PSYCHSTATS REVIEWER FOR CVSU QUALIFYING

STATISTICS

A branch of mathematics which deals with the collection, organization, presentation, analysis and interpretation of numerical data for the purpose of assisting in making a more effective decision

data

STATISTICS Synonymous with the word _____?

DESCRIPTIVE STATISTICS

Includes the methods of collecting, classifying, graphing, and averaging the data.

The objective is simply describing and summarizing the important features, properties or characteristics of the data on hand without attempting to give inference

INFERENTIAL STATISTICS

Demands a higher order of critical judgment and mathematical methods.

The main concern is to analyze the organize data leading to prediction of inferences.

The area of _________ called hypothesis testing is a decision-making process for evaluating the statements about a population, based on the information gathered from the samples

VARIABLES

A characteristic or attribute of persons or objects which assume different values for different objects under consideration. Factors that can be manipulated and measured.

MEASUREMENT

The process of determining the value or label of a particular variable for a particular individual or object on which variable is measured.

DISCRETE

Can assume finite or at most, countable infinite number of values; usually measured by counting or enumeration.

Eg. students, professors, psychologists, parents.

CONTINUOUS

Those that cannot be counted because of their distinct division.

“abstract variables”

Can assume values corresponding to a line of interval.

Eg. intelligence, beauty, effectiveness, cleanliness

QUALITATIVE

Can give categorical responses.

Eg. occupation, gender, civil status, religious.

QUANTITATIVE

Takes on numerical values representing an amount or quantity.

Eg. height, salary, number of children, weight

DEPENDENT

Measures based on the effect of the independent variables.

“outcome variable”

INDEPENDENT

Variables that the researcher controls or manipulate in accordance with the purpose of the investigation.

UNIVARIABLE

There is only one variable involved.

Eg. Age of Grade 7 pupils.

BIVARIABLE

Data are classified on the basis of two variables.

Eg. An ice cream shop keeps track of how much ice cream they sell versus the temperature of the day.

MULTIVARIABLE

Each datum belongs to three or more variables.

Eg. The teacher would like to keep track the enrolment in the College in terms of program, year level and gender.

Discrete and Continuous Variables, Qualitative and Quantitative Variables, Dependent and Independent Variables, Univariable, Bivariable and Multivariable Distribution

CLASSIFICATION OF VARIABLES

NOMINAL SCALE, ORDINAL SCALE, INTERVAL SCALE, RATIO SCALE

LEVELS OF MEASUREMENT

NOMINAL SCALE

Has no numerical value. “categorical scales”

ORDINAL SCALE

Not only **classifies subjects** but also **ranks** them in terms of the degree to which they posses a characteristics of interest.

INTERVAL SCALE

Has all the characteristics of a nominal and an ordinal scale but it is based upon predetermined equal intervals.

**Does not have true zero point.**

RATIO SCALE

Represents the highest, most precise level of measurement.

**Has a meaningful true zero point.**

POPULATION

The total or entire group of individuals, events, objects, observations, reactions to certain stimuli that have unique patterns of qualities and from which information is desired by the researcher.

“the universe”

SAMPLE

A portion or subset of the population used to gather information from the population.

Truly represents the unique qualities or characteristics of the population.

Identify data source (population), Select sample type, Choose sample size.

ESSENTIAL STEPS IN DETERMINING THE SAMPLE SIZE

Reliable studies connect, assess treatment success, guide data collection, aid understanding, draw conclusions, predict outcomes, statistics everywhere.

IMPORTANCE OF STATISTICS IN PSYCHOLOGY

n = N / (1+Ne^2)

Slovin’s Formula

n

sample size

N

population

e

estimated margin of error (acceptable error)

PARAMETERS

Measures of the population or numerical characteristics of the population.

“μ”

PROBABILITY SAMPLING

A sampling process where each unit in the population has known nonzero probability of being included in the sample.

Most unbiased but difficult method.

SIMPLE RANDOM SAMPLING

The sample will be chosen randomly and each member in the population will have an equal chance of being selected.

STRATIFIED RANDOM SAMPLING

The samples are randomly selected from the different groups or sections of the population used in the study.

SYSTEMATIC RANDOM SAMPLING

The method where every k th name in the list of the population members can be selected as part of the sample.

\
K = N/n

CLUSTER SAMPLING

The researcher identifies convenient, naturally occurring group units.

Unlike strata, it is advisable to form clusters with heterogeneous components.

MULTI-STAGE SAMPLING

Used when the respondents of the study are scattered all over a big geographical area such as for national, regional, provincial or country level studies.

Involves several stages in drawing the samples from the population.

NON-PROBABILITY SAMPLING

A sampling process wherein probabilities of selection are not specified for the individual units in the population. When the researcher is not after generalizing the results of the study to the population or universe

Define the population. Cluster the population. Randomly select clusters. Randomly sample units within selected clusters.

MULTI-STAGE SAMPLING STAGES

NON-PROBABILITY SAMPLING

A sampling process wherein probabilities of selection are not specified for the individual units in the population. When the researcher is not after generalizing the results of the study to the population or universe

PURPOSIVE SAMPLING

The researcher selects those who can best help explain or give information based on his judgment.

“judgmental sampling”

CONVENIENCE SAMPLING

The researcher selects respondents who are available at the time and place the data is to be collected.

“haphazard or incidental sampling”

QUOTA SAMPLING

To come up with the desired number of samples no matter how they are selected.

SNOWBALL SAMPLING

Used when respondents are difficult to identify and best located through referral networks.

RESEARCH DESIGN

The researcher’s plan for selecting respondents, research locale and data gathering procedures to answer research questions systematically

ACTION RESEARCH

When the researcher is interested in finding out whether something will work or problem solving in local setting.

DESCRIPTIVE RESEARCH

Used when the researcher’s concern is to understand the nature, characteristics, components or aspects of a situation or phenomenon

EXPLANATORY RESEARCH

Used to explain and predict relationships between 2 or more variables.

Uncovering data on unknown phenomena

CORRELATIONAL RESEARCH

When the researcher is after uncovering data on a phenomenon little is known about

EVALUATION RESEARCH

Appropriate when the researcher plans to assess the impact, effect, result, or outcome of operations, policies and programs.

POLICY RESEARCH

When the researcher is concerned about generating information relevant to the development and formulation of policy and the assessment of the effect of such policy.

EX-POST FACTO RESEARCH

When the researcher is after observing existing conditions and looking back through the data for plausible causal factors.

“causal comparative research”

HISTORICAL RESEARCH

When the researcher is attempting to solve certain problems arising out of historical context through the gathering and examining relevant data from the past

ETHNOGRAPHIC RESEARCH

To come up with a holistic description of phenomenon or situation with the use of multiple data collection techniques.

PHENOMENOLOGICAL RESEARCH

Interprets an experience or fact, by listening to the different stories of the participants.

FREQUENCY DISTRIBUTION

An organized tabulation of the number of individuals located in different categories in different levels of measurements.

This is used to group scores together in order which would allow the researcher in a glance the set of scores.

NORMAL CURVE

A bell-shaped, smooth, mathematically defined curve that is highest at its center.

SKEWNESS

The nature and extent to which symmetry is absent.

An indication of how the measurements in a distribution are distributed.

POSITIVE SKEW (LEFT)

When relatively few of the scores fall at the high end of the distribution. (LEFT)

NEGATIVE SKEW (RIGHT)

When relatively few of the scores fall at the low end of the distribution. (RIGHT)

KURTOSIS

The steepness of a distribution in its center.

Mesokurtic

When the kurtosis is zero, the distribution has a normal or Gaussian shape, and it is called ________.

Leptokurtic

If the kurtosis is positive, the distribution has heavier tails and a sharper peak compared to the normal distribution, and it is called _______.

Platykurtic

If the kurtosis is negative, the distribution has lighter tails and a flatter peak compared to the normal distribution, and it is called _______.

MEASURE OF CENTRAL TENDENCY

A statistic that indicates the average or midmost score between the extreme scores in a distribution.

ARITHMETIC MEAN

Equal to the sum of the observations divided by the number of observations.

Mean = Σ(fX) / n

formula for MEAN

MEDIAN

The middle score in a distribution.

MODE

The most frequently occurring score in a distribution of scores.

PERCENTILES

Indicate the values below which a certain percentage of the data in a data set is found.

Px = (x (n+1)) / 100

percentiles formula

RANGE

Equal to the difference between the highest and the lowest scores.

Example:

HS – 60

LS – 40

Range = 20

VARIANCE

Equal to the arithmetic mean of the squares of the differences between the scores in a distribution and their mean.

STANDARD DEVIATION

Equal to the square root of the average squared deviations about the mean.

Equal to the square root of the variance.

square root of the variance.

A raw score that has been converted from one scale to another scale, where the latter scale has some arbitrarily set mean and standard deviation.

Z SCORE

Results from the conversion of a raw score into a number indicating how many standard deviation units the raw score is below or above the mean of the distribution.

T SCORE

A scale with a mean set at 50 and a standard deviation set at 10.

None of the scores is negative.

T = (z x 10) + 50

T-score formula

HYPOTHESIS

A generally considered most important instrument in research.

An assumption or a supposition which has to be proved or disproved.

A formal question that a researcher has to resolve

Clear and precise, Testable, Relates to a variable, Specific and limited in scope, Simple terms, Consistent with known facts, Testable within a reasonable time, Explains crucial phenomena

CHARACTERISTICS OF A HYPOTHESIS

NULL HYPOTHESES and ALTERNATE HYPOTHESES

Based on their formulation

DIRECTIONAL HYPOTHESES and NON- DIRECTIONAL HYPOTHESES

Based on direction

INDUCTIVE HYPOTHESES and DEDUCTIVE HYPOTHESES

Based on their derivation

NULL HYPOTHESIS

States that independent variable has no effect and there will be no difference between the two groups. Similar to the notion of innocent until proven guilty

ALTERNATIVE HYPOTHESIS

The hypothesis that the researcher is trying to prove and states that independent variable has an effect and there will be a difference between the two groups.

DIRECTIONAL HYPOTHESIS

It predicts that there will be a difference between the two groups and it specifies how the two groups will differ. Using comparison terms such as “greater,” “less,” or “worse.”

NON-DIRECTIONAL HYPOTHESIS

If the hypothesis simply predicts that there will be a difference between the two groups.

It predicts that there will be a difference but does not specify how the groups will differ

DEDUCTIVE HYPOTHESIS

Aims at testing a theory, Moves from broad generalizations to specific observations.

Correct decision

Ho is true, Accept Ho

Type II Error (β)

Ho is false, Accept Ho

Correct decision

Ho is false, Reject Ho

Type I Error (α)

Ho is true, Reject Ho

TYPE I ERROR

Occurs when we reject the null hypothesis when it is true, designated by alpha (α). Ho is wrongly rejected. Often considered to be more serious, and therefore more important to avoid, than the other error.

TYPE II ERROR

Occurs when we accept the null hypothesis when it is false, designated by beta (β). Ho is not rejected when it is in fact false. Frequently due to sample sizes being too small.

ALPHA

Set at the beginning of the research and is the level to which the researcher wishes to limit the probability of making a Type I error. The area of the rejection region. Typical values are .05, .01, or .001.

P-VALUE

The probability of obtaining results at least as extreme as the observed results of a statistical hypothesis test, assuming that the null hypothesis is correct. A smaller p-value means that there is stronger evidence in favor of the alternative hypothesis.

No evidence against the null hypothesis.

P > 0.10

Weak evidence against the null hypothesis in favor of the alternative.

0\.05 < P < 0.10

Moderate evidence against the null hypothesis in favor of the alternative.

0\.0 < P < 0.05

Strong evidence against the null hypothesis in favor of the alternative

0\.001 < P < 0.01

Very strong evidence against the null hypothesis in favor of the alternative.

P < 0.001