted relative occurrence, or relative frequency.
Term
Standard error of difference (SED)
 Definition
e means also has its own mean
and standard deviation. The mean of the sampling distribution of differences between sample means is equal
to the difference between the means of the two populations. The standard deviation of this distribution is
called the
Term
research hypothesis
 Definition
specifies the
predicted outcome of a study.
Term
null hypothesis
 Definition
most commonly used specifies
there is no relationship in the population; for example:
“There is no difference between the population mean of
students using method A and the population mean of
students using method B.”
Term
level of significance
 Definition
It is customary in educational research to view as
unlikely any outcome that has a probability of .05
(p  .05) or less. This is referred to as the
Term
State the research hypothesis
State the null hypothesis
Determine the sample statistics pertinent to the hypothesis
Determine the probability of obtaining the sample
results

If the probability is small, reject the null hypothesis,
thus affirming the research hypothesis

If the probability is large, do not reject the null
hypothesis, which means you cannot affirm the
research hypothesis.
 Definition
logical sequence
for a researcher who wishes to engage in hypothesis
testing is as follows:
Term
statistical significance
 Definition
only means that one’s
results are likely to occur by chance less than a certain
percentage of the time, say 5 percent.
Term
practical significance
 Definition
a very
small correlation coefficient, for example, may turn out
to be statistically significant but have little (if any) _______
Term
one-tailed test
 Definition
Because the researchers’ hypothesis can be supported only if he or she obtains a positive difference between the sample means, the researcher is justified in
using only the positive tail of the sampling distribution
to locate the obtained difference. This is referred to as a
Term
two-tailed test
 Definition
The hypothesis would then be supported by a suitable
difference in either tail. This is called a
Term
type II error
 Definition
this error results when a researcher fails to
reject a null hypothesis that is false
Term
type I error
 Definition
on the
other hand, results when a researcher rejects a null hypothesis that is true.
Term
parametric and nonparametric techniques
 Definition
y be inappropriate for categorical data.
There are two basic types of inference techniques
that researchers use.
Term
parametric technique
 Definition
make
various kinds of assumptions about the nature of the population from which the sample(s) involved in the research study are drawn.
Term
nonparametric technique
 Definition
on
the other hand, make few (if any) assumptions about the
nature of the population from which the samples are
taken.
Term
they are generally more powerful* than nonparametric
techniques and hence much more likely to reveal a true
difference or relationship if one really exists.
 Definition
An advantage of parametric techniques is that
Term
t-test
 Definition
is a parametric
statistical test used to see whether a difference between
the means of two samples is significant.
Term
t-test for independent means and
t-test for correlated means
 Definition
two forms of this t-test,
Term
t-test for independent means
 Definition
is used to compare the
mean scores of two different, or independent, groups.
Term
degrees of freedom
 Definition
This concept is quite important in many inferential statistics tests. In essence, it refers to the number of scores in a
frequency distribution that are “free to vary”—that is,
that are not fixed.
Term
t-test for correlated means
 Definition
is used to compare
the mean scores of the same group before and after a
treatment of some sort is given, to see if any observed
gain is significant,
Term
analysis of variance (ANOVA)
 Definition
When researchers desire to
find out whether there are significant differences between the means of more than two groups, they commonly use a technique called
Term
statistical significance
 Definition
only means that one’s
results are likely to occur by chance less than a certain
percentage of the time, say 5 percent.
Term
practical significance
 Definition
a very
small correlation coefficient, for example, may turn out
to be statistically significant but have little (if any) _______
Term
one-tailed test
 Definition
Because the researchers’ hypothesis can be supported only if he or she obtains a positive difference between the sample means, the researcher is justified in
using only the positive tail of the sampling distribution
to locate the obtained difference. This is referred to as a
Term
two-tailed test
 Definition
The hypothesis would then be supported by a suitable
difference in either tail. This is called a
Term
type II error
 Definition
this error results when a researcher fails to
reject a null hypothesis that is false
Term
type I error
 Definition
on the
other hand, results when a researcher rejects a null hypothesis that is true.
Term
parametric and nonparametric techniques
 Definition
y be inappropriate for categorical data.
There are two basic types of inference techniques
that researchers use.
Term
parametric technique
 Definition
make
various kinds of assumptions about the nature of the population from which the sample(s) involved in the research study are drawn.
Term
nonparametric technique
 Definition
on
the other hand, make few (if any) assumptions about the
nature of the population from which the samples are
taken.
Term
they are generally more powerful* than nonparametric
techniques and hence much more likely to reveal a true
difference or relationship if one really exists.
 Definition
An advantage of parametric techniques is that
Term
t-test
 Definition
is a parametric
statistical test used to see whether a difference between
the means of two samples is significant.
Term
t-test for independent means and
t-test for correlated means
 Definition
two forms of this t-test,
Term
t-test for independent means
 Definition
is used to compare the
mean scores of two different, or independent, groups.
Term
degrees of freedom
 Definition
This concept is quite important in many inferential statistics tests. In essence, it refers to the number of scores in a
frequency distribution that are “free to vary”—that is,
that are not fixed.
Term
t-test for correlated means
 Definition
is used to compare
the mean scores of the same group before and after a
treatment of some sort is given, to see if any observed
gain is significant,
Term
analysis of variance (ANOVA)
 Definition
When researchers desire to
find out whether there are significant differences between the means of more than two groups, they commonly use a technique called
Term
Analysis of variance (ANOVA)
 Definition
actually a more general form of the
t-test that is appropriate to use with three or more
groups.
Term
Analysis of Covariance (ANCOVA)
 Definition
is a variation of ANOVA used when, for
example, groups are given a pretest related in some way
to the dependent variable and their mean scores on this
pretest are found to differ.
Term
Multivariate Analysis of Variance (MANOVA)
 Definition
differs from
ANOVA in only one respect: It incorporates two or
more dependent variables in the same analysis, thus permitting a more powerful test of differences among
means.
Term
multivariate analysis of covariance
(MANCOVA)
 Definition
extends ANCOVA to include two or
more dependent variables in the same analysis.
Term
T-test for r
 Definition
This t-test is used to see whether
a correlation coefficient calculated on sample data is
significant—that is, whether it represents a nonzero correlation in the population from which the sample was
drawn.
Term
Mann-Whitney
U test
 Definition
is a nonparametric alternative to the t-test used
when a researcher wishes to analyze ranked data.
Term
Kruskal-Wallis one-way analysis of
variance
 Definition
is used when researchers have more than two
independent groups to compare.
Term
sign test
 Definition
is used when a researcher wants to analyze two related (as opposed to
independent) samples.
Term
Friedman two-way analysis of variance
 Definition
If more than two related groups are involved,
then the ___________________ test
can be used.
Term
t tests for a difference in proportions
 Definition
The most commonly used
parametric tests for analyzing categorical data are
Term
Mann-Whitney
U test

Kruskal-Wallis one-way analysis of
variance

sign test

Friedman two-way analysis of variance

t tests for a difference in proportions
 Definition
NONPARAMETRIC TECHNIQUES
FOR ANALYZING QUANTITATIVE DATA
Term
The t-Test for independent Means.
T-test for correlated means
Analysis of Variance.
Analysis of Covariance.
Multivariate Analysis of Variance.
The t-Test for r.
 Definition
PARAMETRIC TECHNIQUES
FOR ANALYZING QUANTITATIVE DATA
Term
Chi-Square Test
 Definition
used
to analyze data that are reported in categories.
Term
Contingency coefficient
 Definition
The final step in the chisquare test process is to calculate the
Term
Power of a statistical test
 Definition
is similar to the power of
a telescope
Term
Action Research
 Definition
is conducted by one or more individuals or groups for the purpose of solving a problem or obtaining information in order to inform local practice.
Term
Practical action Research
 Definition
is intended to address a specific problem within a classroom, school, or other “community.”
Term
Participatory action research
 Definition
while sharing the focus
on a specific local issue and on using the findings to
implement action, differs in important ways from practical action research.
Term
stakeholders
 Definition
function as equal partners
Term
collaborative research
 Definition
For this reason, participatory action research is
often referred to as
Term
identify the research question
gather necessary information
analyzing/interpreting information
developing an action plan
 Definition
Steps in Action Research
Term
research proposal
 Definition
is generated before a study begins,
Term
research report
 Definition
is prepared after a study is completed.
In this chapter, we shall describe and illustrate what is
expected and usually included in each section of these
documents.
Term
problem to be investigated
 Definition
(1) the
purpose of the study, including the researcher’s assumptions; (2) the justification for the study; (3) the research
question and/or hypotheses, including the variables to
be investigated; and (4) the definition of terms.
Term
purpose
 Definition
states succinctly what
the researcher proposes to investigate.
Term
justification
 Definition
researchers must make clear why this particular subject
is important to investigate.
Term
Definitions
 Definition
all key terms should be defined.
Term
hypothesis
 Definition
The particular question to be investigated should be stated next.
Term
literature review
 Definition
may be a
lengthy section, especially in a master’s thesis or a doctoral dissertation.
Term
procedures
 Definition
section includes discussions of: (1)
research design, (2) sample, (3) instrumentation, (4)
procedural details, (5) internal validity, and (6) data
analysis.
Term
research design
 Definition
can be described using the
symbols
Term
sample
 Definition
In a proposal, a researcher should indicate
in considerable detail how he or she will obtain the
subjects—the ____________
Term
instrumentation
 Definition
Whenever possible, existing instruments should be used in a study, since construction
of even the most straightforward test or questionnaire
is often a very time-consuming and difficult task.
Term
procedural details
 Definition
Next, the procedures to be
followed in the study—what will be done, as well as
when, where, and how—should be described in detail.
Term
internal validity
 Definition
At this point, the essential planning for a study should be nearly completed.
Term
Data analysis
 Definition
The researcher then should indicate
how the data to be collected will be organized
Term
Publication Manual of
the American Psychological Association (APA)
 Definition
ecks on a computer are a big help here!)
A style manual should be consulted before beginning
the report. A good source, recommended by most journal editors and used by many researchers when preparing their research reports, is the
Term
format
 Definition
The_______ of a report is the way it is organized.
Term
abstract
 Definition
a brief summary of the entire research report.
Term
results
 Definition
can be presented only in a research
report;
Term
discussion
 Definition
section of a report presents the author’s interpretation of what the results
imply for theory and/or practice.
Term
Suggestions for Further Research.
 Definition
Normally,
this is the final section of a report.
Term
references
 Definition
Finally, the references (bibliography)
should list all sources that were used in the writing of
the report.
Term
footnotes
 Definition
Footnotes are numbered consecutively,
using a superscript Arabic numeral, in the order in
which they appear in the text of the report.
Term
figures
 Definition
Figures consist of drawings, graphs, charts,
even photographs or pictures.
Term
tables
 Definition
Tables also should be used only when they
can summarize or convey information better, more simply, or more clearly than the text alone.
Term
pilot study
 Definition
a
small-scale trial of the proposed procedures.
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