Transcript Mostert`s Introduction to Statistics in Research

MSS 905 Methods of
Missiological Research
Introduction to Statistics in
Research
Introductory Concepts
• Empiricism: using direct observation to obtain
knowledge
• Empirical research: acquiring knowledge by
using scientific observational techniques
– Experimental research using dependent and
independent variables to identify causal relationships
in experimental and control groups
– Nonexperimental research are also called descriptive
studies (no treatments; historical analysis, case study,
program evaluation, etc)
4 Levels of Quantitative
Measurement (NOIR)
1. Nominal: (“categorical”) lowest, least
precise, different categories (religious
affiliation, gender, state)
2. Ordinal: difference plus categories can
be ranked in order from high to low
(height, weight, favorite subjects)
4 Levels of Quantitative
Measurement (NOIR)
3. Interval: plus it can specify the amount of
distance between categories (differences
in inches between ten individuals, miles
between five cities)
4. Ratio: plus true zero, can do proportions
or ratios (not important difference from
interval)
4 Levels of Quantitative
Measurement (NOIR)
What are the following?
• Strongly agree/agree/disagree/disagree
• Racial categories?
• IQ scores?
• Temperature?
• Freshman, sophomore, junior, senior?
Types of Statistics
1. Descriptive: to summarize data
2. Corelational: special subgroup of
descriptive statistics that describe the
relationship between two or more
variables for one group of participants
3. Inferential: tools that can tell us how
much confidence we can have when we
generalize findings from a sample to a
population
Descriptive Statistics
• f stands for frequency, or the number of
cases or times a number or attribute
appears “ a score of 17 (f = 23) appeared
the most”
• N is the number of participants (N= 78)
• Frequency distribution: the shape of a set of
scores
• Normal distribution: a bell shaped curve
• Skewed distribution (positive and negative)
Descriptive Statistics
• X (pronounced X=bar): the mean, the most
frequently used average
• Median is an alternative average: it has
50% of the cases above it and 50% below;
the “middle point”
• Mode is the most frequently occurring
score in a distribution
Descriptive Statistics
• Variability refers to the differences among
scores of participants
• Measures of variability are a group of
statistics that are designed to describe the
amount of variability in a set of scores
• Range: the simplest statistic to indicate
variability (the difference between the
highest and the lowest scores)
Descriptive Statistics
• Standard deviation: the most frequently
used measure of variability (dispersion,
spread of scores)
• It provides an average of how far all the
participants scored away from the mean
– The more they differ from the mean of their
group the higher the standard deviation
• Standard deviation can be plotted on a
normal curve (see handout)
Types of Statistics
1. Descriptive: to summarize data
2. Corelational: special subgroup of
descriptive statistics that describe the
relationship between two or more
variables for one group of participants
3. Inferential: tools that can tell us how
much confidence we can have when we
generalize findings from a sample to a
population
Corelational Statistics
• Correlation refers to the extent to which
two variables are related across a group of
participants (eg SAT scores and first-year
GPA in college; spiritual maturity scores
and church attendance)
– Can be positive or negative or orthoganal
– NOT causal (for that you need an
experimental design)
– Pearson r: correlation coefficient (-1.00 to
1.00)
Types of Statistics
1. Descriptive: to summarize data
2. Corelational: special subgroup of
descriptive statistics that describe the
relationship between two or more
variables for one group of participants
3. Inferential: tools that can tell us how
much confidence we can have when we
generalize findings from a sample to a
population
Types of Statistics
1. Descriptive: to summarize data
2. Corelational: special subgroup of
descriptive statistics that describe the
relationship between two or more
variables for one group of participants
3. Inferential: tools that can tell us how
much confidence we can have when we
generalize findings from a sample to a
population
Inferential Statistics
• Population: all the members of a group of
interest to a researcher
• Sample: a representative group of
members from the total population
• Null hypothesis: that the true difference
between the mean scores of two groups is
zero (ie. there is no difference)
– Has to be rejected first before an alternative
hypothesis can be entertained
Inferential Statistics
• Null hypothesis actually says that the
observed difference between the means of
two sets of scores was due to sampling
error
• Significance tests (like t Test) are applied
to the data that yield a probability that the
null hypothesis is true (“p”)
– p<.05 (probability is only 5 in 100)
– P<.01 (probability is only 1 in 100)
Inferential Statistics
• When you test the null hypothesis to
determine the difference between means
– Use a t Test if there are two means
– Use a F Test if there are two or more means
to be tested (this is referred to as the ANOVA
or analysis of variance)
Scales
“A data measure that captures the intensity,
direction, level or potency of a variable
construct along a continuum”
– Often used in survey research
– Most scales are at the ordinal level of
measurement
Scales
1. Likert Scale
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Widely used in survey research
Ordinal-level measure of attitude
Examples on p. 208, Box 7.8
Minimum of 2 categories, but normally 4 to 8
Sometimes reverse scored to avoid response
set (tendency to agree with every question)
– Can be used to form an index of opinion
Scales
2. Thurstone scaling
– Group of judges rank many items into piles
along a continuum
– Seldom used due to limitations
3. Bogardus Social Distance Scale
– Measures the social distance separating
ethnic groups
– Example p. 213, Box 7.11
Scales
4. Semantic Differential
–
–
An indirect measure using polar opposite adjectives
or adverbs
Subjects indicate their feelings by marking the
spaces between these opposites (7.12)
5. Guttman Scaling
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A cumulative scale to determine whether
relationships exist among indicators
A scale based on data that has been collected
already, to determine if a hierarchical pattern exists
among responses
Hypothesis and Causality
1. “Research has proved”: only in journalism,
advertisements, courts of law; not in scientific
language (TV Dr. Jarvic, or eharmony.com)
2. Rather: “evidence supports, or confirms the
hypothesis”
3. Other ways to state a causal relationship (Box
6.7, p. 163)