Statistics

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Independent Variable

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A variable that is believed to affect or alter status on another variable (the dependent variable)

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Dependent Variable

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A variable whose status depends on the status of another variable (the independent variable)

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True experimental research

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Having the control necessary to conclude that observed variability in a dependent variable is actually caused by variability in an independent variable.

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What is important for experimental research?

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To have RANDOM ASSIGNMENT of subjects to groups

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Quasi-experimental research

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An investigator cannot control the assignment of subjects to treatment groups but, instead must use intact (pre-existing) groups or a single treatment group.

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Simple random sampling

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Every member of the population being studied (e.g., ADHD kids) has an equal chance of being included in the sample

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Stratified random sampling

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Dividing the population into the appropriate strata (e.g., age, gender, education level, etc.) and randomly selecting subjects from each stratum.

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Cluster sampling

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Entails selecting units (clusters) of individuals rather than individuals and either including all individuals in those units in the research study or randomly selecting individuals from each unit (the latter technique is called multistaging cluster sampling).

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When is cluster sampling useful?

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When it is not possible to identify or obtain access to the entire population of interest.

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Why is random selection important?

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Because is allows the investigator to generalize his/her findings from the sample to the population.

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What are the 3 factors that can cause variability in teh study's dependent variable?

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1. Independent variable (experimental variance)
2. Systematic error (errors due to extraneous variables)
3. Random error (error due to random fluctuations in subjects, experimental conditions, methods of measurement, etc.)

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Extraneous (confounding) variable

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This is a source of SYSTEMATIC ERROR.

It is a variable that is irrelevant ot the purpose of the study, but confounds its results because it has a systematic effec on (correlates with) the DV.

E.g., symptoms severity may confound effects seen on self-control procedures for achievement in ADHD kids. Don't know if symptoms severity or self-control measures affected achievement.

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What are some techniques used to control the effects of extraneous variable?

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1. Random assignment (randomization)
2. Holding the extraneous variable constant
3. Matching subjects on the extraneous variable
4. Building the extraneous variable into the study (Blocking)
5. Statistical control of the extraneous variable

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Random assignment (randomization)

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It helps to equalize the effects of all known and unknonwn extraneous variables. It is considered the most "powerful" method of experimental control.

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Holding the extraneous variable constant

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You can eliminate the effects of an extraneous variable by slecting subjects who are homogeneous with respect to that variability. However, this limits the generalizability of the research results.

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Matching subjects on the extraneous variable

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Match subjects in terms of their status on the extraneous variable and then randoml assign matched subjects to one fo the treatment groups.

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Building the extraneous variable into the study (Blocking)

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Include it in the study so that its effects on the DV can be statistically analyzed.

E.g., block kids by symptom severity and then randomly assign kids in each block to either the experimental or control group.

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Statistical control of the extraneous variable

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Can use an anlaysis of covariance (ANCOVA) or other statistical technique to remove variability in the DV that is due to the extraneous variable.

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Internal validity

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Allows an investigator to determine if there is a causal relationship between the IV and DV.

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When is internal validity threatened?

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When the 3 sources of variability (experimental variance [want to max], systematic error, & random error) can not be controlled.

If can't max effects of IV and contol effects of extraneous variables and/or min effects of random error, can't be certain whether observed variability (or lack of variability) in the DV is due to the IV or some other factor.

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What are some threats to internal validity?

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1. Maturation
2. History
3. Testing
4. Instrumentation
5. Statistical regression
6. Selection
7. Attrition (Mortality)
8. Interactions with selection

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Maturation (threat to internal validity)

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Refers to any biological or psychological change that occurs within subjects during the course of a study (e.g., fatigue, boredom, hunger, physical/intellectual growth)

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What is the best way to control for maturation?

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To include more than one group in the study and randomly assign subjects to groups.

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History (threat to internal validity)

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An external event that systematically affects the status of subjects on the DV.

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What is the best way to control for history?

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Include more than one group in the study and randomly assign subjects to groups.

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Testing (a threat to internal validity)

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When a test is readministered

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What is the best way to control for testing?

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To administer the DV measure only once, by designing the measure in a way that minimizes memory and practice effects, or by including at least two groups in the study.

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Instrumentation (a threat to internal validity)

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Changes in the accuracy or sensitivity of measuring devices can confound results (e.g., a rater's accuracy improving over time).

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Statistical regression (a threat to internal validity)

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The tendency of extreme scores on a measure to "regress" toward the mean.

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Selection (a threat to internal validity)

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When the method used to assign subjects to treatment groups results in systematic differences between the groups at the beginning of the study.

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What is the best way to control for selection?

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Randomly assign subjects to groups, or when not possible to randomly assign, administer a pretest to determine if groups differ initially with regard to the DV.

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Attrition (a threat to internal validity)

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When subjects who drop out of one group differ in an important way from subjects who drop out of another group.

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Interactions with selection (a threat to internal validity)

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When groups are inititially nonequivalent, selection can act alone and/or can interact with other factors to threaten internal validity.

E.g., Interaction b/t selection and history - when one group of subjects is unintentionally exposed to an external event that does not affect subjects in the other groups.

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External validity

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When findings from a research study can be generalized to other people.

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A study's external validity is ALWAYS limited by its internal validity.

TRUE or FALSE

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TRUE

If you can't conclude that there is a causal relationship b/t variables then you can't generalize findings.

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A high degree of internal validity GUARANTEES external validity.

TRUE or FALSE

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FALSE

A relationship b/t variables might exist for the conditions in which the study was conducted or the particular people who participated in the study, but it cannot be generalized to other conditions or to other people.

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What are threats to external validity?

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1. Interaction between testing and treatment.
2. Interaction between selection and treatment.
3. Reactivity (Reactive arrangements)
4. Multiple treatment interference (order effects, carryover effects)

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Interaction between testing and treatment (a threat to external validity)

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The administration of a pretest can "sensitize" subjects to the purpose of the research study and thereby alter their reaction to the IV.

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What is the best way to control for "interaction between testing and treatment?"

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1. Don't administer a pre-test
2. Use a Solomon 4-group design, which enables a researcher to measure the impact of pretesting on both the external and interal validity of the study. In this way the pre-test is treated as an additional IV so that its effects on the DV can be statistically analyzed.

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Interaction between selection and treatement (a threat to external validity)

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Subjects included in a research study can have characteristics that make them respond to the IV in a particular way, making it difficult to generalize the results to people who don't have these characteristics (e.g., volunteers tend to be more motivated)

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Reactivity (a threat to external validity)

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Subjects can respond to an IV in a particular way simply because they know their behavior is being observed.

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What are some other phenomena that are included under reactivity?

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1. Evaluation apprehension - causes subjects to act in ways they believe will help them avoid negative evaluations
2. Demand characteristics - cues in the experimental setting that inform subjects of the purpose of the study or suggest what behaviors are expected of them
3. Experimenter expectancy - unintentially providing subjects with cues that let them know what behavior is expected or can act in ways that do not affect subjects directly but bias the results of the study.

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What are some ways to control for reactivity?

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Use:
1. Deception
2. Unobtrustive (nonreactive) measures
3. Single- or double-blind study

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Multiple treatment interference (a threat to external validity)

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When using a within-subjects design, in which a person is exposed to multiple levels of treatmen(IV), the effects of one level of IV may affect response to other levels

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What is the best way to control for multiple treatment interference?

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Counterbalanced designs - different subjects receive the levels of the IV in a different order.

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What is a Latin Square Design?

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It is a counterbalanced design that involves administering each level of the IV so taht it appears the same number of times in each position (1st, 2nd, 3rd, etc.)

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What are the two basic types of research designs?

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1. Group designs
2. Single-subject designs

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What are the 3 kinds of Group Designs?

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1. Between-subjects
2. Within-subjects
3. Mixed

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What is a factorial design?

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When a study includes two or more IVs.

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What is an advantage of factorial designs?

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It allows one to analyze the main effects of each IV and the interaction between the IVs.

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What is a main effect?

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The effect of one IV on the DV, disregarding the effects of all other IVs.

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What is an interaction effect?

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When the effects of two or more IVs are considered together.

An interaction effect occurs when the effects of an IV differ at different levels of another IV.

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What is a within-subjects (repeated measures) design?

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When all levels of the IV are administered sequentially to all subjects.

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What is a single-group time series design?

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When the effects of a treatment (IV) are evaluated by measuring the DV several times at regular intervals both before and after the treatment is applied.

This allows subjects to act as their own "no-treatment" control.

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What is a disadvantage to the single-group time series design?

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Internal validity is threatened by history. An external event could occur at about the same time as the IV and counfound results.

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What is the disadvantage of a within-subjects design in which 2 or more levels of the IV are applied sequentially to each subject?

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Carryover effects

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What is a mixed design?

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It combines between-groups and within-subjects methodologies.

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What are the two characteristics that distinguish single-subject designs from group designs?

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1. Each single-subject design inlcudes at least one baseline (no treatment) phase and one treatment phase. This way each subject acts as their own control.

2. The DV is measured repeatedly at regular intervals throughout the baseline and treatment phases. This helps to control of maturational effects.

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What is a reversal design?

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ABA, ABAB, etc.

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What is the advantage of a reversal design over an AB design?

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It leads to greater certainty that observed changes in the DV is due to the IV rather than to an historical event or other extraneous factor.

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What is a multiple baseline design?

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It involves sequentially applying the treatment either:
1. to different behaviors of the same subject
2. to the same subject in different settings
3. to the same behavior of different subjects

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What are the two types of statistical methods?

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1. Descriptive
2. Inferential

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Descriptive Statistics

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Used to describe and summarize the data collected on a variable or the relationship b/t variables.

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Inferential Statistics

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Used to determine if obtained sample values can be generalized to the populaltion from with the sample was drawn.

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Nominal Scale

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Divides variables into unordered categories.

E.g., gender, religion, political affiliation, place of birth, eye color, DSM diagnosis, etc.

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Ordinal Scale

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Divides observations into categories and provides information regarding the order of those categories.

When using, it is possible to say that one person has more or less of the characteristic being measured than another person.

E.g., ranks, Likert-scale scores

They do not, however, tell HOW MUCH difference there is between scores.

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Interval Scale

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It has the property of order as well as the property of equal intervals b/t successive points on the measurement scale.

E.g., IQ test scores; the interval between scores 90 and 90 is equal to the interval b/t 100 and 105.

This makes it possible to perform mathematical operations of addition and subtraction.

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Ratio Scale

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It has the properties of order, equal intervals, and an absolute zero point. This makes it possible to multiply and divide ratio scores and to determin more preciesly how much more or less of a characteristic one person has compared to another.

E.g., temperature on a Kelvin scale, number of calories consumed, number of correct items on a test, and reaction time in seconds

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Descriptive techniques include:

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1. Tables
2. Frequency distributions
3. Frequency polygons
4. Measures of central tendency
5. Measures of variability

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What is a frequency polygon?

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A graph of ordinal, interval, or ratio scales.

The scores are recorded on the horizontal axis, while the frequencies are recorded on the vertical axis.

When a sufficiently large number of observations are made, the date for amny variables take the shape of a Normal Curve.

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Kurtosis

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Refers to the relative peakedness (height or flatness) of a distribution.

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Leptokurtic

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When a distribution is more "peaked" than the normal distribution.

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Platykurtic

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When a distribution is flatter than the normal distribution.

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Mesokurtic

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A normal curve.

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Skewed distribution

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When distributions are asymmetrical. More than 1/2 of the observations fall on one side of the distribution and a relatively few observations fall in the tail on the other side of the distribution.

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Positively skewed distribution

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When most of the scores are in the negative (low) side of the distribution and the tail is in the positive direction.

"It is the tail that tells the tale."

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Negatively skewed distribution

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When most of the scores are in the positive(high) side of the distribution and the tail is in the negative direction.

"It is the tail that tells the tale."

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What are measures of central tendency?

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1. Mode
2. Median
3. Mean

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What is the disadvantage of Mode?

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1. It is very susceptible to sampling fluctuations
2. Any one sample might not provide an accurate estimate of the population mode
3. It is not useful for other statistical purposes and serves only as a descriptive technique

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What is the advantage of Median?

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It is not affected by one or a few extreme scores.

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What is a disadvantage of the Median?

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Like Mode, its use in ohter quantitative procedures is limited, and it serves primarily as a descriptive statistic.

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What are the advantages of using Mean?

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1. It is the least susceptible to sampling fluctuations.
2. It can be used in a number of statistical procedures

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What is the disadvantage of using Mean?

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It is affected by the magnitude of every score in the distribution; therefore, when the distribution is skewed, the mean can be misleading.

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What does a measure of variability tell us?

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It indicates the amount of heterogeneity or dispersion within a set of scores.

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What are measures of variability?

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1. Range
2. Variance
3. Standard deviation

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What is Variance?

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Sum(X-M)2/N-1

It is the "mean of the squared deviation score"

It provides a measure of the average amount of variability in a distribution by indicating the degree to which the scores are dispersed around the distribution mean.

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What is a standard deviation?

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Square root of Sum(X-M)2/n-1

Because calculation of the variance requires squaring each deviation score, the variance represents a unit of measurement that differes from the original unit of measurement. Therefore, the standard deviation is more often used as a measure of variability.

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Sampling distribution of the mean

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The distribution of mean scores for mutiple samples of subjects.

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Do researchers actually conduct studies to determine the sampling distribution of the mean?

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No, they depend on probability theory to tell them what a sampling distribution would look like (a.k.a. a theoretical sampling distribution), which is based on the assumption that an infinite number of equal-sized samples have been randomly drawn from the same population.

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Central Limit Theorem

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Makes the following predictions:

1. Regardless of the shape of the distribution of individual scores in the population, as teh sample size increases, the sampling distribution of the mean approaches a normal distribution.

2. The mean of the sampling distribution of the mean is equal to the population mean.

3. The standard deviation of the sampling distribution of the mean is equal to the population standard deviation divided by the square root of the sample size (a.k.a. Standard Error of the Mean)

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Standard Error of the Mean

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It provide an estimate of the extent to which the mean of any one sample randomly drawn from a population can be expected to vary from the population mean as the result of sampling error.