Chapter 1: Introduction C ap e oduc oto Statistics
St ti ti S i d Ob tiStatistics, Science, and Observations
• Definition: The term statistics refers to a set of mathematical procedures for organizing, summarizing, and interpreting information.
• Statistics serve four general purposes:
– Statistics are used to organize and summarize the information so that the researcher can see what happened in the research study and can communicate the results to others.
– Statistics help the researcher to answer the general questions that initiated the research by determining exactly what conclusions are justified based on the
l h b i dresults that were obtained.
Statistics, Science, and Observations , ,cont.
– Statistical procedures help ensure that the information or observations are presented and interpreted in an accurate and informative way.
– In addition, statistics provide researchers with a set of standardized techniques that are recognized and understood h h h fthroughout the scientific community.
P l ti d S lPopulations and Samples
• Definition: A population is the set of all the individuals/units of interest in a particular study.
• Definition: A sample is a set of individuals selected from a population, usually intended to represent the population in a research study.
V i blVariables
• Definition: A variable is a characteristic or condition that can change or take on different values.
• Definition: Data (plural) are measurements or observations. – A data set is a collection of
measurements or observations. – A datum (singular) is a single
measurement or observation and is commonly called a score or raw score.
P t d St ti tiParameters and Statistics
• When describing data it is necessary to distinguish whether the data come from a population or a sample.
• A characteristic that describes a population for example, the population average, is called a parameter.
• On the other hand, a characteristic that describes a sample is called a statistic.
– Thus, the average score for a sample is an example of a statistic.
• Typically, the research process begins with a question about a population parameter.
• However, the actual data come from a sample pand are used to compute sample statistics.
Descriptive and Inferential Statistical pMethods• Definition: Descriptive statistics are statistical
procedures used to summarize, organize, and simplify data.
• Definition: Inferential statistics consist of techniques that allow us to study samples and then make generalizations about the populations from which they were selected.
• Definition: Sampling error is the discrepancy, or amount of error, that exists between a sample statistic and the corresponding
l ipopulation parameter.
S hStatistics in the Context of R hResearch (Example 1.1)
Data Structures, Research Methods, and , ,Statistics• Most research is intended to examine the
relationship between two or more variables.
• To establish the existence of a relationship, researchers must make observations-that is, measurements of the variables under study.
• The resulting measurements can be classified into two distinct data structures that also help to classify different research methods and different statistical techniques.
• In the following section (next couple of slides) we identify and discuss these two data structures.
Data Structures, Research Methods, and , ,Statistics cont.
– (1) Measuring two variables for each individual: The Correlational Method
• In the correlational method, two different variables are observed to determine whether there is a relationship between them.
• Occasionally, the correlational method produces scores that are not numerical values.
• This type of data is typically summarized in a table showing how many individuals are classified into each of the possible categories.
• Table 1.1 shows an example of this kind of summary table.
Data Structures, Research Methods, and , ,Statistics cont.
• The relationship between variables for non-numerical data, such as the data in Table 1.1, is evaluated using a statistical technique known as a chi-
(Chsquare test. (Chi-square tests are presented in Chapter 18. )
• The results from a correlational study d h fcan demonstrate the existence of a
relationship between two variables, but they do not provide an explanation for the relationshipexplanation for the relationship.
• In particular, a correlational study cannot demonstrate a cause-and-effect relationshipeffect relationship.
Data Structures, Research Methods, and , ,Statistics cont.
• To demonstrate a cause-and-effect relationship between two variables, researchers must use the experimental method, which is d d hdiscussed in the next section.
– (2) Comparing two (or more) groups of scores: The Experimental Method and
l h dnon-experimental methods
• The goal of an experimental study is to demonstrate a cause-and-effect
l i hi b i blrelationship between two variables.
Th E i t l M th dThe Experimental Method
• Specifically, an experiment attempts to show that changing the value of one variable will cause changes to occur in the second variable.
• To accomplish this goal, the experimental method has two characteristics that differentiate experiments from other types of
h dresearch studies:
– Manipulation: The researcher manipulates one variable by changing its value from
l l hone level to another.
– A second variable is observed (measured) to determine whether the manipulation
hcauses changes to occur.
Th E i t l M th d tThe Experimental Method cont.
– Control: The researcher must exercise control over the research situation to ensure that other, extraneous variables do not influence the relationship being
dexamined.
• There are two general categories of variables that researchers must consider:
– Participant Variables: These are characteristics such as age, gender, and intelligence that vary from one individual
hto another.
– Environmental Variables: These are characteristics of the environment such as li h i i f d d hlighting, time of day, and weather conditions.
Th E i t l M th d tThe Experimental Method cont.
• Researchers typically use one of the three basic techniques to control other variables:
– Random assignment
– Matchingg
– Holding them constant
• The Seven Factors Needed for a Classic Experimental DesignExperimental Design
– Independent variable
– Dependent variable
C l di i /– Control condition /group
– Experimental condition /group
– Random assignment
– Pre-test
– Post-test
Oth T f St diOther Types of Studies• Other types of research studies, known as
non-experimental or quasi-experimental, are similar to experiments because they also compare groups of scores.
• These studies do not use a manipulated ariable to differentiate the gro psvariable to differentiate the groups.
• Instead, the variable that differentiates the groups is usually a pre-existing participant variable (such as male/female) or a timevariable (such as male/female) or a time variable (such as before/after).
• Because these studies do not use the manipulation and control of true experiments, they cannot demonstrate cause and effect relationships.
• As a result, they are similar to correlational research because they simply demonstrate andresearch because they simply demonstrate and describe relationships.
V i bl d M tVariables and Measurement
• Constructs and Operational Definitions
– Constructs are internal attributes or characteristics that cannot be directly observed but are useful for describing and explaining behavior.
– An operational definition identifies a measurement procedure (a set of operations) for measuring an external behavior and uses the resulting measurements as a definition and a
f h h i lmeasurement of a hypothetical construct.
Di t d C ti V i blDiscrete and Continuous Variables• Definition: A discrete variable consists of
separate indivisible categoriesseparate, indivisible categories.
• Thus, no values can exist between two neighboring categories.
Di t i bl l– Discrete variables are commonly restricted to whole countable numbers.
• For example, the number of children i f il th b f t d tin a family or the number of students attending class.
– A discrete variable may also consist of b ti th t diff lit ti lobservations that differ qualitatively.
• For example, a psychologist observing patients may classify some
h i i di d thas having panic disorders, others as having dissociative disorders, and some as having psychotic disorders
Di t d C ti V i bl tDiscrete and Continuous Variables cont.
• Definition: For a continuous variable, there are an infinite number of possible values that fall between any two observed values.
• In other words, a continuous variable is divisible into an infinite number of fractional parts.
• Two other factors apply to continuous variables:
– When measuring a continuous variable, it should be very rare to obtain identical measurements for two different individuals. Because a continuous variable has an infinite number of possible values, i h ld b l i ibl fit should be almost impossible for two people to have exactly the same score.
Di t d C ti V i bl tDiscrete and Continuous Variables cont.
• When measuring a continuous variable, each measurement category is actually an interval that must be defined by boundaries called “real limits”. (upper real limit and lower real l )limit).
S l f M tScales of Measurement
• Nominal: A nominal scale consists of a set of categories that have different names.
– Measurements on a nominal scale label and categorize observations, but do not make any quantitative distinctions between observations.
• Ordinal: An ordinal scale consists of a set of categories that are organized in an ordered sequence.
– Measurements on an ordinal scale rank observations in terms of size or magnitude.
S l f M t tScales of Measurement cont.
• Interval: An interval scale consists of ordered categories that are all intervals of exactly the same size.
– Equal differences between numbers on scale reflect equal differences in magnitude.
– However, the zero point on an interval scale is arbitrary and does not indicate a zero amount of the variable being measured.
• Ratio: A ratio scale is an interval scale with the additional feature of an absolute zero point.
– With a ratio scale, ratios of numbers do reflect ratios of magnitude.
O d f M th ti l O tiOrder of Mathematical Operations
• Any calculation contained within parentheses is done first.
• Squaring (or raising to other exponents) is done second.
• Multiplying and/or dividing is done third.
– A series of multiplication and/or division operations should be done in order from pleft to right.
• Summation using the ∑ notation is done next.
• Finally, any other addition and/or subtraction is done.