Ch 11-12
11: Correlational Research
Important ideas
- Correlational research designs and group comparison research designs have the same
purpose but involve different types of statistical analysis
- Correlational research takes into account all of the values of at least one of the variables
that have been measured in a research study
- Correlation coefficients and scattergrams provide information about both the direction
and degree of relationship between a sample’s scores on two or more measures
- The direction of relationship between 2 variables can be positive, negative, nonlinear, or
zero
- The larger the value of a correlation coefficient, the more accurate we can be in using an
individual’s score on one measure to predict his score on another measure
- To determine the statistical significance of a correlation coefficient, researchers typically
test the null hypothesis that the correlation coefficient between 2 variables in the entire
population represented by the sample is zero
- Multivariate correlational techniques show how three or more varibales relate to each
other for the purpose of either explanation or prediction
- The introduction of a correlational research report should explain the importance of the
study, its research questions or hypotheses, the variables of interest, and the review of
relevant literature
- Correlational research differs from experimental research in that the researchers do not
manipulate their independent variable
- In correlation research the researchers should attempt to select a sample that is
representative of the population to which they wish to generalize their results
- In the discussion section of a report of a CS, the researchers should summarize the
study’s findings, consider flaws in the design, and state implications of the study for
improvement
In group comparison studies, groups are formed to represent the independent variable,
dependent variable, or both
Correlational research
- Could involve forming a sample of rural schools and using their population size as one of
the variables rather than artificially putting all rural students into one category
- Could be used to determine the effect of variations in population size within suburban
communities and within urban communities
- Capable of considering all of the values of absenteeism and include them in the
statistical analysis
Continuous variable
- Denotes variables all of whose values has been measured and used by researchers
- Is one that can assume different values between points
- Ex: height: 6 feet or 6.1 feet
Discrete variables
- Has fixed values
- Family can have 2 or 3 children but not 2.4
Correlation coefficient
- A mathematical expression that provides information about the direction and magnitude
of the relationship between a samples scores on measures of two or more variables
- Range from -1.00 - +1.00
- Provides more info about the sample’s scores on the measured variable
- A CC tells us how well we can predict the score on an individual on variable y if we know
that individual’s score on variable x
- The higher the value of the correlation coefficient, either r+ or -, the better the
prediction
Scattergram / scatter plot
- Graph of the relationship between 2 variables, such as the scores of individuals on one
variable are plotted on the x axis and other variables are on the y axis
- Useful because they provide a simple, clear picture of the correlation between a group’s
scores on two variables
- Negative correlation
o When one increases, the other decreases
o Higher scores of one are linked with low scores of another
o Slopes down from the left to the right side
- Positive correlation
o Occurs when higher scores on a measure of one variable are associated with
higher scores on a measure of the other variable
Linear Correlation
- If 2 variables are correlated with each other, the correlation is linear in nature
- If the linear correlation is perfect and positive in a sample of individuals having scores on
2 variables, each increase in the score on one variable will be accompanied by an
increase in the score of the other variable
- If the linear correlation is perfect and negative, each increase in the score on one
variable will be accompanied by a decrease in the score of the other variable
Line of best fit
- The line that allows for the best prediction of an individual’s score on the y axis from
knowing her score on the x axis
Nonlinear correlation
- The variables are correlated with each other, but not in a linear manner
- Ex: physical strength and age
- Not always curvilinear
‘
curvilinear correlation
- Positive up to a point, and after than point, the correlation is negative
- The line of best fit forms a curve, such that low values of variable A are associated with
low values of variable B, medium values of variable A are associated with high levels of
variable B, and high levels of variable A are associated with low values of variable B
Bivariate correlational statistics
- Bivariate refers to the fact that the statistic indicates the magnitude of relationship
between 2 and only 2 variables
- Best known of these stastics is r, also called the Pearson product-moment correlation
coefficient
o Researchers often compute r for any two sets of scores, even if they are not
continuous scores
Dichotomous variable
- Can have only 2 values
- To express true dichotomy, it has to only have 2 possible values in reality
- Ex: high school graduation
Artificial dichotomy
- Has only 2 values because they have been created
- Ex: high-stakes poverty and low-stakes poverty
Tetrachoric correlation coefficient
- Determines whether 2 values are related to scores on another measured value
Test of statistical significance
- The likelihood that the statistical results obtained from a study is chance deviations from
the results that would have been found in it was done on the entire population that the
sample represents
Effect sizes
- Helpful in determining the practical significance of statistical results
Multivariate correlation
- Involves a statistical analysis of the relationships between three or more variables
- Types
o Canonical correlation
▪
Between set of predictor variables and a set of criterion variables
▪
Type of multiple regression used when there are multiple dependent
variables that can be viewed as different facets of an underlying factor
▪
Ex: students attitudes toward school
o Differential analysis
▪
Same for groups having different characteristics
▪
Used sometimes in prediction research
▪
Technique of using moderator variables to form subgroups when
examining the relationship between two other variables
o Discriminant analysis
▪
Type of multiple regression that enables researchers to determine how
well scores on several independent variables predict scores on a
dependent variable when those scores are in the form of categories
o Factor analysis
▪
Purpose: determine whether a set of variables reflects a smaller number
of underlying factors
▪
Examines the sample’s scores on all eight variables and determines
whether they cluster inot smaller nuber offactors based on high
correlations within each cluster
▪
Reveals an underlying structure of factors of it exists
o Hierarchical linear regression
▪
Same for different levels
o Logistic regression analysis
▪
Can be used for the same purpose as discriminant analysis, but is more
commonly used when the dependent variable is dichotomous
▪
Ex of dichotomous variables: enrolled/not enrolled in school
o Multiple regression
▪
Mathematical technique that enables researchers to determine
•
How well the scores for each of a set of measured independent
variables predict the scores on the measured dependent variable
and
•
How well the combination of scores for all the measured
independent variables predict the scores on the measured
variables
•
Math is complex and requires statistics
•
Used when scores on dependent variables are continuous
o Path analysis
▪
Casual links
o Structural equation modeling
Nesting
- Situation where a variable exists at several levels of an organizational structure
- Students are nested in the classroom and are affected by the teachers behavior
Heirarchical linear modeling
- A sophisticated statistical technique that enables researchers to determine how the
correlation between two variables is affected by different levels of nesting
- If not nesting occurs, the correlation between the varibales is robust and is not affected
by the structure.
- If nesting does occur, there is a correlation
Path analysis and structural equation modeling
- Sophisticated multivariate techniques for testing casual links among the different
variables that have been measured
- Methods for testing validity of the hypothesized casual links
- Goal is to help researchers understand causal relationships rather than to maximize
prediction of a criterion variable from some combination of independent variables
Moderator variable-
- mediates the relationship between the first two variables
Correlational Research
Introduction
- the introduction should expalain the importance of the study, the questions to be
answered, or hypotheses to be tested
- should also include a review of relevant literature so that the reader can understand
how the study is attempting to build off of existing knowledge
Prediction research
- type of investigation that involves the use of data collected at one point in time to
predict future behavior or events
DIBELS (dynamic indicators of basic early literacy skills)
- assesses oral reading fluency and accuracy
- theory underlying this is that if students have mastered lower-order reading skills, they
can advance their skills
predictor variables
- ex: oral reading fluency
- variables that are measured at one point in time and then correlated with a criterion
variable
criterion variable
- ex: reading achievement
- measured at a subsequent point in time and because it is the outcome that reasearchers
are attempting to predict
correlation matrix
- a complete correlation matrix is one that shows the correlation coefficient for all pairs of
variables that were measured
CH 11 SELF CHECK TEST
- correlational research
o can be used to explore causal relationships
- Correlational research is primarily intended for determining
o How variations in a sample’s scores on one measure are related to variations in
their scores on one or more other variables
- A correlation coefficient provides information about
o The magnitude and direction of the relationship between two variables but not
its linearity
- Inspection of a scattergram provides information about whether
o The correlation between two variables is linear or nonlinear
- As a correlation coefficient increases in size, it means that
o Scores on one variable are better able to predict scores on the other variable
- The null hypothesis in a typical correlational study states that
o The true correlation coefficient in the population represented by the research
sample is zero
- If researchers wish to determine the influence of multiple independent variables on a
single dependent variable, the appropriate statistical technique would be
o Multiple regression
- If researchers wish to determine whether the correlation between two variables is
affected by different levels of “nesting”, the appropriate statistical technique would be
o Hierarchical linear modeling
- A correlational research design can include
o Multiple predictor variables
- In their report of a correlational study, the researcher should
o Identify and discuss flaws in the study
CH 12: Experimental Research
Important ideas
- Educational fads perhaps would be less prevalent if we required rigourous experiments
testing their effectiveness before putting them into practice
- The essential feature of an experiment is an intervention by researchers and
collaborators in a particular setting
- Experiemnts typically have 4 phases
o Formation of experimental and control groups
o Initial administration of a measure of the outcome variable
o An intervention of the experimental group for a period of time and
o Second administration of a measure of the outcome variable
- Introduction section of a report of an experiment should state its importane, purposes,
and variables, and also provide a review of relevant literature
- A pretest-posttest control group experiment with randomization has 3 features
o At least 2 groups with each one receiving different interventions or one receiving
no intervention
o Random assignment of individuals in the sample to the different intervention or
no intervention conditions and
o Administration of one or more pretests and posttests
- In a pretest posttest control group ex., statistical adjustments can be made to control for
preexisting differences between the experimental and control groups on pretest
measures
- Of the various quantitative research designs, experiments have the strongest
implications for practice, especially if they are conducted in a real-life setting
- If random assignment is not possible, a quasi-experiment is a viable option, especially if
the experimental and control groups can be matched on critical variables that might
affect the posttest variables
- Factorial experiments enable researchers to determine whether each of several
independent variables has an effort on the dependent variable and also whether a
particular independent variable has an effectonly under certain conditions
- An experimental is internally valid to the extend that extraneous factors can be ruled out
as possible causes of observed differences between the experimental and control groups
on an outcome variable
- The extraneous factors commonly considered to be threats to the internal validity of an
experiment in education are history, maturation, testing, instrumentation, statistical
regression, differential selection, selection-maturation interaction, and experimental
mortality
- An experimental loses value if treatment fidelity departs from the researchers
specifications for each treatment condition or if the treatment lacks sufficient potency
- An experiment is externally valid to the extent that the results of an experiment can be
generalized to other individuals, settings, and time periods
- Single case experiments involve the application of an intervention to a single individual
or a few, wheras group experiments involve the application of an intervention to a
substantial sample of individuals or groups
- Typical features of a single case experiment are baseline and treatment conditions,
behavior analysis, focus on low incidence populations, detailed descriptions of each
research participant, repeated administration of one measure, and graphical
presentation of data
What Works Clearinghouse
- Highlights the innovative programs whose effectiveness has been demonstrated by
experiments
Experiment
- An empirical study in which researchers manipulate one variable to determine its effect
on another variable
Experimental condition
- Situation where a group of research participants receives an intervention to determine
its effect on the dependent variable
Control Condition
- A situation where a group of research participants receives no intervention or an
alternative intervention, against whose performance the experimental group’s
performance
Randomized trials or randomized control trials
- Experiments but unlike small scale experiments conducted underlaboratory like
conditions, they typically are large-scale, well funded, and conducted in real life settings
- Involve an intervention addressing outcomes that are important to the general public
and random assignment of individuals or groups to the experimental and control
conditions
- Used in medicine
- Often called the gold standard
Random assignment
- Each participant has an equal chance of being in either group
Pretest
- A measure that is used to determine whether the experimental and control groups are
similar on the variable that the intervention is designed to affect
Posttest
- A measure that is administered at the end of the intervention same measure as the
pretest
Group experiments
- Experiments that involve samples of research participants, 10 or more in each
experimental condition
Quasi-experiment
- An experiment with experimental and control groups but without random assignment of
participants to these groups
Factor
- Has the same meaning as the term independent variable
- Each factor is viewed as an independent variable that exists prior to the dependent
variable measured by the posttest and therefore possibly having a causal influence on
that variable
Factorial experiment
- Used to refer to an experiment having more than one factor
Interaction effect
- An independent variable has an effect on the dependent variable but only under certain
conditions
Extraneous variable
- Factor other than the treatment variable that might have an effect on the outcome of
the variable.
Internal validity
- The observed differences between experimental and control groups on an outcome
variable are solely attributable to the treatment variables
History effect
- When events influence the outcome variables
Maturation effect
- If developmental changes affect the outcome variables in an experiment
Soloman 4 group experiment
- If administration of a pretest affects posttest scoes, the two groups that took the pretest
but didn’t participate in the experimental or control condition will show a significant
change fro their pretest scores
Testing effect
- Repeated administration of a test affects the outcome
Instrumental phenomenon
- If changes in the measuring instrument affect the results of an experiment
Statistical regression
- Whenever a pretest posttest procedure is used
Differential selection effect
- If the different intial characteristics of the selected groups affect the outcome variable
Selection maturation interaction effect
- When the experimental group made significantly greater achievements than the control
group
- Researchers cant answer the question of the effects
Experiment mortality
- Attrition
- The loss of research participants over the course of the experimental treatment
Treatment fidelity
- The extent to which the experimental intervention is implemented according to the
specifications of the researcher
- Ineffective because it was implemented haphazardly
Hawthorne effect
- An improvement in the experimental group’s performance because of the special
attention thatthey have received from the researchers
External validity
- When results can be generalized to other individuals, settings, and time
Population validty
- When results can be generalized from the study to the population it was drawn
Ecological validity
- The degree to which an experimental result can be generalized to settings other than the
one studied
Single case experiment
- Aka single subject experiment or time series experiment
- Research study in which the effect of an intervention on a dependent variable is
determined by applying that intervention to a single individual or more than one
individual treated as a single group
Behavior analysis
- Involves careful observation of an individual in a setting, determination of dysfunctional
behaviors in that setting, and specification of desired behaviors
Behavior modification
- Techniques such as reinforcement, modeling, and discrimination training to increase or
decrease the frequency of behaviors
Baseline condition
- The set of typical conditions under which the research participant behaves
- Designated as A
treatment condition
- The set of conditions that represent the experimental intervention
- Esignated as B
ABA research design
- Includes an initial period of time during which the research participant is observed
under typical conditions
ABAB research design
- Involesone more phase: reinstatement of the experimental intervention
- Behavior change occurs after the intervention b
- Return the the behavior after intervention is stopped
- Includes a reversal phase
o A second condition a is used to demonstrate active control of the target behavior
by removing the intervention that is hypothesized to have cause the initial
change
Multiple baseline research design
- Includes situations other than the naturally occurring condition as a control for
determining the presence of intervention effects
CH 12 SELF CHECK TEST
- Unlike group comparison and correlational research designs, experiments
o Introduce an intervention into a laboratory or real-life situation
- The pretest posttest control group experiment with randomization
o Is generally regarded as the most powerful of the experimental designs
- In a pretest posttest control group experiment with randomization,
o The variables measured by the pretest and the experimental intervention are
independent variables
- The statistical significance of group differences found in a pretst posttest control group
experiment with randomization can be determined by
o Analysis of variance
o Analysis of covariance
o Multiple regression
- A quasi-experimental research does not include
o Random assignment of research participants to the experimental and control
conditions
- Statistical regression is likely to occur if
o The research participants score very high or low on the pretest
- An experiment has treatment fidelity of
o The experimental treatment is implemented according to its developers
specifications
- All of the following are threats to the external validity of experiments except
o Selection-maturation interactions
o *these are threats
▪
lack of population validty and ecological validity
▪
interaction between personal characteristics of the research sample and
the experimental intervention
- the baseline condition in a single case experiment
o is the set of typical conditions under which a research participant behaves
- a typical single case experiment
o has multiple administrations of the same measure, each measuring the same
dependent variable
