Week 12: Lecture/Tutorial 12
Chi-Square, Referencing and
Review
BCPC 301: RESEARCH METHODS
1st Semester, 2019
Lecture outline
The following are covered in this lecture:
• Chi-square
• What is Referencing
• Reasons for Referencing
• APA referencing Style
– In-text referencing
– References list
– Using Mendeley to in-text referencing and referencing list
• Course review
Learning outcomes
By the end of this lecture/tutorial you should be able to:
1. Understand chi-square test and the interpretation of results
2. Explain why referencing is important is research
3. Understand how to do in-text referencing and reference list
4. Understand how to use Mendeley to do in-text referencing and
reference list
CHI-SQUARE
What is chi-square?
• Karl Pearson in 1900 developed Static procedure for
testing the significance of the discrepancy between
experimental values and theoretical values obtained
under some theory or hypothesis.
• This test is known as x2 (Chi-square) test.
• It is used to find whether the deviation between
observation (survey/experiment) and theory may be
attributable to chance (fluctuations in sampling) or any
other factor.
• Chi-square test is applicable to categorical or nominal
data and not to data collected on continuous scale
Conditions for validity of chi-square
test
• Chi-square test can be used only if the following conditions are
satisfied:
– N, the total number of frequency should be reasonably large, say
greater than 50
– The observations in the sample should be independent. This means
that no individual item should be included twice or more in the
sample
– No theoretical frequency should be small. Preferably, each
theoretical frequency should be larger than 10 but should not be
less than 5
Application of chi-square test
1. chi-square test of goodness of fit or chi-square with a
priori hypothesis.
– That is, how far an observed frequency distribution fits well
with the expected frequency distribution based on some
theory or hypothesis
– In this case, null hypothesis (H0) is “there is no difference
between observed frequency and expected frequency”.
– The alternate hypothesis (HA) is “there is difference between
observed frequency and expected frequency”
Application of chi-square test
2. chi-square test for association between attributes or
independence of attributes or chi-square test without a priori
hypothesis.
– This is used to find whether two characters have the tendency to
remain together or remain independently. E.g curing a disease and
drug
– Null hypothesis is ”there is no association between curing a disease
and drug taken”.
– Alternative hypothesis is “there is an association between curing a
disease and drug taken”
Application of chi-square test
3. chi-square test to test the quality of proportions.
– Chi-square test enables one to find out the significance of difference
between two or more population proportions.
– If an investigator is interested in finding out whether the proportion of
married men is same in four major cities.
– The null hypothesis (H0) is “The proportion of married men is the same in
four major cities.
– The alternate hypothesis (HA)is “The proportion of married men is not the
same in four major cities”.
Application of chi-square test
4. Chi-square test of homogeneity
– Sometimes we need to compare samples taken from two
populations differing in some characters.
– E.g., samples are drawn from two populations namely “normal” and
“liver disease patients”
– These two samples are then classified into two: persons with
hepatitis and persons without hepatitis
– Chi-square is can be used to find out whether the two populations
from where the samples are drawn are homogenous or not.
– In this case the null hypothesis (H0) is “The two populations from
where the samples are drawn are homogenous”.
– The alternate hypothesis is “The two populations from where the
samples are drawn are not homogenous”.
Running a Chi-square test
• Although, four different applications are given
for test, all these tests are basically the same
• They find whether the observed frequency fits
well with expected frequency, but the statement
of null hypothesis differs.
1.
2.
3.
4.
5.
6.
7.
Procedure To Carry Out Chi-Square
Test
Propose Null and Alternate hypothesis
Calculate expected frequencies
Find the deviations between expected and observed frequencies
Square the deviations and divide by respective expected frequencies
Substitute in the formula
Write the degrees of freedom
Refer the tabulated test values for the specified degrees of freedom at
0.05 (or 0.01) probability level
8. Compare calculated chi-square values with tabulated chi-square values
9. Interpret the results.
Interpreting chi-test results from
spss
Goodness of Fit for a Categorical Variable
•
Example 1
It is believed that the general human population in a region consists of 10%
Hispanic, 10% Asian, 10% African–American and 70% White folk. In a
sample survey it was recorded that there were 24 Hispanic, 11 Asians, 20
African–American and 145 White folk. Test whether the observed
frequencies differ significantly from the hypothesized values.
• Null and alternate hypotheses:
– H0 There is no difference between observed and expected frequencies.
– HA There is real difference between observed and expected frequencies.
SPSS output/results
SPSS output/results
•
•
•
The observed and expected frequencies are given in the first table.
In the second table, the Chi-square value is 5.029 for 3 df and asymptotic
significance is 0.170, (i.e., p-value)
Since, the p-value 0.170 is greater than 0.05 (p > 0.05), the difference between
observed frequencies and expected frequencies is insignificant.
•
Therefore, the null hypothesis (H0), i.e., there is no difference between
observed and expected frequencies is accepted at 5% level of significance.
•
The answer to our problem is that the racial composition of our sample does
not differ significantly from the hypothesized values for human population in
that region.
Interpreting chi-test results from
spss
Chi-square Test for Independence of Attributes
•
• As noted, this test is used to find out whether two
categorical variables are associated with each other.
number of categories).
Example 2
• A group of students were classified in terms of
gender (male and female) and blood group (A, B, AB
and O).
• Find whether there is association between gender
and blood group.
Interpreting chi-test results from
spss
Hypothesis and SPSS output/results
• Null and alternate hypotheses
– H0 There is no association between gender and
blood group.
– HA There is real association between gender
and blood group.
Hypothesis and SPSS output/results
SPSS output/results
• The first table gives the frequencies of blood groups
in male and female in the table form (Cross
tabulation).
• The second table shows 3 degrees of freedom i.e., [(r
– 1) (c - 1)] = [(2 – 1) (4 – 1)] = 3,
• The p-value 0.852 is greater than 0.05.
• The difference is considered insignificant.
• The null hypothesis is accepted and therefore, there is
no association between sex and blood group.
Example 3
• Two groups A and B consist of 100 people each having a
particular disease. A drug is given to group A and not to group B.
Otherwise both are treated identically. It is found that in group A
and B, 80 and 65 persons have recovered from the disease.
• Test the hypothesis that the drug helps to cure the disease at
0.05 level of significance.
• Null and alternate hypothesis
– H0 The drug is not effective in curing the disease.
– HA The drug is effective in curing the disease. Step
SPSS output/results
SPSS output/results
Pearson’s for 1 degrees of freedom, i.e., [(r –
1) (c – 1)] = [(2 – 1) (2 – 1)] . The p-value
0.018 is less than 0.05. Therefore, null
hypothesis is rejected and the drug is
effective in curing the disease (p < 0.05).
REFERENCING
Conceptualising Social research
Epistemology
Theoretical Framework
Methodology
Methods
See Crotty (1998, p4)
Referencing
(Crotty 1998)
What is Referencing?
• It is about showing and acknowledging all
sources of information or ideas that you
have used in your research or assignment
• When a researcher/student uses another
person words or ideas without
acknowledging them it is referred to as
Plagiarism
26
Why do we do Referencing?
• To avoid plagiarism by giving credit to the original
source of an idea, piece of information or
resource
• To avoid plagiarism
– Learn good note-taking techniques
– Paraphrase appropriately
– Summarise correctly and efficiently
– Use direct quotations appropriately
– Organise your sources
– Reference your sources correctly
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Why do we do Referencing cont’d?
• To support your work with the authoritative work
of another author
• To demonstrate your knowledge and familiarity
with a topic that you have researched
• To help readers of your work to find the original
source of information or ideas that you have used
28
Types/Parts of Referencing
Referencing is in two parts:
1. The in-text referencing which is normally done in the
text and
2. List of references which is normally at the end of the
report. There are two ways of listing the references
a. List of references: This refers to sources of materials
cited in the text. Any material used for the
preparation of the report but was not cited in the
text cannot be part of the list of references
b. Bibliography: This refers to all sources of
informational materials used for the presentation of
the whether cited in the text or not.
29
Referencing Styles
• There are many different referencing styles. Each style
includes the same basic information, but organizes it
slightly differently.
Some of the known formats/styles are:
1. American Psychology Association (APA)
2. Modern Language Association (MLA)
3. Harvard Type
4. Oxford format
5. Chicago format etc
30
APA Referencing Style
• The APA reference style uses the Author-Date format.
• It is used by psychologist, sociologist and other social
scientist
• The APA format requires short notes, or citations, put in
parenthesis with the text instead of footnotes or endnotes
• The complete format can be found in the publication
manual of the American Psychological Association available
http://student.ucol.ac.nz/library/onlineresources/Documen
ts/APA_guide_2015.pdf
31
In-text Referencing
• In-text referencing can take two form:
1. Direct quotation: use quotation marks around the
quote and include page numbers in the Last
name and publication date
2. Indirect quotation: Identify source material that
you are paraphrasing by citing the author’s last
name and the publication date, either in your
sentence or in parenthesis.
You do not have to cite page number(s) for
paraphrases.
32
Examples of Direct Quotation
— Samovar and Porter (1997) point out that "language
involves attaching meaning to symbols" (p.188).
— Alternatively, “Language involves attaching meaning
to symbols" (Samovar & Porter, 1997, p.188).
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Notes on Direct Quotation
• Shorter quotations (fewer than 40 words) should be
incorporated within your paragraph with quotation
marks: they should not be indented separately but
should have page numbers preceded by p. or pp.
• Longer quotation (over 40 words) should be blockindented five spaces from the left margin and typed
without quotation marks
34
Examples of Indirect Quotation
1. If you mention the author’s name and the
publication date in your sentence, you will not
need any additional citation.
Example: In 1983 study, Deborah Mayo began to question
the scientific validity of experience involving laboratory
animals.
2. If you mention the author’s last name in your
sentence, place the date of publication in
parentheses right after the name.
Example: Mayo (1983) questioned the scientific validity of
experiments involving laboratory animals
35
Examples of Indirect Quotation cont’d
3. If you do not mention the author’s name or the
publication date in your sentence, put both
parentheses with comma between them (Kofi, 2001)
4. If you cite two works by one author published in the
same year, distinguish them by placing an (a) and a (b)
after the date within the parenthesis e.g. (Kofi, 2001a)
5. If you cite authors with the same last name, use their
first and middle initials within the parentheses (Salifu,
A. 2016); Salifu, J. 2016)
36
Examples of Indirect Quotation cont’d
6. If a work has two authors, combine the names with
“and” in your sentence. Use an ampersand “&” instead of
“and” in a parenthetical citation. (Kofi & Ama, 2001)
7. If a work has no author, cite it by the first two or three
words of the article, starting with the first important word
and placing these two words or three words in quotation
marks (”Business Ranking”, 2011)
8. If you use a quotation from an indirect source, precede
the source information in the parenthetical citation with
the words “as cited in”. In the reference list include an
entry only for the secondary source. Chang (as cited in
Polit & Beck, 2008) outlined the four main concepts…
37
Examples of Indirect Quotation cont’d
9. If you cite two or more works by different authors
in one parenthetical citation, give the work in
alphabetical order and separate them with
semicolons (;) e.g. (Adam, 2003; Kofi, 2001; Taku,
2005)
10.If a work has more than two to five authors, cite all
of them in your sentence or parenthetical citation in
the first instance and in all other subsequent
references use the last name of the first author
followed by “et al.”
(Taku, Toyu, & Naam, 2001) Taku et al. (2001)
38
Examples of Indirect Quotation cont’d
11.If a work had six or more authors, use et al. after
the first authors last name in all references in
the text e.g. (Adam et al., 2003)
39
Reference list (examples by type of
publication)
• Alphabetize entries in the list of references by
authors last names
• If a work has no author, alphabetize it by its title
• The first element of each entry is important
because citations in the text of the paper refer to
it and readers will be looking for it in the
alphabetized list. Make sure the first element of
each entry corresponds with your in-text citations
• The date of publication appears immediately after
the first element of the citation, followed by titles
40
Reference list (examples by type of
publication cont’d)
1. Book with one author
King, M. (2000). Wrestling with the angel: A life of Janet
Frame. Auckland, New Zealand: Viking.
N.B. The first letter of the first word of the main title,
subtitle and all proper nouns have capital letters.
2. Book with two to five authors
Krause, K. L., Bochner, S., & Duchesne, S. (2006). Educational
psychology for learning and teaching, (2nd ed.). South
Melbourne, Vic., Australia: Thomson.
N.B. Use & between authors’ names, except when
paraphrasing in text.
41
Reference list (examples by type of
publication cont’d)
3. Edited Book: use (Ed.). Before the date. e.g. DeGenova,
M.K. (Ed.). (1997). Families in cultural context: Strength
and challenges in diversity. Mountain View, CA: Mayfield
4. Edition other than the first: place the edition number in
parenthesis after the title; for a revised edition, use Rev.
ed. e.g. Bennett, L., Jr.(1984). Before the Mayflower: A
history of Black America (5th ed.). Harmondsworth,
England: Penguin Books.
5. Books by a corporate Author or Group: e.g. U.S Bureau
of the Census. (1999). Statistical abstract of the United
states, 1999 (11th ed.) Washington, DC: Government
Printing Office
42
Reference list (examples by type of
publication cont’d)
6. Books without an author or editor: e.g. The control of
the campus: a report on the governance of higher
education. (1982). Lawrenceville, NJ: Princeton University
Press
7. Multivolume work: e.g.
— The entire set: Neather, C.A., & Richardson, G.F. (1930). A
course in English for engineers (vols. 1-2). Boston:Ginn.
— One volume: Battle, K.P. (1912). History of the university of
North Carolina: vol. 2. Raleigh, NC: Edwards and
Broughton.
If the volume has it own title, include it after the volume
number.
43
Reference list (examples by type of
publication cont’d)
9. Essay or Article in a Book: e.g. Wilkinson, D.
(1997). American families of African descent. In
M.K. DeGenova (Ed.), Families In Cultural Context
(p. 35-51). Mountain View, CA: Mayfield.
The selection title is written without quotation marks
and with lower-case letters (except for the first letter
of the title, of proper names and of a subtitle after a
colon). The book title is in the same lowercase format
but is italicized. Place the page numbers for the
complete title.
44
Reference list (examples by type of
publication cont’d)
Citing from Reports, Documents and Dissertation
Government documents, research report, monograph
— U.S Census Bureau. (1999, September). Money
income in the united states. Current population
reports (p60-206).Washington, DC: author.
— Kreshner, L., Addams, B., & Winestein, C. (2001). Use
of manipulatives in teaching mathematics in grades
four through six (Report No. 6). New Orleans: state
Mathematics Service
— A report or document number, if there is one should
appear in parentheses immediately after the
number.
45
Reference list (examples by type of
publication cont’d)
Dissertation
Fredericks, C. (1999). HIV testers and non-testers
at a university students health centre: A study of
college students sexual risk taking (Doctorial
dissertation, University of South California, 1999)
Dissertation Abstracts International, 60 (02A),
0346.
46
Reference list (examples by type of
publication cont’d)
Articles in a scholarly journal paginated by year or volume
• The entire year’s issues are paginated as a unit
• Battaglia, D. M., Datteri, D., & Lord, C. (1998). Breaking up
is (relatively) easy to do: A script for the dissolution of
close relationships. Journal of social and personal
Relationships, 15, 829-845
• Do not italicise the title of the article, and do not capitalize
it (except for the first word, proper names and the first
word after a colon.
• Capitalise and italicise the title of the journal. Underline
the volume number. It is followed by a comma and the
complete page numbers of the article.
47
Reference list (examples by type of
publication cont’d)
— Article in a scholarly journal paginated by issue
— Each issue begins with page 1.
— Blanton, J.S. (2000). Why consultants don’t
apply psychological research.
Consulting psychological journal: practice and
research, 52 (4), 235-247
— Underline the volume number. It is followed by
the issue number in parentheses (not
underline), a comma, and the complete page
numbers of the articles.
48
Reference list (examples by type of
publication cont’d)
Internet Article Based on a Print Source
• O’Barr, W., & Conley, J. (2000). When cultures collide:
Social security and the Market [electronic version]. Journal
of psychology and Financial Market, 1, 92-100
• Article in an Internet-only Journal
• Wagner, L. (2001). Virtual Advertising: Delivering Student
services. Online journal of Distance Learning
Administration, 4(3). Retrieved June 1, 2002, from
http://www.westga.edu/distance/main11.htm
• World Wide Web Site
• International Society for Mental Health Online. (n.d.).
Children and trauma: Reflections on the World Trade
Centre disaster. Retrieved October 15, 2001, from
http://www.ismho.org
49
Using Mendeley as a referencing tool
Course Review
Positivism
Objectivism
Research problem/topic/issue/question
Epistemology
Literature review
Theories
Constructionism
Subjectivism/
interpretivism
Theoretical Framework
Methodology
Sampling
Data
collection
Method
Data
analysis
Ethics
Exam (suggested topics)
1. Case study--- test your understanding of the
entire research process.
2. Literature review
3. Methodology/research design
4. Methods for data collection
5. Sampling
6. Qualitative data analysis
7. Quantitative data analysis (chi-square, conditions,
statement of hypothesis and interpretation)
8. Referencing
52