Statistics 310.01 Chapters 2-4 and APA

Describing Distibutions

- Roughly 70% of scores in a distribution are within one standard deviation of the mean. - Generally considered normal or typical scores. - 95% Fall within 2 standard deviations. Beyond this, extreme scores.

SS

sum of the squared deviations

SS formula

sumation(X-mu)squared

Weighted mean formula

sumationX1+sumationX2/ n1+n2

Standard deviation

the average of the squared deviations of the scores from the mean in a set of data

midpoints of the interval

the exact middle

mode

the score or the category with the greatest frequency

percentile of interest

LRL= (i)x((%)(n)-sumationfb) divided by fw

Range for continuous variables

URLmax=LRLmin

Quotations

You must give page numbers for direct quotes. For example, Smith (1978) noted that "the world is round" (p. 1). Display a quotation of more than 40 words as free-standing block of text indented 5 spaces from the left margin (doubles spaced as usual). Omit the quotation marks and include the page number in parentheses after the last period.

i

bin width

typing

typed, double spaced, one inch margins, 12 pt. font, single space after sentence terminators, make sure the text is left aligned and not justified , just staple or clip the finished process

Symmetrial Graph

you can draw a line through it and have 2 mirror images

deciding which measure of central tendency to use

- The default is to use the mean - Use the median when: You have extreme scores You have undetermined values You have an open-ended distribution Ordinal scale data - Use the mode when: Nominal data Discrete variables Describing shape

Figures

- 'Figures' is the technical term for graphs, charts, drawings and pictures. - If the figure is a chart or graph, verbally label the axes (do not use "X" and "Y") and provide a key if necessary (e.g., explaining what open vs. filled circles are). - Below each figure is a figure caption - Each figure caption is typed flush left in block format. - The word 'Figure' and the number are italicized, for example, Figure 1. The effects of...

Number Rules

- 1st word in a sentence... spell out - If abstract... don't spell out - Less than <10... spell out - Spell out any number when it is the first thing in a sentence. - Try to be consistent with number formats (e.g., equal number of decimal places).

Other Sections

- After the above sections come any tables and any figures. Each belongs on a separate. - Tables and the figures have a manuscript page header and page number just like all the other typed pages. - Tables and figures should be able to stand alone (i.e., you should not have to read the manuscript to be able to understand a table or figure). - Tables and figures should not duplicate the same information. - Tables and figures are most often used to present results, but may also be used to present other information, such as the design or a theoretical schema. - If you include a table or figure, you must introduce it in the text of the results section (e.g., Table 1 displays the...) and describe to the reader what should be seen in it.

Numbers

- All measurement reporting is done in metric units. - The numbers zero through nine are spelled out (except when it is a table or figure number, or a metric measurement, etc.). The numbers 10 and above are written as numbers. - Capitalize nouns followed by numerals or letters that denote a specific place in a numbered series (e.g., Figure 3). - In the abstract, use digits for all numbers except when they begin a sentence.

Discussion

- Do not purposely start a new page for this section. Simply center the word Discussion (bold) and continue typing on the very next double-spaced line. - The purpose of this section is to evaluate and interpret the results, especially with respect to the original research question. - Start off with a brief, non-technical summary of the results. In other words, tell the reader about the main findings without using statistical terminology. - Then go on to discuss the implications of the results. In other words, whatever was found needs to be discussed. - It is also important to discuss how the results relate to the literature you cited in the introduction. - Mention any limitations of the study and any suggestions for future research in this section. - Finally, you need an ending paragraph in which you make a final summary statement of the conclusions you have drawn. You are also encouraged, when appropriate, to comment on the importance and relevance of your findings. - Thus, this section should contain an absolute minimum of three paragraphs: the non-technical summary, discussion of the results and their implications, and the concluding paragraph.

Method

- Do not purposely start a new page for this section. Simply center the word Method (bold) and continue typing on the very next double-spaced line. - The purpose of this section is to describe in detail how you performed the study. Someone should be able to replicate your study based on the information you provide in this section. - Avoid unnecessary details like the data were displayed on the computer screen and recorded on the data sheet(s). - Three subsections: participants (or subjects if animals), apparatus, and procedure. - Participants/Subjects..... - This section is labeled as subjects for animals or participants for humans. - Do not purposely start a new page for this section. Type the appropriate title for this subsection flush with the left margin and bold it. On the next line, begin typing normal paragraphs. - Indicate who participated in the study, how many, and how were they selected. With human subjects, be sure to address the issue of informed consent. - Include any details which are relevant to the study (e.g., gender, age, etc.). - Apparatus... - Do not purposely start a new page for this section. Type the word Apparatus flush with the left margin and bold it. On the next line, begin typing normal paragraphs. - Describe what materials were used and how they functioned in the study. - If you use a piece of equipment, you must give the model number, company, and state where the company resides (as a two-letter abbreviation). - You must give the dimensions (and perhaps other descriptive details) of any important items used in the study. - Standard equipment such as furniture, stopwatches, pencils and paper, can usually be mentioned without providing a lot of details. - Be careful not to describe procedures in this section. - Procedure.... - Do not purposely start a new page for this section. Type the word Procedure flush with the left margin and bold it. On the next line, begin typing normal paragraphs. - Carefully summarize each step in the execution of the study. Indicate what a typical test, trial, or session involved. - When referring to groups, try to use descriptive labels.

Results

- Do not purposely start a new page for this section. Simply center the word Results (bold) and continue typing on the very next double-spaced line (i.e., do not insert any extra blank lines here). - Briefly state the main findings in words. That is, first give a general description, then go into the details. - When presenting the results of statistical tests, give descriptive statistics before the corresponding inferential statistics. - The general format for presenting an inferential statistic is: Statistic(df) = value, p = value. Note that exact p values are preferred. Also, if the computer output says the probability is .0000, then report it as .001. - When actually presenting the results, try to emphasize the meaning of the statistics. That is, clearly describe what it is you are testing and what significance means for the variables involved. - Do not discuss the implications of the results in this section. - Do not talk about the meaning of the alpha level or the null hypothesis, and what chance factors have to do with it. - If you are presenting a lot of material here, you may wish to employ subheadings (as is done in the methods section). These subheadings should have meaning and relevance to the data and should help to organize your presentation of it. - Do not use the word "prove". - You can only use wording that implies causality if you actually manipulated the independent variable (i.e., performed an experiment).

frequency distribution graphs

- Horizontal Axis - X - abscissa measurement scale (values of X) are plotted here from low to high label!! - Vertical Axis - Y - ordinate frequency is plotted here from low to high label!! - Note: the Y axis should be 2/3 to 3/4 as long as the X axis.

In text citations

- If you use someone's words or ideas, you must give them credit with a citation. - The first time the reference is cited in the text, spell out all of the authors last names. With articles that have three or more authors use the Latin abbreviation for "and others" (e.g., et al.) when the reference is cited a second (or third) time. - If 6 or more authors, use et al. each time. If the citation is in parentheses and you need to use the word "and", use the ampersand ('&') instead. - Multiple citations in parentheses are placed alphabetically and are separated by a semicolon and a space. - If you cite something second hand, you must make it clear (e.g., Some fact (Smith, as cited in Jones, Year)). Note that in this example, only the Jones reference would be placed in the reference section.

Graphing Cumulative Frequency

- Put % on the Y axis - On the X-axis, plot the upper real limits - The median lies at the 50th percentile - draw a horizontal line from the 50 - draw a vertical line down - get approximate X - You can do this for any percentile.

frequency polygon

- Put the midpoints of the intervals on the X axis. - Put a dot above that number that corresponds with its frequency. - Connect the dots.

References

- Start on a new page. Center the word References (bold) at the top. - Any citations made in the manuscript must be presented in this section and vice versa. - This section is alphabetized by last name (of the first author involved in the study). - A hanging indent is employed for each reference, that is, the first line is not indented and the rest are five-space indented. - For each author, give the last name followed by a comma and the first (and middle) initials followed by periods. - Separate multiple authors with commas and the last author with the ampersand ('&') rather than the word "and". - After the author(s) comes the year (in parentheses and followed by a period). - For a journal reference, italicize the title of the journal and the volume number. Note that issue numbers are typically not included. Also, capitalize the important words of the journal title. - For a book reference, just italicize the title. Only capitalize the first word of the title. Do include the city, state (as a two-letter abbreviation without periods), and the publisher's name. - DOI should be used if available.

Introduction

- The introduction begins on Page 3. - Start this page by retyping your title (centered & bold), then begin typing the section. - The main purpose of this section is to tell the reader why you performed the study. In other words, you have to inform the reader of the research question and indicate why it is important, and how it is unique when compared to previous studies. - It starts out broad and becomes more specific. - Include any hypotheses and the rationale for them. - The final paragraph usually contains a statement which clearly and explicitly states why the study was performed. - Thus, this section should contain an absolute minimum of four paragraphs: the general introduction, the literature review, the connection of the present study to the literature and the explicit statement of purpose.

Abstract

- The purpose of this section is to provide a brief and comprehensive summary of the study. It is very important because it is all that many people will read. It should include a brief description of the problem being investigated, the methods used, the results, and their implications. - The abstract page is Page 2. - Center the word Abstract (bold) on this page, then begin typing on the very next double-spaced line. - Do not indent. - It should be accurate, self-contained (spell out abbreviations), concise (120 word maximum), and specific. - As part of the theme of being concise, use digits for all numbers except when they begin a sentence. - Avoid citing references in the abstract. - Use active rather than passive voice. - Write this section last.

Title Page

- The running head is no more than 50 characters (including punctuation and spaces). It typically consists of a couple of key words from the title. Type this running head flush left and in all capital letters. - The running head (without the words running head should then be in the top left hand part of each subsequent page) - Page number should be in top right hand corner of each page. - Choosing a title. The title should summarize the main idea of the paper in 10-12 words. - When typing the title, center it on the page and capitalize only the first letter of important words. - On the next double spaced line is the author's name and on the next double spaced line is the institutional affiliation. - Author's note is at the bottom (not applicable in our class)

Tables

- Type the table number and then (on the next double spaced line) type the table title flush left and italicized. - There are different ways to format tables. Your best bet is to set the tabs for the table or to use your word processor's table generating ability. - When using columns with decimal numbers, make the decimal points line up.

Abbreviation Rules

- When abbreviating any terms, spell them out the first time (in both the abstract and again in the body of the manuscript, if need be). - Do not use too many abbreviations. - Note that (except for et al.) these abbreviations are only used in parenthetic material. In non parenthetic material, use the - English translation.

Writing in general

- You must use complete sentences. - Try not to use slang. - Do not use contractions. - A lot of the formatting details can be learned by carefully modeling another APA journal article - Avoid the use of sexist language. - Conciseness is a virtue. Avoid using 'empty words' or words which serve no purpose. - Generally speaking, use past tense in the abstract, introduction, and method. Results and discussion sections can be in the present tense. - Get friends to read it

variance

- before we take the square root, we have the variance. - The variance is the sd squared. - Variance = the average squared deviations.

Characteristics of the mean

-Changing the value of any score will change the mean. - Doing a mathematical operation to every score will do that same thing to the mean.

Grouped frequency distribution tables.... grouped by intervals

1. About 10 intervals are good. 2. The width of the intervals should be a relatively simple number: 3, 5, 10, 20, 100 3. Each interval should start with a score that is a multiple of the width. 4. All intervals must be the same width and there can be no gaps between intervals.

Elements of Research Reports

1. Title page 2. Abstract 3. Introduction 4. Methods 5. Results 6. Discussion 7. References 8. Tables 9. Figures

Frequency Distribution

An organized tabulation of the number of individual scores in each category on a scale

Bar Graph

Like a histogram but spaces between bars

Mean formula for a sample

M=sumationX/n

Range for discrete variables

Max-Min

Median

the score that divides the distribution exactly in half... if the median is between 2 numbers you add them and then divide in half.

3 common ways to formally cite a reference in the text

Researchers (Keen, 2007) found that... Keen (2007) found that... In 2007, Keen found that...

SS for standard deviation sample formula

SS-sumation(X-M)squared

Mean

The average score, add all of the scores together and divide by the number of scores

standard deviation of a sample

biased: underestimates the standard deviation of a population correction for this: using n-1 in the denominator instead of N

sumationfb

cumulative frequency below critical interval

Abbreviations

e.g. = for example (in parenthesis) et al. = and others etc. = and so forth (in parenthesis) i.e. = that is (in parenthesis) vs. = against, versus (in parenthesis cf. = compare (in parenthesis) cm = centimeters mg = milligrams min = minutes g = grams hr = hours s = seconds IQ = intelligence M = mean

Notation used to denote frequency

f

Scientific Writing

formal, concise, clear, progress logically from one idea to the next

fw

frequency within the critical interval

bimodal distribution

has 2 modes

Variability

how spread out the scores are about the mean

The range of a sample is biased

it underestimates the population range

LRL

lower real limit of the critical interval

Mean formula for population

mu=sumationX/N

percentages

multiplying p by 100

n

number of people/scores in your sample

Proportion

p=f/N Expressed as a decimal

%

percentile you are looking for

Skewed Graph

positive or negative: based on tail

standard deviation formula for sample

s=square root of the SS/n-1

definitional formula

sigma=square root of SS/N

Central Tendency

the score that defines the center of a distribution