M.Educ. 6000

Session 5

Are the findings presented clearly?

Is sufficient detail evident in the findings?

Examples and interpretation

Enough 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 numbersMeasures of Central Tendency

Mean: the average ( X ) Mode: the most common Median: the middle number when the data is

put in order from least to greatestWhen should you use which measure?

Measures of VariabilityStandard 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 of AssociationCorrelation coefficient (r ) : a number between -1

and 1 that describes the relationship between two data sets 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 betweenSquare 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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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

It is likely that there is a real difference

Degrees of freedom (typically n-1)

Value calculated by the t-test

Probability that this difference is due to chance alone

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 differenceStandardized mean difference effect size: difference between means divided by the standard deviation

Use figures forNumbers 10 and aboveNumbers in an abstract Number that immediately precede a unit of

measurementNumbers 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. Grade 3 (but third grade) Row 5

3.31 (p. 111)

Use words to expressNumbers below 10Number beginning a title, sentence, or headingCommon fractionsUniversally accepted usage

The Five Pillars of Islam The Ten Commandments

Combine words and numbersBack to back modifiers (unless it’s more clear to

write out both words 3 two-way interactions

4.32 (p. 112)

Ordinal numbersTreat ordinal numbers (first, 12th) as you would

the cardinal base (one, 12) Plurals of numbers

Add an s or es alone, without an apostrophe 1960s Fours and sixes

Use a CommaBetween 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

4.03 (p. 88)

Use a Comma (continued)To set off the year in exact datesTo set off the year in parenthetical

reference citationsTo separate groups of three digits in

most number of 1,000 or more

DON’T use a CommaBefore 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 predicateTo separate parts of measurement

Use a SemicolonTo separate two independent clauses that

are not joined by a conjunctionTo separate elements in a series that

already contain commas

3.03 (p. 80)

Use a ColonBetween 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

4.05 (p. 90)

DON’T use a ColonAfter an introduction that is not a complete

sentence

Use a DashTo indicate only a sudden interruption in the

continuity of a sentence. Overuse weakens the flow of material.

Use Quotation MarksTo 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 use Quotation MarksTo 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

4.07 (p. 91)

Use ParenthesesTo set off structurally independent elementsTo set off reference citations in textTo introduce an abbreviationTo set off letters in a series (a), (b)To group mathematical expressionsTo enclose statistical values

4.09 (p. 93)

DON’T use ParenthesesTo enclose materials within other

parentheses [use brackets]Back to back

Use a SlashTo clarify a relationship in which a

hyphenated compound is usedFor some units of measurement , per (e.g.

m/s)To set off English phonemesTo cite a republished work in text

DON’T use a SlashWhen a phrase would be clearerFor simple comparisonsMore than once to express compound units

4.11 (p. 95)

Capitalize . . . 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

4.14, p. 101

Use 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

4.21, p. 104

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.

4.22, p. 106

Read Chapters 6 and 7 Bring rough draft of Literature Review,

highlighters (multiple colors), scissors, and tape