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                                                                      CHAPTER 2

I.  Variables and Hypotheses

 

    A.   Recognizing Research Variables

Variable: a characteristic to which numbers or values may be assigned

    B.   Variables as Used in Hypotheses

Independent variables: “variables that can be used to predict or explain the values of another variable” (Vogt, 2005, p. 151)

Dependent variables: variables whose values are predicted by independent variable(s), whether or not caused by them (after Vogt, 2005, p. 86)

Moderator variable: a type of independent variable that affects the ways in which the primary independent variables are related to the dependent variables

Mediating variable: “a variable that ‘transmits’ the effects of another variable” (Vogt, 2005, p. 190)

Intervening variable: “a factor that theoretically affects observed phenomena but cannot be seen, measured, or manipulated; its effect must be inferred from the effects of the independent and moderator variables on the observed phenomena” (Tuckman, 1999, p. 101)

Control variable: a “nuisance” variable that is held constant for the purposes of controlling its influence

Suppressor variable: a “variable that conceals or reduces (suppresses) a relationship between other variables” (Vogt, 2005, p. 318)

C.     Hypothesis Types

1.   Research or “Alternative” Hypotheses:  Because the research hypotheses stand as alternatives to the null hypotheses, they sometimes are called “alternative hypotheses.”

 

Forms:

·  comparisons of dependent variable means: directional and nondirectional hypotheses

(when researchers examine

sample characteristics, they use symbols from the Roman alphabet; when describing or estimating population characteristics, they use symbols from the Greek alphabet. For conceptual purposes researchers usually hypothesize general relationships that may exist in the population as a whole.)

Directional hypotheses: hypotheses that state the direction of the difference in means (or, in a broad sense, they state the direction of the relationship) (e.g., H: μ1 > μ2).

Nondirectional hypothesis: a hypothesis that states the existence of a relationship, but not its direction (e.g., H: μ1 ≠μ2)

 

·  comparisons of proportions

(the sample proportion is often symbolized as p and the population proportion is symbolized as B(pi)

 

·  examination of correlations

--the symbol for the sample correlation is r  (or some variation of r, including R), and the abbreviation for the population correlation is ρ (rho)

Correlations measures that identify the degree of coincidence between variables (in numbers that usually range from –1 to 1)

 

          2.  Null Hypotheses

--researchers can determine how unlikely it is that they could find data such as observed in a study if the null hypothesis were true. If researchers reject the null hypothesis as improbable, then the alternative hypothesis, the research hypothesis, is supported.

Null hypothesis: a statistical hypothesis that states that there is no relationship between the variables presented in the research hypothesis (when differences between the means of groups are hypothesized, the null hypothesis is stated as H0: μ1 = μ2 ).

 

 

II.  Measurement of Variables

Measurement: systems by which numbers are associated with characteristics of interest.

     A.  Levels of Measurement

Nominal level measurement: the use of numbers as simple identifications of variables (Reinard, 2001, p. 439)

Ordinal level measurement: the use of rank order on some variable

Interval level measurement: assignment of numbers to items as a matter of degree such that “the intervals between numbers are equal in size” (Cozby, 1989, p. 149)

Ratio level measurement: assignment of numbers to items such that “any adjoining values are the same distance apart and in which there is a true zero point” (Vogt, 2005, p. 264).

Absolute zero: a value that would indicate the complete absence of the property being measured

B.   Statistical Debates Regarding Measurement Levels

·  Distinguishing between pure interval and ordinal scales: some believe that many so-called interval scales used in the social sciences really only tell relative differences among respondents

--the consensus is that the importance of violating assumptions of pure interval measurement has been overstated and many such scaled responses could be considered “quasi-interval”

Quasi-interval measure: a measure that is “close enough to interval to allow interval methods to be used” (Ender, 2003, ¶ 9).

·  Distinguishing between continuous and discrete variables

--some continuous variables may be composed of units which, in themselves, are discrete

Continuous variable: a variable that can take any of a large number (often infinite) of values

Discrete variable: a variable “made up of distinct and separate units or categories” (Vogt, 2005, p. 92)

·  Distinctions between attribute and variable data

--since researchers dealing with attribute data cannot making interpretations of the degrees to which the variables are present, they serve primarily to identify “attributes” or qualitative characteristics of data

Attribute data: data are measured on the nominal or ordinal levels

Variable data: data measured as true “variable data” or ratio measures that feature an absolute zero.

 

III.  Sampling

  1. The Importance of Careful Sampling

1.   important to ensure a representative sample

 

 

 

Representative sample: a sample that adequately reflects the population from which it was drawn.

Parameters (or population parameters): numbers that are computed from or characterize populations

 

2.   required to avoid bias

 

 

Bias (or sampling bias): systematic error that prevents the researcher from correctly identifying the population characteristic

Biased estimators: estimates in which “the expected value of a sample statistic tends to over- or underestimate a population parameter” (Vogt, 2005, p. 25)

3.   important because statistical tools often require certain forms of sampling or assignment

 

  1. Types of Sampling

1.    Probability Sampling

 

Probability sampling  when “each case that could be chosen has a known probability of being

included” (Vogt, 2005, p. 248)

a.       random sampling

--not to be confused with periodic or systematic sampling

Random sampling selecting data in such a way that each event “in the population has an equal chance of being chosen and . . . every combination of N members has an equal chance of being chosen” (Frankfort-Nachmias & Leon-Guerrero, 2002, p. 404)

Periodic or systematic sampling: sampling  in which events samples are taken at preset intervals (such as sampling every 10th event)

·  simple random sampling

 

Simple random sampling: identifying all members of a population and then selecting events at random from this universe of events

Random assignment: placing events in experimental and control conditions such that individuals are not “intact” groups but are chosen to receive experimental or control treatments at random

·  stratified random sampling

 

Stratified random sampling: after dividing the population into categories based on known proportions, simple random sampling is completed within each category to represent

subjects with characteristics consistent with the population proportions

b.   cluster sampling

Cluster sampling (also called “multistage cluster sampling” or “area” sampling): Groups or regions called “clusters” are identified and then, in at least two stages, a random selection is made from the groups or areas followed by a random

sampling of events from them

2.  Nonprobability Sampling

Nonprobability sampling: samples for which it is not possible to apply tools that reveal how closely the samples probably represent various population characteristics

·  Accidental or convenience sampling

 

Accidental or convenience sampling: selecting events that are easy to obtain rather than those that are representative of the population.

·  Quota sampling.

 

Quota sampling: Nonrandom sampling completed to secure events matching known proportions of types of events within the population

·  Known group sampling

 

Known group sampling (also known as “purposive sampling”): collecting “a sample composed of subjects selected deliberately (on purpose) by researchers, usually

because they think certain characteristics are typical or representative of the population” (Reinard, 2001, p. 293).

·  Snowball sampling

Snowball sampling: samples gathered from referrals from participants already in the sample

  1. Testing Sampling Adequacy

1.    Sampling Error and Confidence Intervals

 

Sampling error: the difference between the sample statistic and its corresponding population parameter

Confidence interval: “a range of values of a sample statistic that is likely (at a given level of probability, called a confidence level) to contain” (Vogt, 2005, p. 55, italics added)

2.      How Big a Sample Is Big Enough?

--for types of studies:

·  pilot studies: a sample of between 10 and 30 is recommended

·  cross-validation studies: at least 200 recommended

 

--for types of measures:

·  physiological measures: small samples (often as few as 8 events) studies

--affected by size of effect researchers wish to detect

--for types of statistics researchers wish to use

·  chi-square test of independence: no more than 20% of expected frequencies lower than 5

·  multiple regression correlation: at least 15 events for every predictor or independent variable

·  factor analysis: at least 10 events for each item included

·  multivariate analysis of variance:  42–54 events per group when comparing 3 groups; 48–62 events per group when comparing 4 groups;  54–70 events per group when comparing 5 groups;  58–76 events per group when comparing 6 groups

 

  1. Illusions in Sampling

1.    Volunteers and Nonparticipants    

 

2.    Confusing Sample Size With Representativeness