a practical guide to statistics
TRANSCRIPT
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Statistics, not Sadistics!
A Practical Guide to Statistics
for Non-Statisticians
By
James Riley Estep, Jr., Ph.D.
Professor of Christian Education
Lincoln Christian Seminary (Lincoln, Illinois)
Visiting Professor of Statistics
Southern Baptist Theological Seminary (Louisville, Kentucky)
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Table of Contents2013 Edition
Section 1: Foundational Concepts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2
Section 2: Overview of the Statistical Landscape . . . . . . . . . . . . . . . . . . . . . . 6
Section 3: Descriptive Statistics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10
Section 4: Inferential Statistics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13
Section 5: Correlation Statistics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18
Section 6: What to Look Out For . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22
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Section 1
Foundational Concepts
Where do the numbers come from?
Education is at least in part based on theories derived from the findings of the
social sciences, e.g. learning, developmental, or administrative theories. Social science
research takes two different forms: Qualitative and Quantitative.1Qualitative research
generates data in the form of words, e.g. interview transcripts, written descriptions of
observations, or historical documents; and is hence does not rely on statistical analysis.
Quantitative research generates numerical data, e.g. satisfaction rated on a scale of 1-5,
rankings, scores on standardized tests, or preparation times. The analysis of the
numerical data generated form quantitative research methods is called statistics.Statistics is not just math. It is a specialized form of math. It is mathematics
applied to social science research, i.e. quantitative research. Statistics are also used in
the field of assessment, which is becoming increasingly important to educational
institutions and student standardized testing. This guide to statistics is notintended to
be an introduction or survey of quantitative research, nor is it intended to replace an
introduction to statistics textbook. Rather, this paper makes several assumptions:
You are in or have had a statistics class (such as the one may be in right
now). You have access to a basic textbook on statistics that contains more in
depth material, especially the formulas. This paper will notshow the
formulas since (a) most of you will use a computer and hence not even see
the formula, and (b) some of the formulas has very complex in detail, but
show nothing about their usein research.
You will do most of your statistical computations on a computer, using
Excel, SSPS
You make use of user-friendly websites like www.surveymonkey.com,www.questionpro.com or the dissertation helps on
1A third form of social science research may be considered the mixed-method, but this form
is in fact the intentional combination of qualitative and quantitative, and not really a new form
of research. However, mixed method is becoming the preferred form of social science research.
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www.leadership.sbts.edu; and so you dont need to generate the numbers
yourself.
You will probably employ a statistician to do most of your number
crunching for a thesis or dissertation.
In any of these cases, you will still need to comprehendstatistics, so as to design
the appropriate research and request the appropriate computations. In short, you have to
be smart enough to ask the statistician for the right stat! This paper is a crash course in
statistics for non-statisticians. It focuses more on understanding statistics than actually
doing the math.
Population, Sample, Soup and Statistics
How was thesoup? Technically, you cannot tell the waitress how
the soupwas, since you did not actually consume all the soup in the
pot (or at least I hope not). Rather, you base your response on the
bowl that was drawn from pot, only a sample of the soup that your
waitress provided. Thepopulationis the pot, and the sampleis what
you draw from the pot. Sample size is important, so you need to stir the pot and use a
ladle to gather a suitable sample from which to draw your conclusion, since using just a
small spoon may not give you an accurate taste of the whole pot. Also, stirring the pot
before pulling out the sample is important, so as to guarantee that the appropriatemixture of all the soups ingredients is represented. This is all part of the research
design.
All research design starts with a question, such as What does the soup taste
like? It is an unknown. We design research to gather data about the soup so as to
answer the question. It is concerned with the procedures that involve gathering
accurate data from a population being studied. The numbers used in statistics are
generated by doing quantitative research on a population or sample. Hence, the more
precisely a population is described and the more accurately a sample is pulled from thepopulation, the more accurate the numbers will be describing the population/sample.
For example:
QUESTION: How many hours does the average SBTS student study for
an exam in Greek 1 class?
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Figure 1.1
Since a researcher may not be able to
contact everystudent in Greek 1 (population),he/she decides to randomly select a representative
group of Greek 1 students (sample) which is a
more manageable project. The survey is then used
on the sample to generate numerical data for
statistical analysis. A sample/population
calculator is available on www.leadership.sbts.edu
on dissertation helps and the Articles and Resources page. This resource will help
you avoid making a basic mistake in research design, and flaw the data upon which thestatistics are calculated. The findings of the survey are then reported based on
statistical analysis.
A Tale of Three Datas
Where do the numbers come from? Obviously quantitative research methods, as
described above. These numbers represent the reality being studied. But, not all
numbers are alike. It is criticalto keep in mind the three kinds of dataas they relate to the
three kinds of data: Categorical, Ordinal, Interval (also known as ratio). Categorical/Nominal: Data separated into mutually exclusive categories; A scale
that measures in terms of names or designations of discrete units or categories.
o For example: age groups, gender, academic major
o Enables statistician to determine the mode, the percentage values, or a chi-
squared
SURVEY
generating
numerical responses
ReportFindings
Statistical
Analysis
POPULATION
All students at
SBTS in Greek 1
SAMPLE
20 studentspulled from
population ???? DATA
Spoiler Alert:
If the entire population can be
reached, then one need only use
descriptive statistics.
However, if a sample is used,
inferential and/or correlative
statistics must be used, which
are far more complicated.
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Ordinal: Logically ordered categorical data; a scale that measures in terms of such
values as more or less, larger or smaller, but without specifying the size of the
interviews
o
For example,a Likert scale surveys withStrongly disagree;Disagree;
Neutral;Agree;Strongly agree.o
Enables statisticians to determine the median, percentile rank, and rank
correlation.
Interval/Ratio: The distinctions between interval and ratio data are subtle, but
fortunately, this distinction is often not important. Certain statistical methods, i.e.
geometric meanand a coefficient of variationcan only be applied to ratiodata.
o Interval: A scale that measures in terms of equal intervals or degrees of
difference, but whose zero-point, or point of beginning, is arbitrarily established
(not absolute).
For example: Intelligence Quotient (IQ), since there is not real zero.
Enables statisticians to determine the mean, standard deviation, and
product movement correlation; also allows for most inferential statistical
analyses
o Ratio: A scale that measure in terms of equal intervals and an absolute zero-point
of origin.
E.g., birth weight in kilograms or a measurement of distance or height
Enables one also to determine the geometric mean and the percentage
variation; allows one to conduct virtually any inferential statistical
analysis.
These three kinds of data require different statistical treatment, e.g. certain
formulas only work with ordinal data rather than categorical. Mismatch the data with
the statistical formula . . . its like asking how many sides a circle has. The type of data
can also influence how data is presented and what kind of chart one uses to report
findings.
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Section 2
Overview of the Statistical Landscape
Not all Statistics are Alike!
Anyone who has traveled across country can readily tell
the difference between the United States southwest vs. the
Midwest vs. the deep South vs. New England. While certain
similarities exist in all three regions, distinctive geographic and
geological features mark the regions rather distinctively. The
American landscape is in fact s mosaic, a set of landscapes, each
with its own features, ecologies, and resources.
Statisticsis a plural term. The statistical landscape consists of three distinctive
regions: Descriptive, Inferential, and Correlation. Table 2.1 provides a ready reference
to the basic idea of each of these three statistics (Sections 3-5 will address each in detail).
StatisticsType of Question: What is
X ?
Type of Question: What
are the odds of X
happening?
Type of Question: Are and
How Related are X and Y?
Statistics: Descriptive Statistics: Inferential Statistics: Correlation
Metaphor: Snapshot Metaphor: Gambling Metaphor: Thermometer
Formulas/Tests:Mean, Median, Mode, Range,
Quartile, Whisker-Box Plot, Z-
score, and Standard Deviation
Formulas/Tests:Hypothesis testing, p-value,
Z-test, t-Test, Chi-squared,
ANOVA (1-way and 2-way)
Formulas/Tests:Pearson r, Coefficient of
Determination, Scattergram;
Spearman rho, Kendalls tau
Applications:I want toknow what my congregations
membership is like?, e.g. age,
height, weight, gender mix,
ethnicity, income levels, yearsattending this congregation.
Applications:Given theaverage age of a congregation
member, what are the odds of
finding a 72 year old?OR
How sure am I that theopinion of a sample of my
congregation about the new
program represents the whole
congregations?
Applications:Is there asignificant correlation
between the education level of
my congregation members
and their participation inSunday school?
Table 2.1
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Descriptive Statistics
Descriptive statistics . . . describe. It is the most basic form of
statistical analysis of a body of numbers. How many people
attend your church? How do you respond? Do you read off
all the Sunday morning attendances for the previous year?
Probably not. Rather, summarize all those attendances into a
single number, the average attendance (statistically called the mean). How did you do
in seminary? You dont recount your academic transcript; you probably give your
g.p.a. (grade point average) as a means of summarizing your academic performance
into a single, concise number. We use descriptive statistic most frequently and often do
not even realize it. Descriptive statistics are like a snapshot. Tell me what you see?
Descriptive statistics are used to summarize, analyze and share any set of numbers.
However, like a good photograph, you must be able to get everyone in the shot, or the
picture is incomplete. Descriptive statistics are useful only when the entire population
can be reached. While they are the basis of all the other forms of statistics, when you
only have a sample, descriptive statistics are not enough to reach a firm conclusion.
Descriptive statistics cannot answer all the questions or serve all our statistical needs,
and hence two other forms of statistics exist.
Inferential Statistics
What are the odds? Many of us have felt the frustration
of playing the board game Risk and having a territory
defended by one single army that consistently rolls a 6 every
time against your superior forces. What are the odds?
Thats not right! Youre cheating! and the battle ensues. Inferential statistics are
typically used in regard to the probability of a response occurring. More specifically, if
a sample is pulled from a population, how certain can the researcher be that the
numbers gained from the sample accurately reflect the population being studied; i.e.,
what are the odds of the population data occurring outside the sample data? This is
used in political polling when projecting a winner in an election. With a small
percentage of the vote cast (sample) certain statistical extrapolations can be made to
indicate if this is reflective of the voting public (population), answering the question
What are the odds the other candidate can still catch the leading candidate? This also
speaks to the assurance one has that their descriptive statistics are accurate. It becomes a
matter of confidence. How confident are you that your study of the sample is an accurate
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depiction of the population? Las Vegas odds-makers are the heir apparent to this
form of statistics, since it began with a gambling question.
In the mid-1600s a professional gambler named Chevalier de Mere made fortune.
He would bet unsuspecting patrons that in 4 rolls of a die he could get a six at least
once. He was so successful at the game that soon people refused to play him. He then
challenged them that he could roll two sixes in 24 rolls of the die . . . he failed.
Confused, he contacted Blaise Pascal famous mathematician. He corresponded with a
friend, Pierre de Fermat, and they developed the first successful theory of probability . .
. inferential statistics!2 This may be the only beneficial development from the gambling
industry!
Correlation Statistics
When the temperature rises, so does the red line in athermometer. As it cools, the red line lowers. There is an obvious
relationship between the red line and the temperature. However, if
someone had never seen a thermometer before, they could incorrectly
conclude, Amazing, if the red line drops, the temperature lowers; and if it goes up, the
temperature rises! Correlation statistics is a special form of descriptive statistics in
which the relationship between two or more variable relate to one another. Correlation
can not only determine the presence of a relationship, but the nature of the relationship
as well. Is there a connection between small group participation and involvement in
the congregations ministry? This is a question that correlation statistics can answer.
In its most basic form, only thefactof the relationship can be demonstrated, not theform
of the relationship, e.g. causation. More advanced correlation statistics can determine
not only the existence of a relationship, but the event of causation. Correlation statics
are in part based on Inferential statistics, since it is dealing with a sample and
explaining the probability of an event, i.e. if this happens to X, then Y occurs this much.
Variables?
A variable is the item or items being analyzed. If I want to see the correlation
between a students grade point average and their score on a standardized test (such as
SAT, ACT, or GRE), then Im studying the relationship between two variables.
2Cf. Allan G. Bluman (1995), Elementary Statistics, 2ndEdition (Chicago: Irwin), 13.
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Variables come in two different types: Categoricalare those that are non-numerical,
such as gender, which has two categories male and female. Numerical variables are
counted or measured. Discrete numericalvariablesare counted in whole numbers, e.g. 1,
2, 3, 4; like asking how many times someone attended worship annually. Continuous
numerical variables are continuous because they are not simply counted, but are
measured, i.e. using decimals, and hence are continuous; e.g., the distance a household
is from your church building, 5.239 miles. You could say discrete is a count, continuous is
an amount. The type of variable does appropriate statistical formula and the way in
which data is presented (Section 6).
Common Problem: Mismatching!
As Table 2.1 illustrates, the appropriate use of statistics requires alignment. The
question being asked requires the application of the appropriate type of statistics.
Different types of statistics have different formulas associated with them. Finally, the
outcomes of the different statistical formulas lend themselves to different analyses of
the data. In short, mismatching creates an irreconcilable error to occur in research. For
example, if statisticians hear the phrase Chi-squared, they know that inferential
statistics are involved; whereas if someone mentions Pearson r, then correlation
statistics are being discussed. [If you are slightly panicking right now; fear not, these
will be explained later in the paper, and all these functions are calculated by Excel. For
now, just realize that all statistics are not alike.] Likewise, if inferential statistics arebeing applied, then one can assume that hypothesis testing or sample reliability are
involved. Similarly, if correlation statistics are being used, one can assume that the
question involves the relationship of two variables. Table 2.1, as well as Figure 4.1 and
5.1, are designed to maintain statistical alignment in research design.
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Section 3
Descriptive Statistics
Whats going on here?
You have a large set of numbers . . . how do you
describe them? Descriptive statistics are designed to
provide an accurate overview of any set of numbers. Like a
photograph, they capture certain elements of the scene.
Like the photo to the left, you could say, It has palm trees,
a beach, an ocean, and mountains in the distance. While
there may be more the photo, such as waves in the ocean, or mountains closer than
others in the distance, the descriptive given is enough to identify the photo andaccurately describe the contents. Descriptive statistics has several standard methods of
describing a set of numbers. It is not designed to project or capture an image beyond
the limits of the frame, or explain the relationship between items in the photo. Photos
capture one moment in time within the limited scope of the lens. That is descriptive
statistics.
Descriptive Statistics Computations
Mean: The technical term for average, the balancing point of all the data. It is
derived by adding all the values in a data set and dividing by the number of values.
This is designed to identify the center of the data, i.e. central tendency.
Median: The middle value when all the values in a data set are arranged lowest to
highest. This is designed to identify the center of the data, i.e. central tendency.
Mode: The value in a data set that occurs most frequently.
Range: The difference between the lowest and highest number in a data set. This is
designed to demonstrate the spread of values in a data set, the variance.
Quartiles: The three values that split a data set into four equal parts, or quarters.
This is designed to summarize large data sets into 25th, 50th, and 75thpercentiles, i.e.
quarters. Note: standardized educational testing uses the quartile system.
o Q1, the first quartile, 25%, means that a quarter of the values in the data set are
smaller than this value and 75% are larger
o Q2, the second quartile, 50%, means that half of the values in the data set are smaller
than this value and half are larger.
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o Q3, the third quartile, means that 75% of the values in the data set are smaller than
this value and 25% are larger.
Whisker-Box Plot: It is like a graphic representation of quartiles. It is a test of
skewness, i.e. the relation of the mean and median in a data set (See Figure 3.1).
o
Symmetrical Shape: When the mean and median are the same
o Left-Skewed Shape: When the mean is less than the median, and hence more
values are to the left of the mean.
o Right-Skewed Shape: when the mean is more than the median, and hence more
values are to the right of the mean.
o NOTE: This is critical since inferential statistics assumes that data has a
symmetrical shape, or bell curve.
Figure 3.1: Symmetric, Left, and Right Skewed Data Sets
Z-score: The difference between a value and the mean, divided by the standard
deviation. This is designed to identify the spread of data from the mean, the variance. Z-
score is a score; meaning it is used to assess variance. A Z-score of +/- 3 identifies
that that value is an extreme value, far from the mean.
Standard Deviation: The measure of variation of a set of data from the mean, like the
width of the mean. This is designed to demonstrate the spread of data from the mean of the
data set.
ILLUSTRATION
You are an instructor in a seminary. You give a midterm exam to a class of 20
students. The following are the scores on the midterm (the data set), arranged smallest
to largest:
0
1
2
3
4
5
6
Symmetric Left Right
Mean Mean Mean
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58 59 63 68 74 77 83 85 87 88
88 88 90 90 91 92 95 96 97 99
At lunch, a colleague asked, How did your student do on the midterm? Rather
than rattling off the grade book, you could simply respond as follows:
Mean: 83.4
Median: 88.5 (since it is an even numbered data set, 20 values, the median is
between the 10thand 11thvalue).
Mode: 88 (That value occurs three times in the data set, more than any other
value) Range: 41 points (the highest value the lowest value, i.e. 99-58 = 41)
Quartiles: Q1 = 76.25
Q2 = 88
Q3 = 91.25
Skewness: 0.931 (using Microsoft Excel, this figure was provided. Since a value of
0 would indicate a symmetrical skew, and this is close, i.e. it is still a zero-
point-something, then the data is almost symmetrical, maybe only slightly
skewed! Z-score: Since the Z-score for the lowest test was -2.0 and the Z-score for the
highest was +1.23; neither being outside the +/- 3 range, none of the scores are
considered extreme.
Standard Deviation: 12.65 points, meaning most of the grades were between 96.05
(the mean + the standard deviation) and 70.75 (the mean the standard
deviation).
This is probably more information than your colleague requested, required, or
even expected, but it does provide an accurate depiction of the class performance on
the midterm exam!
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Section 4
Inferential Statistics
How sure am I that my description is accurate?
Inferential statistics can be described in a variety of
ways, but perhaps the most common phrase is, What
are the odds of that happening? Inferential statistics is
the mathematical basis of gambling, or more
specificallyprobability. However, for our purposes, the
basic description for our purposes is to discuss the
difference between sets of data. It is used in research to determine the level of confidence
one can have generalizing conclusion about the population from a sample. How
confident can I be that the samples data is an accurate reflection of the population in
general? This is the task of inferential statistics. We can assumethat the data drawn from
a sample of a population will accurately reflect the actual population; but thats an
assumption! Inferential statistics serves to validate more objectively the accuracy of the
samples data in relation to the population. Rather than having to say, Ifeelconfident .
. . or Well, I hopeits accurate!, a statistician can say, Im 90% confident that the
sample data accurately reflects the population.
Inferential Statistic Calculations
Hypothesis Testing refers to a set of methods used to make inferences about
expected or hypothesized values between a sample and population. What methods
(plural) are available for testing hypotheses?
p-value approach: Given the null hypothesis is true, the p-value tests for extreme
values in the sample.You reject the null hypothesis if the p-value is less than , you
do not reject the null hypothesis is the p-value is more than . Hence the phrase, If
the p-value is low, then the null hypothesis must go.o , also known as level of significance, refers to the odds of a Type 1 error
occurring in a hypothesis test. It should be measured at .05 to insure a Type 1
error does not occur.
Z-test (not Z score): What level of confidence do you have that a given set of data is
normally distributed and that a given value falls into a predictable pattern, not in
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the extreme? This is the Z-test or Z-value. Typically, 95% is the level of certainty
used in research. This corresponds to a Z-value of +/- 1.96. If a test statistic is
greater than 1.96, you reject the null hypothesis. If you lower the level of certainty,
this may change . . . but
Inferential Statistics Flowchart3
Figure 4.1
Figure 4.1
DESCRIPTIONS
Wilcoxin Matched Pairs t-Test: It is like the Matched samples t-Test. See below
3Adapted from Dr. Rick Yount, (2006). Research Design and Statistical Analysis in
Christian Ministry, 4thEdition. (self published, Southwestern Baptist Theological
Seminary, Fort Worth, Texas), pp. 5-3, and subsequent material from pp. 5-4 to 5-7.
Group
Differences
Ordinal Interval
2 Groups 3+ Groups 1 Group 3+ Groups
Wilcoxin
Matched
Pairs T-test
Mann-
Whitney
U-test
Wilcoxin
Rank-Sum
test
Kruskal-
Wallis H
test
One-sample
z-test
Sample &
Population
mean known;
n>30
One-sample
t-test
unknown
Independent
Samples t-test
2 Independent
Groups
Matched
Samples t-test
2 matched
groups
2 Groups
One-way
ANOVA
1 ind. var., 1
dep. var. ind.
groups
Factorial
ANOVA
2+ ind. var., 1
dep. var. ind.
groups
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Mann-Whitney U Test: Compares two independent samples; e.g. Did learning, as
measured by the number correct on a quiz, occur faster for Class 1 or Class 2? It is like
the Independent Samples t-Test.
Wilcox Rank Sum: Compares the magnitude and direction of differences between two
groups, e.g. Is Bible college twice as effective as no Bible college experience for helping
develop writing skills?It is like the Independent Samples t-Test.
Kruskal-Wallis H Test: A form of ANOVA that compares the difference between two or
more independent samples; e.g. How do rankings of associate deans differ between
four academic fields? Like the one-way ANOVA.
One-sample z-test: Is data from one sample significantly different from its population?If the sample is > than 30, use this test
One-sample t-test: Is data from one sample significantly different from its population? If
the sample is < than 30, use this test. See below
For example: You know the average age of pastors in the SBC. You collect
information from a single sample of SBC pastors with seminary educations. Is
there a significant difference in the average age of the sample and the
population?
Independent Samples t-Test: Like the ones above, this test computes whether data from
two independently randomly selected samples is significantly different. See below
Matched Samples t-Test: This test computes whether data from two groups of paired
subjects (e.g. husbands and wives; elders and deacons) samples is significantly
different. See below
One-way ANOVA (Analysis of Variance): Also known as a F-test, it tests for difference
between two or more means on one dimension, e.g. How do rankings of associate deans
differ between four academic fields?
Factorial/Two-way ANOVA (Analysis of Variance): tests for difference between two or
more independent samples on more than one dimension; e.g. How do rankings of
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associate deans differ between four academic fields and gender? It measures the
interaction among the independent variables.
t-Test, but which one?
When you are testing for differences between groups, a variety of t Tests are available.How do you know which one to use?
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Figure 4.24
4Adapted from Neil J. Salkind (2008), Statistics for People Who Think They Hate Statistics
(Los Angeles: Sage Publications), 190.
Same
Participants
YES NO
2 Groups 3+ Groups 3+ Groups
t-test for
dependent
samples
Related
measures
of analysis
t-test for
independentsamples
2 Groups
Simple
Analysis ofVariance
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Hypothesis Testing Made Easy!
Figure 4.3
State a Hypothesis
(Null & Alternative)
Set the Level of
Significance ()
(typically .05)
Select the Appropriate Test
Mean/Variance, z-Test, t-Test, X2, ANOVA
Calculate p-value &
compare to
Reject or Accept the Null Hypothesis!
General Rule: If p is low, then the
hypothesis must go.
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Section 5
Correlation Statistics
How does X influence Y?
I wonder if there is a relationship between the temperature in
my dorm room and the red liquid in the thermometer? What
might be that relationship? Correlation statistics is used to
determine the existence, strength, and direction of variables in a
study, especially similarities among variables. Yes, there is a
relationship between the temperature in my dorm room and the red liquid in the
thermometer. When temperature rises, the red liquid rises in direct relation to the
temperature, and this is very strong relationship. Correlation statistics are sometimes
called coefficient of similarityor just association.
Different tests are used depending on the type of variable:
Categorical or Nominal: one that has two or more categories, but there is no
intrinsic ordering to the categories, e.g gender has two categories (male and
female) or hair color having more than two categories (blonde, brown, brunette,
red). Neither of these categories have an order highest to lowest.
Two Categories: Spearman rho () and/or Kendalls tau ()
Three or More Categories: Kendalls W
Ordinal: Like a categorical or nominal variable, except there is an obvious
ordering of the variables, e.g. economic status with three categories (low,
medium and high) or educational experience with levels such as elementary
school graduate, high school graduate, some university and university graduate.
In both instances, the spacing between the values may not be the same across the
levels of the variables.
One Categories: Chi-squared (2
), Goodness of Fit Two Categories: Chi-squared (2), Test of Independence
Interval: Like an ordinal variable, except that the intervals between the values are
equally spaced, e.g. measuring economic status in increments of $10,000, the
space between the variables is equal.
Two Categories: Pearsons r and Linear Regression
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Three Categories: Multiple Regression
Specific types of tests are tied to specific types of variables. Mismatch the variable and/or
test, bad data!
Correlation Flow Chart5
Figure 5.1
Figure 5.1
DESCRIPTIONS
Spearman rho (): Computes correlation between ranks (used when at least 10 or more
pares of rankings are available) given by two groups; e.g. What is the correlation
between rank in the senior year of college and rank during the first year of seminary?
5Adapted from Dr. Rick Yount, (2006). Research Design and Statistical Analysis in
Christian Ministry, 4thEdition. (self published, Southwestern Baptist Theological
Seminary, Fort Worth, Texas), p. 5-3, and subsequent material from pages 5-4 to 5-7.
Relationships/
Similarities
CategoricalOrdinal Interval
2 Ranks 3+ Ranks 1
Variable
2
Variables
2
Variables
3+
Variables
Spearman
rho ()
Kendalls
tau ()
Kendalls
W
Chi-square
Goodness
of Fit
Chi-square
Test of
Indepen-dence
Contingency
Coefficient;
Cramers Phi
Pearsonsr
SimpleLinear
Regression
Multiple
Regression
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Kendallstau (): Similar to Spearman rho, but used when less than 10 ranks are
available given by two groups; e.g. two church staff membersranking a list of seven
characteristics about church health, this could compute the degree of agreement
between the rankings.
KendallsW(also known as Kendalls Coefficient of Concordance): Similar to the
Spearman rho and Kendalls tau, it measures the degree of agreement in ranking from
more thantwo groups, 3+. e.g. five church staff members ranking a list of seven
characteristics about church health, this could compute the degree of agreement
between the rankings.
Chi Square (2): Determines if the number of occurrences across categories is random;
e.g. Did coffee, hot chocolate, and hot tea sell an equal number of cups during the last
week?
Chi Square Goodness of Fit: Compares actual categorical counts with expected
categorical counts, e.g. did actual gender enrollment match what was expected?
How good did the expectation fit the actual?
Chi Squared Test of Independence: Compares two categorical variables to
determine if any relationship exists between them, i.e. are they independent
variables.
Pearson r(or Pearsons Product Moment Correlation Coefficient): Directly measures the
degree of relationship between two interval variables.
Simple Linear Regression: Computes an equation of a line which allow researchers to
predict one interval variable from another, e.g., If x . . . theny.
Multiple Regression: A statistical procedure where several interval variables (3+) are
used to predict one.
t Test, but which one?When you are testing for relationships or similarities between groups, a variety of t
Tests are available. How do you know which one to use?
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Figure 5.26
6Adapted from Neil J. Salkind (2008), Statistics for People Who Think They Hate Statistics(Los Angeles: Sage
Publications), 190.
How many
variables?
2 Groups 3+ Groups
t-test for significance
of the correlation
coefficient
Regression,
factor
analysis
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Section 6
What to Watch Out For
Common Errors, Mistakes, Misfortunes, and Resources of
Statistics (& Quantitative Research)
Appropriate Presentations
If the variable is categorical. . .
Determine 1-2 variables to present
If one, use summary chart, or a bar, pie, orparetochart
If two, 2-way cross table
If the variable is numerical. . . Determine 1-2 variables to present
If one, use frequency and percentage distribution, histogram or a dot scale
If two, determine if time order is important:
o If yes, time-series plot
o If not, use a scatter plot
Resources for Statistical Work7
www.statistics.com
http://www.psychstat.missouristate.edu/scripts/dws148f/statisticsresourcesmain.asp
http://www.stat.ucle.edu/calculators/
http://www.Anselm.edu/homepage/jpitocch/biostatshist.html -- history of statistics
http://www.anu.edu.au/nceph/surfstat/surfstathome/surfstat.html
http://www.davidmlane.com/hyperstat/index.html -- tutorials!
http://www.lib.umich.edu/govdocs/stats.html
http://mathforum.org/workshops/sum96/data.collections/datalibrary/data.set6.html
http://www.stat.ufl.edu/vlib/statistics.html
http://noppa5.pc.helsinki.fip/links.html
Survey Dilemmas8
Ill-defined Population
7Neil J. Salkind (2008), Statistics for People Who Think They Hate Statistics(Los Angeles:
Sage Publications), Chapter 19.8Adapted from Deborah Rumsey (2003), Statistics for Dummies(Hoboken, New Jersey:
Wiley Publishing), Chapter 20.
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Mismatched Sample and Population
Sample wasnt randomly selected
Sample wasnt large enough
Insufficient response to requests
Inappropriate form of survey
Misworded survey items (statements or questions)
Timing of the Study
Inadequate training for research assistants
Survey items didnt relate to the research questions
Avoiding Erroneous Statistical Conclusions9
Statistics dontprove anything.
Conclusions cannot be based on statistically insignificant data
Correlation does not mean causation
Assuming a normal distribution without demonstrating a normal distribution. Partial reporting of the findings
Assuming a larger sample size is better and solves all problems
Intentional omission of unexpected findings
Misapplication of results beyond the population.
Conclusions based on non-random sample
Selected vs. Responded
9Adapted from Deborah Rumsey (2007), Intermediate Statistics for Dummies(Hoboken,
New Jersey: Wiley Publishing), Chapter 21.
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Bibliography
Levine, David M. and David F. Stephan (2005). Even You Can Learn Statistics. Upper
Saddle River, New Jersey: Pearson/Prentice Hall.
Pyrczak, Fred (2006). Making Sense of Statistics: A Conceptual Overview, 4thEdition.
Glendale, California: Pyrczak Publishing.
Rumsey, Deborah (2003). Statistics for Dummies. Hoboken, New Jersey: Wiley
Publishing.
________ (2007). Intermediate Statistics for Dummies. Hoboken, New Jersey: Wiley
Publishing.
Salkind, Neil J. (2008). Statistics for People Who (Think They) Hate Statistics, 3rd
Edition.Los Angeles: Sage Publications.
Yount, Rick (2006). Research Design and Statistical Analysis in Christian Ministry, 4th
Edition. Fort Worth, Texas: Southwest Baptist Theological Seminary.