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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 numbers
- Measures 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 greatest

- When should you use which measure?

- Measures of Central Tendency

- Measures 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 of Association
- Correlation 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 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.

- Correlation coefficient (r ) : a number between -1 and 1 that describes the relationship between two data sets

Association does not mean Causation!

r=.431

r=.463

r=.073

- 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

Probability that this difference is due to chance alone

Degrees of freedom (typically n-1)

Value calculated by the t-test

- 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

Probability that this difference is due to chance alone

(number of groups -1, roughly the number of subjects)

Value calculated by the ANOVA

- 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)

Probability that this difference is due to chance alone

Value calculated by the statistic

- 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

3.31 (p. 111)

Use figures for

- 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.
- Grade 3 (but third grade)
- Row 5

4.32 (p. 112)

Use words to express

- Numbers below 10
- Number beginning a title, sentence, or heading
- Common fractions
- Universally accepted usage
- The Five Pillars of Islam
- The Ten Commandments
Combine words and numbers

- Back to back modifiers (unless it’s more clear to write out both words
- 3 two-way interactions

- Ordinal numbers
- Treat 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

- Add an s or es alone, without an apostrophe

4.03 (p. 88)

- Use 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 a Comma (continued)
- To 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 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 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 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 use a Colon
- After an introduction that is not a complete sentence

- Use 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 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 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 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 use Parentheses
- To enclose materials within other parentheses [use brackets]
- Back to back

4.11 (p. 95)

- Use 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 use a Slash
- When a phrase would be clearer
- For simple comparisons
- More than once to express compound units

4.14, p. 101

- 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

4.21, p. 104

- 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

4.22, 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