Transcript Session 5 - Results, Style and Organization

M.Educ. 6000
Session 5
 Are
 Is
the findings presented clearly?
sufficient detail evident in the findings?
 Examples
 Enough
and interpretation
information to assess the adequacy of
the finding, but not so much as so be
overwhelmed by extraneous information
 Were
the results the researchers found likely
to occur by chance alone?
 This
question LEADS US TO . . . . .
 Descriptive
statistics: describing an outcome
with numbers
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Measures of Central Tendency
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Mean: the average ( X )
Mode: the most common
Median: the middle number when the data is put in
order from least to greatest
When should you use which measure?
 Measures

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
of Variability
Standard Deviation (SD): a measure of how spread
out the data are; roughly, the average of how far
each data point is from the mean
Range: difference between the lowest data point
and the highest data point
Interquartile Range: rank order the data, split it in
half and in half again, subtract the median of the
bottom half from the median of the top half
 Measures

Correlation coefficient (r ) : a number between -1
and 1 that describes the relationship between two
data sets
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of Association
r=0 if there is no relationship
r=1 if there is a perfect positive relationship (as one goes up,
the other goes up a perfectly predictable amount)
r=-1 if there is a perfect negative relationship (as one goes
up, the other goes down a perfectly predictable amount)
Most correlation coefficients are somewhere in between
Square the correlation coefficient to show how much
(%) of the second variable can be attributed to
differences in the first variable. This is called the
coefficient of determination.
Association does not mean Causation!
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Anxiety about Mathematics
40
50
r=.431
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50
Anxiety about Teaching Mathematics
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Anxiety about Mathematics
Anxiety about Mathematics
r=.463
r=.073
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 What
is the probability that the difference
found between these samples would have
occurred if there was really no difference in
the total populations?
 What
is the probability that the differences
between TWO groups has occurred by chance
alone?
The way it is reported:
t(49) = 1.34, p<.05
Degrees of freedom
(typically n-1)
Value
calculated
by the t-test
Probability that this
difference is due to chance
alone
It is likely that there is a real difference

What is the probability that the differences
between more than two groups has occurred by
chance alone?
The way it is reported:
F(3,53) = 26.26, p<.001
(number of groups -1,
roughly the number of
subjects)
Value
calculated
by the
ANOVA
Probability that this
difference is due to chance
alone
 ANOVA
doesn’t indicate where the
differences occur, just that there is a
difference
 Researchers must then pair the means to find
the differences
 Like
ANOVA but some covariate
(something that is in common between
the two groups) is statistically held
constant when the comparison is
calculated.
 For
example: comparing the achievement
level of different schools with SES held
constant
 Comparisons
when data can’t be averaged
 Nonparametric: without assumptions about the
shape of the data distribution
The way it is reported:
Χ2 (2, N=120) = 12.39, p=.002
(number of groups -1,
number of subjects)
Value
calculated
by the
statistic
Probability that this
difference is due to chance
alone
 Method
used to develop a predictive
equation based on the relationship between
two variables
 Multiple
regression is when two or more
variables are used to predict another
variable using an equation
 Confidence
interval: accuracy band around
the predicted scores.
When a difference is found that appears
unlikely to have occurred by chance, that
difference is identified as being statistically
significant. It does not mean the difference
is important, crucial, or practically
significant.
Effect size: a standard measure of the size of
the difference
Standardized mean difference effect size:
difference between means divided by the standard
deviation
Use figures for
3.31 (p. 111)
Numbers 10 and above
Numbers in an abstract
Number that immediately precede a unit of
measurement
 Numbers that represent statistical or mathematical
functions, fractional or decimal quantities,
percentages, ratios, and percentiles and quartiles
 Numbers that represent time; dates; ages; sample,
subsample or population size; specific numbers of
subjects or participants in an experiment; scores
and points on a scale, exact sums of money; and
numerals.
 Numbers that denote a specific place in a series,
parts of books and tables, and each number in a list
of four or more numbers.
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Grade 3 (but third grade)
Row 5
4.32 (p. 112)
Use words to express
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Numbers below 10
Number beginning a title, sentence, or heading
Common fractions
Universally accepted usage
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The Five Pillars of Islam
The Ten Commandments
Combine words and numbers
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Back to back modifiers (unless it’s more clear to write
out both words
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3 two-way interactions
 Ordinal
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Treat ordinal numbers (first, 12th) as you would the
cardinal base (one, 12)
 Plurals

numbers
of numbers
Add an s or es alone, without an apostrophe
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
1960s
Fours and sixes
4.03 (p. 88)
 Use
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
a Comma
Between elements in a series of three of more
items (including before and and or)
To set off a clause that embellishes a
sentence but if removed would leave the
grammatical structure and meaning of the
sentence intact (nonrestrictive clause).
To separate two independent clauses joined
by a conjunction
Use
 To
a Comma (continued)
set off the year in exact dates
 To set off the year in parenthetical
reference citations
 To separate groups of three digits in
most number of 1,000 or more
 DON’T
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use a Comma
Before a clause that limits or defines the
material it modifies (restrictive clause).
Removal of such a clause from the sentence
would alter the intended meaning
Between two parts of a compound predicate
To separate parts of measurement
3.03 (p. 80)
 Use
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
a Semicolon
To separate two independent clauses that are
not joined by a conjunction
To separate elements in a series that already
contain commas
4.05 (p. 90)
 Use
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a Colon
Between a grammatically complete introductory
clause and a final phrase of clause that illustrates,
extends, or amplifies the preceding thought.
In ratios and proportions
In references between the place of publication and
publisher
 DON’T

After an introduction that is not a complete
sentence
 Use

use a Colon
a Dash
To indicate only a sudden interruption in the
continuity of a sentence. Overuse weakens the
flow of material.
4.07 (p. 91)
 Use
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Quotation Marks
To introduce a word or phrase used as an ironic
comment, as slang, or as an invented or coined
expression. Use quotation makes the first time the
word or phrase is used; thereafter, do not use
quotation marks.
To set off the title of an article or chapter in a
periodical or book when the title in mentioned in
text.
To reproduce material exactly
4.07 (p. 91)
 DON’T
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use Quotation Marks
To identify anchors of a scale (italicize)
To cite a letter, word, phrase, or sentence as a
linguistic example (italicize)
To introduce a technical or key term (italicize)
To hedge
4.09 (p. 93)
 Use
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Parentheses
To set off structurally independent elements
To set off reference citations in text
To introduce an abbreviation
To set off letters in a series (a), (b)
To group mathematical expressions
To enclose statistical values
 DON’T
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
use Parentheses
To enclose materials within other parentheses
[use brackets]
Back to back
4.11 (p. 95)
 Use
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a Slash
To clarify a relationship in which a hyphenated
compound is used
For some units of measurement , per (e.g. m/s)
To set off English phonemes
To cite a republished work in text
 DON’T
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use a Slash
When a phrase would be clearer
For simple comparisons
More than once to express compound units
4.14, p. 101
 Capitalize
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...
Words beginning a sentence
Major words of titles of books and articles within
the body of the paper (but not the reference list
Proper nouns
Nouns followed by numerals or letters that
denote a specific place in a numbered series
Titles of tests
When a capitalized word is hyphenated,
capitalize both words
4.21, p. 104
 Use
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italics for
Titles of books, periodicals, films, videos, TV
shows
Genera, species, varieties
Introduction of a new, technical, or key term or
label
A letter, word, or phrase cited as a linguistic
example
Words that could be misread
Statistical symbols or algebraic variables
Journal volume numbers in the reference list
Anchors of a scale
4.22, p. 106
Use abbreviations sparingly. Communication
can be garbled rather than clarified if the
abbreviation is unfamiliar to the reader.
Abbreviations introduced and then used fewer
than three times thereafter in a long paper,
may be difficult for a reader to remember
See pp. 107-109 for common abbreviation and
abbreviations used as words.
 Read
Chapters 6 and 7
 Bring rough draft of Literature Review,
highlighters (multiple colors), scissors, and
tape