1. MSS 905 Methods of Missiological Research
Introduction to Statistics in Research

2. 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)

3. 4 Levels of Quantitative Measurement (NOIR)
Nominal: (“categorical”) lowest, least precise, different categories (religious affiliation, gender, state)
Ordinal: difference plus categories can be ranked in order from high to low (height, weight, favorite subjects)

4. 4 Levels of Quantitative Measurement (NOIR)
Interval: plus it can specify the amount of distance between categories (differences in inches between ten individuals, miles between five cities)
Ratio: plus true zero, can do proportions or ratios (not important difference from interval)

5. 4 Levels of Quantitative Measurement (NOIR)
What are the following?
Strongly agree/agree/disagree/disagree
Racial categories?
IQ scores?
Temperature?
Freshman, sophomore, junior, senior?

6. Types of Statistics Descriptive: to summarize data
Corelational: special subgroup of descriptive statistics that describe the relationship between two or more variables for one group of participants
Inferential: tools that can tell us how much confidence we can have when we generalize findings from a sample to a population

7. 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)

8. 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

9. 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)

10. 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)

11. Types of Statistics Descriptive: to summarize data
Corelational: special subgroup of descriptive statistics that describe the relationship between two or more variables for one group of participants
Inferential: tools that can tell us how much confidence we can have when we generalize findings from a sample to a population

12. 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)

13. Types of Statistics Descriptive: to summarize data
Corelational: special subgroup of descriptive statistics that describe the relationship between two or more variables for one group of participants
Inferential: tools that can tell us how much confidence we can have when we generalize findings from a sample to a population

14. Types of Statistics Descriptive: to summarize data
Corelational: special subgroup of descriptive statistics that describe the relationship between two or more variables for one group of participants
Inferential: tools that can tell us how much confidence we can have when we generalize findings from a sample to a population

15. 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

16. 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)

17. 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)

18. 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

19. Scales Likert Scale 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

20. Scales 2. Thurstone scaling Bogardus Social Distance Scale
Group of judges rank many items into piles along a continuum
Seldom used due to limitations
Bogardus Social Distance Scale
Measures the social distance separating ethnic groups
Example p. 213, Box 7.11

21. Scales Semantic Differential Guttman Scaling
An indirect measure using polar opposite adjectives or adverbs
Subjects indicate their feelings by marking the spaces between these opposites (7.12)
Guttman Scaling
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

22. Hypothesis and Causality
“Research has proved”: only in journalism, advertisements, courts of law; not in scientific language (TV Dr. Jarvic, or eharmony.com)
Rather: “evidence supports, or confirms the hypothesis”
Other ways to state a causal relationship (Box 6.7, p. 163)