NCE – “Research & Program Evaluation”

What is Research & Why is it important?

ACA Ethics states that counselors have a responsibility to entrance the profession VIA research.  The object of research is to produce findings that can be replicated by others using the same methods.  There are two types of research.  Basic research contributes to a theory whereas applied research addresses real-world problems.  Cozby (2009) states that “scientific research has four general goals: (1) to describe behavior, (2) to predict behavior, (3) to determine the causes of behavior, and (4) to understand or explain brehavior” (p. 7).

  1. Basic Research – contributes to theory development.  “Basic research tries to answer fundamental questions about thenature of behavior.  Studies are often designed to address theoretical isssues concerning phenomenta such as cognition, motivation…” (Cozby, 2009, p. 10).
  2. Applied Research – Solves a real-world problem.  “Applied Research is conducted to address issues in which there are practical problems and practical solutions” (Cozby, 2009, p. 10).

In other words, basic research is guided by theory, and applied research is guided by a research investigation (Cozby, 2009).  If an experiment can be replicated it is said to be reliable.    Psychoeducational research is based on the principle of simplicity (K.I.S.S).  Parsimony is a term which means that findings should be interpreted in the simplest manner possible.  Occam’s Razor states that the simplest explanation is usually the best.

Experimental Method

What is the Experimental Method?

Experiments are the most common type of research. They are conducted in a laboratory or other highly controlled settings allowing for management of all relevant variables. The experimental method involves direct manipulation and control variables.  The researcher manipulates the first variable of interest (I.V.) and then observes the response (D.V).  In the experimental method, the researcher has control of all relevant variables.  In order to increase the accuracy of results it is important to keep out all undesirable variables. These variables are called extraneous and reduce opportunity for confounding (not accurate) of results.

  1. Extraneous/Confounding variables – cause confounding in experiment & increase the accuracy of results in your research.  It can varies along with the independent variable and make it determine how much the independent variable affects the dependent variable (Cozby, 2009).
  2. (Example of an Experimental Design)  Counterbalancing is a type of experimental design in which all possible orders of presenting the variables are included. For example, if you have two groups of participants (group 1 and group 2) and two levels of an independent variable (level 1 and level 2), you would present one possible order (group 1 gets level 1 while group 2 gets level 2) first and then present the opposite order (group 1 gets level 2 while group 2 gets level 1). This way you can measure the effects in all possible situations.

What are Variables?

“A variable is any event, situation, behavior, or individual characteristic that varies….Variables represent a general class within which specific instances can vary.  These specific instances are called levels or values.  A variable must have two or more variables….numeric or quantitative” (Cozby, 2009, p. 66).

Four General Categories of Variables…

“Situational variables describe characteristics of the situation…response variables are the responses…of individuals…subject variables…are the characteristics of individuals…mediating variables are psychological processes that mediate the effects of a situational variable on a particular response” (Cozby, 2009, p. 66).

Operational Definitions of Variables…

The operational definition of a variable defines the manner in which a researcher intends to manipulate and/or measure a variable (Cozby, 2009).   For example stress is a general variable.  A specific operational definition of it might be pulse rate.

Independent vs. Dependent Variables….

Variables in research are conceptualized in some sort of cause-and-effect fashion (Cozby, 2009).  The Independent variable is the cause and the dependent variable is the effect.   WHAT IS THE IMPACT OF BLANK(IV) on BLANK(DV)

  1. Independent (IV) – experimenter manipulates this variable in order to assess its effects on the dependent variable.  Two types of independent variables are organismic & manipulated (see below).
    *Organismic – height, race, etc.
    *Manipulated – Researcher’s can alter willingly.
  2. Dependent (DV) – The dependent variable are the results of “Data/Scores” experimenter measures. If a causal relationship exists then various levels of the independent variable will influence the dependent variable data or scores.   It is always a form of human response…
  3. Parameter vs. Value –Parameters are numbers that summarize data for an entire population. Statistics are numbers that summarize data from a sample, i.e. some subset of the entire population.

Two Key Characteristics of Experiments…

As stated earlier, there are two characteristics that define a true experiment: (1) experimental control of all extraneous variables and (2) random sampling to reduce chance of research bias.  Below are various terms reviewed by Rosenthal (2005).

  1. Control Group – Not experimented upon, don’t receive the independent variable.
  2. Experimental Group – are experimented upon and receive independent variable.  Occasionally, there is more than one experimental group if more than one independent variable exists –  (6 weeks of REBT vs. 8 weeks of REBT)
  3. Random Sampling – used when assigning subjects to control and experimental groups.  It is useful in avoiding sampling bias and “keeps the researcher honest” (Rosenthal, 2005).  Every member of the population has an equal probability of being selected for the study.  The selection of one number doesn’t effect selection of another.  However there is one more step.
  4. Random Assignments – Random Selection of subjects not enough alone. You must also randomly assign as well to experimental and control groups.  Random Selection & Assignment, are both required for true randomness….

Quasi-experimental Research…

Key Characteristics of Quasi-Experimental Research

True Experiments are rare in social sciences.  The term quasi-experimental research is a study in which subjects or clients cannot be randomly assigned to groups.  Research that fails to use random assignments or lacks a control group, will be considered a quasi-experiment.  If there are intact groups, it is quasi-experimental.  Need to be careful with interpretation and apply results to the specific population sample.

  1. No Random Assignment

  2. No control Group

  3. Intact Groups Studies.

Sampling Methods used in Quasi-Experimental Studies…

“Some researchers use what is called stratified sample in which persons from subgroups (a.k.a strata) are sellected.  An even more precise method is proportional stratified sampling in which the sample mimics the general population” (Rosenthal, 2005)….. Cluster sampling utilizes a naturally existing group (i.e. high school students, residents of a nursing home, etc).  Nth or Kth sampling involves picking the every tenth person from your population.

  1. Stratified Sample Persons from certain social groups or strata are studied.
  2. Proportional Stratified Sample – Sample designed to mimic the general population.
  3. Cluster Sampling – use a naturally existing group (client’s at treatment center) and randomly select from there.
  4. Nth Sampling (AKA Systematic or K’th Sampling) – involves picking every 10th person from the population.   

Random vs. Systematic Sampling….

What is the Goal of Sampling…

Which is better?  “From an empirical standpoint, the results in most experiments seem to be similar no matter which method you use…..many researchers are turning to systematic sampling since it is easier” (Rosehtnal, 2008).  “The representativeness of the sample is more important than the procedure used to acquire the subjects”  

Initial Considerations….

When starting a research project there are several things to consider;  FIRSTLY, you need to define the speciic population of interest from which you choose to draw your sample.  SECOND, in order to make inferencesabout a population from the research you need to determine a level of confidence (i.e. confidence interval/or sampling error).  THIRDLY, you need to determine your sample size.

Probability Sampling

All sampling methods discussed previously are called probability samples.  Probability samples are based on probability theory, which analyzes uncertain events with the goal of developing statements regarding the likelihood of occurrence. Sampling methods discussed previously are an excellent example.  “In probability sampling each member of the population has a specifiable probability of being chosen….is very important when you want to make spefici statements about a specific population.” (Cozby, 2008, p. 138).

  1. Simple Random Sampling – every member of pop has equal probability to be selected…computer program randomly chooses 100 students from list of all 10,000 students at College X” (Cozby, 2008, p. 140-141).
  2. Stratified Random Sampling – “The population is divided into subgroups and random sampling techniques are used to select sample members from each stratum…Names of all 10,000 college X students are sorted by major…” Cozby, 2008, p. 140-141).
  3. Cluster Sampling – “Two hundred clusters of psychology majors are identified at schools all over the U.S. out of these 200 clusters, 10 clusters are chosen randomly” (Cozby, 2008, p. 141).

Nonprobability Sampling

Not based on probability theory.  “In nonprobability sampling, we dont know the probability of any particular member of the population being chosen…are quite arbitrary.  A population may be defined, but little effort is expentded to ensure that the sample accurately represents the population…cheap and convenient” (Cozby, 2008, p. 139).

  1. Judgment Sample – relies on judgment of the researcher to use subjects not representative of the population.  Cozby (2008) mentions a purposive smampling that simply adheres to the selection of people who fit a specific criteria…
  2. Convenience Sampling – an intact group is used without randomness in the selection process.  “Ask students around you at lunch tor in class to participate” (Cozby, 2008, p. 141).
  3. Quota Sample – subjects have pre-specified characteristics so that sample mimics what exists in population …”Collect specific proportions of data representative of percentages of groups within the population” (Cozby, 2008, p. 141).

Hypothesis

Starting with a Definition…

When researcher begins experiment, he/she begins with a hunch (or hypothesis).  “The motivation to conduct scientific research derives from a natural curiosity about the world” (Cozby, 2008, p. 17).  In order to this, researchers develop hypotheses.

  1. Hypothesis = “…a type of idea or question, [that] makes a statement about something that may be true…a tentative idea…Once the hypothesis is proposed, data must be gathered and evluated in terms of whether the evidence [supports it]” (Cozby, 2008, p. 17).
  2. Operational Definitionoperationally define a variable into a measurable form that allows for easy replication for researchers.

Each experiment has a minimum of two hypotheses.

    1. Null Hypothesis – Pnedicts no relationship between IV & DV (H0 = Null Hypothesis)
    2. Experimental Hypothesis – the hunch or predicted relationship between the DV & IV.   Each predicted outcome can then be indicated as follows (HH2)
    3. Alternative / Affirmative Hypothesis – alternative hynch that also describes how IV causes a change in the DV (Ha)

New Terminology…

“TEST HINT: As of late a new term is popping up called the modern form of describing a hypothesis. In the modern form, the hypotehsis is written in present tense without the word ‘significant’ and no mention of measurement…“There was no difference between alcoholics receiving REBT and those that don’t” (Rosenthal, 2005).  Sub-hypotheses are also present….(more examples…)

  1. Directional Hypothesis = asserts a direction of change…. “Alcoholics who receive therapy will drink less”
  2. Non-directional Hypothesis = “alcoholics who receive therapy will be statistically different” – does not predict direction

Tests of Significance…

Firstly, A Quick Definition…

Inferential statistics are used in research to “determine whether we can…make statements that the results reflect what would happen…if we were to conduct the experiment again” (Cozby, 2008, p. 245).  Social scientists require a standards of significance based on the concept of probability: “The likellihood of the occurance of some event or outcome” (Cozby, 2008, p. 247).

  1. Tests of Sigificance = AKA Confidence Level or Alpha Level.  Operate on the principle of probability (p).  Which tells us the likelihood that the relationship between the IV & DV occured as a matter of chance.  This helps us learn if the results are generalizable to the overall population.
What is the “P value” –  It is a measure of strength of evidence in favor of the null hypothesis. A probability value.
In social sciences the level of significance is (p <.05) = probability that reults d/t chance are less than .05.  “The P at the .05 level” (Rosenthal, 2005).
In other words, a high P supports the Null hypothesis, and a low P rejects it
If (P = .05) then 5% likelihood that the difference is d/t chance.
IF (P >.05) there is weak evidence to reject null
If (P < .05) you can reject null
The smaller the P the more convincing the experiment.  .

A statistical definition of error….

“TEST HINT – Some exams call the level of signifiance (which is set at .05 or .01), they will refer to it as the confidence or alpha level….No matter how precise a satistical test is, there is still a probability that results were caused by chance factors. we call this error.

  1. ERROR the likelihood that random chance and not the independent variable caused changes in dependent variable. Two types of error (Alpha & Beta)….
  2. TYPE ONE/ALPHA ERROR: Reject NULL when it is true”. In other words, we conclude significance in IV as cause of DV when this is a false conclusion.
  3. TYPE TWO/BETA ERROR: “We accept Null when it is false”.  Conclude that IV didn’t cause DV when it really did.
  4. AN INVERSE RELATIONSHIP:  When Type One Errors Increase, Type Two errors decreases.
  5. TYPE ONE ERROR = LEVEL OF SIGNIFICANCE:  The probability of making a type one error is the level of significance. In other words P = .05 indicates 5% chance of failing to reject null.

Extraneous Variables/Error & Probability…

AKA Error, emphasized a lot on comprehensive exams in the last few years.  Specifically, they are discussed quite a bit as it pertains to the issue of internal and external validity.  Here are a few more critical concepts to know for the exam;

  1. VALIDITY – does the test measure what it is supposed to.  “Validity refers to ‘truth’ and an accurate representation of information.” (Cozby, 2008, p. 85).
    1. Criterion-Related Validity – how well does a construct measure agree with other assessments of an individual’s abilities.  (i.e. compare your IQ test to others).
        1. Concurrent Validity:  Criteron Validity can be “assessed by examinning whther groups of people differ on the measure in expected ways” (Cozby, 2008, p. 373)
        2. Predictive Validity:  “Criterion Validity “can be assessed by examining the ability of the measure to predict future behavior.” (Cozby, 2008, p. 378).
    2. Construct Validity – “The degree to which a measurement device accurately measures the theoretical construct it is designed to.” (Cozby, 2008, p. 374).  The following concepts are useful in assessing a construct’s validity.
      1. Convergent validity – Can assess construct validity by assessing the degree to which “scores  on the measure are related to the socres on other measures of the same construct or similar constructs” (Cozby, 2008, p. 374).
      2. Disciminant validity:  Can assess construct validity by assessing the “extent to which scores on the meausre are not related to scores on conceptually unrelated meaures.” (Cozby, 2008, p. 374).
    3. Face Validity – Can assess construct validity by assessing the “degree to which a measurement device appears to accurately measure a variable” (Coby, 2008, p. 375).
    4. Content-Related Validity – How well does a measure capture all aspects of a particular abstract concept.  “An indicator of construct validity of a measure is comapred to the universe of conent that defines the construct” (Cozby, 2008, p. 374).

  2. Internal & External Validity – Popularized by David T. Cambpell & Julian C. Stanley….. TEST HINT – “A study cannot have good external validity unless it has good internal validity. Good internal validity will not guarantee good external validity”
    1. Internal Validity does the experiment demonstrate that DV changes are D/T IV??? Does the experimental condition make a difference????
      1. Threats to internal Validity occur when researcher cannot control procedures that affect the experiment.
        1. Countertransference/transference
        2. Instrumental error – instrumental or measurement error impacts the experiment results.
        3. Maturation – occurs in longitudinal studies when the impact of the IV deteriorates over time.  Getting older throughout longitudinal study or simply getting tired…
        4. Statistical regression – Statistical regression to the mean occurs when extreme scores regress toward the mean after re-administration…
        5. Unusually high initial scores fall.
        6. Unusually low initial scores rise
        7. Selection of Groups – Groups are not the same at the beginning of the study d/t intact groups used as a samply method.  Random sampling is used as a solution.  .
        8. Attrition or experimental morality – an issue in longitudinal studies when individuals drop out. Study can be invalidated this way.
        9. Subject Demoralization.  R
        10. John Henry Effect – compensatory rivalry of comparison group strives to prove the researcher right or wrong. (Solution – observe before beginning of study)
  3. External Validity – Can findings of the study be generalized to the larger population.  The labratory is not always the same as the real world.  A study cannot have good external validity unless it has good internal validity.  However, good internal validity will not guarantee good external validity.
      1. Hawthorne Effect – Reactive effect d/t being observed. Subjects don’t perform as they do naturally. Problem with Laboratories. motion that people are getting special attention or know they are being monitored in a study and may perform differently than normal. (demand characteristics)
        1. Received name from the old Western Electric Hawthorne workers plant study that included Elton Mayo from 1927-1932.
        2. Workers output did not go down even when lighting conditions were purposely crappy.
      2. Laboratory – not the same as the real world.
      3. Halo Effect – occurs when you rate an individual on one characteristic but are influenced by others.
      4. Rosenthal Effect (AKA Pygmalion Effect) – experimenter’s expectations inadvertently affect subjects in a study.
        1. Rosenthal & Jacobson Study – experimenters lied to teachers and told certain students were bloomers and would improve during the year.
        2. Teacher’s Expectations influenced their behavior toward children and their outcome (Robert Rosenthal)
        3. These effects can be overcome by blind experiments.
        4. Double Blind Study – neither the experimenter nor study participants know who get the IV….

Validity vs. Reliability

The degree to which an assessment produces consistent results wiht repeated administrations.  In other words, validity tells us if something measures what it intends to, and reliability measures something in a consistent matter after repeated uses of an instrument.  There are three kinds:

**Inter-rater – different observers, consistent estimate…
**Parallel Forms – two tests on something…
**Internal consistency – compare test items….
**Test-Retest – when retaking it…

Mathematical Tests of Significance….

You will not be asked mathematical tests of significance.  However, you should familiar with the names and purposes of the more popular tests.  “Different statistical tests allow us to use probability to decide whether to reject the null hypothesis” (Cozby, 2008, p. 250).

  1. Descriptive Statistics – “statistical measures that describe the results of a study…(i.e. measures of central tendency (mean/median/mode) variablity (standard deviation) and (Correlation)…” (Cozby, 2008, p. 374).
  2. Inferential Statistics – “statistics designed to determine whether results based on sample data are generalizable to a population” (Cozby, 2008, p. 375).

Inferential Statistics – Parametric Testing

Are based on the assumption that the defining properties of a sample distrubtion reflect a normal distribution.  These tests help us define the amount of difference between scores/data along a continuum…

  1. Parametric numbers = define the amount of difference along a continuum.
  2. Interval’s = on a continuum without an absolute zero
  3. Ratio Scales = on a continuum with an absolute zero….

Scales of Measurement

This differentiation is useful in understanding difference between parametric and nonparametic tests.

  1. NOMINAL – uses numbers to identify or classify and is qualitative. (“Baseball player 8 isn’t 2x better than player 4)
  2. ORDINAL – used to describe variables that can be rank ordered (good, better, & best)….
  3. INTERVAL – numbers scaled at equal distances but there is no zero point. (Can add and subtract but not divide or multiply)
  4. RATIO SCALE – Has a true absolute zero point. Can add, subtract, multiply and divide.   Difficult to use in social sciences.

T  Tests (AKA “Student’s T Test”)

Tests a hypothesis between two normally distributed samples. Is there a significant difference between mean scores in the control & experimental groups.   According to Cozby (2008) the T Test is simply the difference between two groups of data.  T = (Group Difference / Within Group Variability).

ASSUMPTIONS:  
  1. Studies must have 30 subjects or more.
  2. There must be two groups of IV
  3. Sample must be random
  4. Scores must be figured along a bell curve
TWO TYPES:  
  1. If the same group is measured on two occasions it is called a dependent/correlated T Test.
  2. Otherwise called an independent sample/uncorrelated T Test.
What Question Does it Answer?  

It tells us if the means of the two samples are different.  You figure out by (1) calculating T, (2) consulting a table, and (3) determing if your result is greater than the T level on the table.  If it is you reject.

ANOVA (Analysis of Variance)

If you want to compare more than two groups in a study when different levels of an IV are used. R.A. Fisher’s F Statistic used to express “an F Value”

ASSUMPTIONS:  
  1. Comparing >2 experimental groups or >2 levels of IV.
  2. Assume bell curve….
  3. Populations have common variance
  4. Homogeneity of variance…
What Question Does it Answer?  

“The F Statistic is a ratio of two types of variance; systematic variance and error variance…Systematic variance is the deviation of the group means from the grand mean or the mean score of all individuals in all groups…Error variance is the deviation of the individual scores in each group from their respective group means….between-group variance and within-group variance” (Cozby, 2008, p. 253).

2 SUB-TYPES…
  1. MANOVA  (AKA Multivariate Analysis of Variance) – If you want to compare more than two groups in a study and have more than two dependent variables .
    1. More than two groups
    2. More than two DV’s
  2. ANCOVA – (analysis of covariance). Used when more than two groups and you need to control extraneous variables or covariates.
    1. It is a way of statistically removing the effects of the extraneous variable.
    2. It can eliminate differences between groups not solely attributed to the experimental variable.
    3. Evaluates whether population means are equal across levels of a categorical IV…

Inferential Statistics – Non-parametric Testing

Firstly, a brief definition…

These tests are useful for nominal data that does not lie on a continuum.  They cannot be graphed on an x/y axis and results do not operate on the assumption that scores fall along a normal distribution.

  1. Parametric – Numbers can be arranged from nominal to ratio scales.
  2. Nonparametric numbers – do not lie on a continuum cannot be graphed on an X/Y axis.
  3. Nominal = weak scale that provides little information. Is used for identification purposes. Qualitative in nature.
  4. Ordinal = provides rank and identification information.

How To Tell Difference Between Parametric & Nonparametric…

  1. First ask what kind of numbers make up the data?
  2. If categorical and nonparametric….
    1. Chi Square –
    2. Kruskal Wallis – Nonpara ANOVA
    3. Wilcoxin – NonPara T Test
    4. Mann Whitney – assess correlation of uncorrelated means.
  3. If parametric and continuum-oriented
    1. T-Test – (test of sig) compares mean of two samples…
    2. Anova – (test of sig) compares mean of >2 samples
    3. Manova – (test of sig) compares means with >2 samples and >2 DV’s
    4. Ancova = (test of sign) compare means when >2 samples and a IV and extraneous variable that needs to be controlled.

Types of Nonparametric Tests

  1. Kruskal Wallis = nonparametric 1-way ANOVA.   Replaces the one-way ANOVA for nonparametric data and more than three groups in a study.
  2. Wilcoxin = used instead of T-Test for nonparametric testing and you want an estimation of significance. Examines whether two correlated means differ significantly when data is nonparametric.
  3. Mann Whitney – Used to determine whether two uncorrelated means differ significantly when data is non-parametic
  4. CHI SQUARE – used for categorical data, used frequently in social sciences.  For example can be used to determine effectiveness of therapy amongst sample groups.  Compares expected frequency with observed frequencies and tells us whether the observed distribution differes significantly from what you’d expect.

Correlational Research

Purpose of Correlational Research…

Asks the question, “does a relationship between two variables exist & if so what’s the magnitude and direction of relationships??”  Important things to note:

  1. It is important to note that correlation does not imply cause nad effect.
  2. There is no direct manipulation of the IV.  DV is just measured.
  3. EXAMPLE:  the relationship between IQ and panic disorder…

Correlational Statistics…

Correlational statistics indicate the degree of magnitude of a relationship between two variables is known as a correlational coefficient.

  1. A coefficient of correlation makes a statement regarding the association between two variables and how the change in one is related to the change in the other.  It is a descriptive statistic that indicates the degree of a linear relationship between two variables.
  2. The sign of the correlation coefficient (- / +) indicates the direction of the relationship between variables….
    1. (+) = direct relationship
    2. (-) = inverse relationship
    3. The higher the number the stronger the relationship
  3. Correlation does not imply causation….

Types of Correlation Coefficients….

Pierson Product Moment Correlation (r)

Is the correlation of choice in most counseling studies and is used for interval and ratio data.  Correlation co-efficients can go from -1 to 0 to +1.   +1 & -1 are considered perfect correlations – very rare in real life.   Most positive correlations are not very strong.

  1. A perfect correlation of +1 or -1 is rare in the social sciences.
  2. +1 describes a perfect direct relationship.  Most positive correlations are not that strong.
  3. -1 describes a perfect inverse relationship – one goes up and the other goes down.
  4. 0 indicates no relationship.
  5. The higher the number the stronger the correlation…

Spearman Rho Correlation

Is a nonparametric measure of rank correlation bertween variables and is useful for ordinal data.  To read more about this the Spearman Rho Correlation click here.

Descriptive Statistics…

“statistical measures that describe the results of a study…(i.e. measures of central tendency (mean/median/mode) variablity (standard deviation) and (Correlation)…” (Cozby, 2008, p. 374)

The Normal Bell-Shaped Curve

(AKA Gaussian Curve) Mean/Median/Mode all fall in the middle of the curve. Most physical/psychological characteristics exist as a bell-shaped curve.  If you were to survey any people on a variety of given traits and you plot a curve, they normally look like a bell shape.

  1. Raw Score.… Unchanged Results….
  2. Percentile Rank = a client’s percentile rank tells you how many people scored equal to or less than another individual.
    1. 80% percentile rank =
      1. 79% of population did worse than you.
      2. 19% did better.
    2. Does not mean you scored an 80% on the test…..

Measures of Central Tendency

The hightest center point of a bell shaped curve or even skewed distributio.  In other words, the most common score or DV level.  There are three measures of central tendency.

MODE –

most frequently occurring score at the highest point of the bell curve…. Often indicated by “Mo” Abbreviation

  1. BIMODAL CURVE = tow modes, looks like a camel’s back. Indicates the researcher is dealing with two populations.
  2. MULTIMODAL CURVES  – More than two modes…

MEDIAN –

Cuts the distribution in half if you rank from highest to lowest.  It is the exact middle.

  1. The 50th percentile, or exact middle.
  2. Data must be rank ordered first.
  3. If even number of scores, add middle scores and divide by two

MEAN

The mean most useful measure of central. Indicated by x with bar over it. You calculate it by adding up scores and dividing it up by the number of scores. Not useful with skewed distributions that has extreme values. The tail indicates if it is positively or negatively skewed.

  1. Positively skewed – bell leans right and tail points left & an abundance lf low scores…
  2. Negatively skewed – bell leans left and tail points right & an abundance of high scores.
  3. Skewed distributions have mean, median, mode in different places.

Drawing Curves…

  1. Frequency Polygon = When we draw a curve of scores we call it a frequency polygon.  The Y axis is the ordinant – the vertical line where DV’s go.  The X axis is the absyssa – the horizontal line where the IV’s go.
  2. Bar Graph / Histogram – intervals of IV….
  3. Scattegram – dots on x/y axis
  4. Types of curves
    1. Mesokurtic – peak in the middle
    2. Kurtosis – peakedness of a frequency distribution
    3. Platykurtic – is flatter and spread out….
    4. Leptokurtic – superman. Tall and skiny….

Measures of Variability…

Explain how individuals in a research study vary amongst themselves in a sample.  Examples include range, variance, standard deviation, etc….

Range

Calculated by substracting by highest from the lowest.  It is the difference between highest and lowest scores.  It is affected by sample size and increases with sample size.  Some tests define the range as the highest score minus the lowest score…

Variance

A measure of dispersion or how spread out from the mean scores are.  “A measure of the variability of scores about the mean; the mean of the sum of squared deviations of scores from the group mean” (Cozby, 2008, p. 380).

Standard Deviation

square root of variance. Useful in discussing the spread of scores.    Usefuls since it is easy to know how many cases fall within a range.  Should know how many cases are included in each +/1 standard deviations.

  1. Know 68-95-99.7 rule.
  2. +1 & -1 SD = 68.25% of all cases.
  3. +2 & -2 SD = 95.4% of all cases.
  4. +3 & -3 SD = 99.74% of all cases

Z-Scores

Z-Scores are the same as SD’s. It describes a score’s relationship to the mean in terms of standard deviations.

  1. A Z score of +2.5 means it is 2.5 standard deviations above the mean.
  2. A Z score of -2.5 means it is 2.5 standard deviations below the mean.

T – Scores

T-Scores are also variations of the SD score.  However the mean is 50 and each SD is 10 points.  It assumes a bell shape curve and is useful with sample sizes of 30 and below.  They are useful in eliminating negative results.  Here are examples of questions you might be asked:

  1. “What T score is 1 SD above the mean?” (ANSWER 60)
  2. “What T score is 1 SD below the mean?” (ANSWER 40).

Stanines –

Were originally called “standard nine scores”.  Divide Standard Deviations into nine equal intervals with the mean of 5 and a SD of 2.  The SD’s rank from the lowest to the highest.

Key Test Hints Regarding Descriptive Statistics!!!

  1. averages also called measures of central tendency, the range, the variance, the standard deviation and any other statistical device that is used to describe a group is called a DESCRIPTIVE STATISTIC… (other kind is called an INFORMATIONAL STATISTIC)
  2. “The benefit of standard scores such as percentiles, t-scores, standard deviations, etc. is that they allow you to analyze the data in relation to the properties of the normal bell shaped curve.

Finally, Miscellaneous Statistical Terms…

  1. Survey – the simplest approach to research conducted by giving a questionnaire or opinion poll to a sample population.
    1. Return rate is commonly 30-50%.
    2. When below 75% can’t make generalizations about data…
    3. Some says a minimum of 100 responses is essential.
  2. Ethnographic research – an old anthropological approach in which the researcher looks at the overall dynamic in a culture or situation.
    1. Not focusing on a single factor.
    2. It is Qualitative and non-statistical
    3. Observational case studies & naturalistic observation are ethnographic
    4. Do not manipulate IV’s
    5. Holistic and inductive.
      1. Inductive – a process where you generalize based on specific observations.
      2. Deductive – a specific hypothesis is derived from general principles.
  3. Halo Effect – occurs when you rate an individual on one characteristic but you are really rating on the basis of another statistic.
  4. Hawthorne Effect – Reactive effect d/t being observed. Subjects don’t perform as they do naturally. Problem with Laboratories. motion that people are getting special att
    1. Received name from the old Western Electric Hawthorne workers plant study that included Elton Mayo from 1927-1932.
    2. Workers output did not go down even when lighting conditions were purposely crappy.
  5. Rosenthal Effect (AKA Pygmalion Effect) – experimenter’s expectations inadvertently affect subjects in a study.
    1. Rosenthal & Jacobson Study – experimenters lied to teachers and told certain students were bloomers and would improve during the year.
    2. Teacher’s Expectations influenced their behavior toward children and their outcome (Robert Rosenthal)
    3. These effects can be overcome by blind studies…
  6. Double Blind Study – neither the experimenter nor study participants know who get the IV…
  7. Norms –  Testing / experimenting norms, the normal and typical or average person who to that particular test for purposes of comparison.
  8. “N” Research Design:  The N=1 Single subject design is also known an intensive experimental intra-subject design or case study…  Focuses on behavior of one person and is often used for behavior therapy and behavior modification.
    1. “N” – in research indicates the number of participants in a study.
    2. AB DESIGN
      1. FIRST – take a baseline (no treatment/intervention) = A
      2. SECOND – Then apply the treatment = B
    3. ABC DESIGN – like AB design except two treatment interventions used.
    4. ABA DESIGN – like AB but return to baseline
    5. ABAB DESIGN = lets you see if the treatment really works on two occasions.  It ends the experiment in the desirable treatment phase.  If it attracts more than one behavior it is called a multiple baseline design.
  9. Counterbalancing – Counterbalancing is a type of experimental design in which all possible orders of presenting the variables are included. For example, if you have two groups of participants (group 1 and group 2) and two levels of an independent variable (level 1 and level 2), you would present one possible order (group 1 gets level 1 while group 2 gets level 2) first and then present the opposite order (group 1 gets level 2 while group 2 gets level 1). This way you can measure the effects in all possible situations.
  10. Percentile Rank = a client’s percentile rank tells you how many people scored equal to or less than another individual.
    1. 80% percentile rank =
    2. 79% of population did worse than you.
    3. 19% did better.
    4. Does not mean you scored an 80% on the test…..
  11. Raw Score = unchanged results…Done nothing to scores…
  12. Longitudinal Research – AKD developmental research follow same group of people over time also known as trend studies.
  13. Directional Hypothesis = asserts the direction of change…. “Alcoholics who receive therapy will drink less”
  14. Non-directional Hypothesis = “alcoholics who receive therapy will be statistically different” – does not predict a direction of change….

References

Cozby, P.C. (2009). Methods in behavioral research.  Boston: McGraw-Hill.
Rosenthal, H. (2005). Vital information and review questions for the NCE and state counseling exams. Routledge

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