Elementary Statistics Chapter 1,2,3

Validity

"Accuracy" of measurement ~ is the instrument measuring what it is supposed to measure?

Reliability

"Consistency" of measurement ~ is the instrument measuring the same each time? (bathroom scale)

Frequency Distribution

A distributional count of scores, items, or whatever is being measured n= Sample amount x= Groups f= Frequency P= Proportion

Standard Error of the Estimate

A measure of the prediction error. A form of (sample standard deviation) appropriate to the bivariate world

The Scientific Method

Identification of problem, Formation of Hypothesis, Statements of relationship/differences, solutions to the problem,Collection,Organization & Analyses of data & Formation of conclusions

Pearson r

Pearson Product Moment Correlation Coefficient (Pearson r) *Scale ranges from negative 1 to positive 1 *Positive correlations stregthen as they approach +1.00 *Negative correlations strehgthen as they approach -1.00

mu

Population mean

P=Rho

Population measure of bivariate relationship

sigma

Population standard deviation

sigma (squared)

Population variance. It is a measure of dispersion

Median

The middle score or position/50th percentile / 50%le

Variable

A characteristic under study or investigation that assumes different values for different elements

Constant

A characteristic under study that has a fixed value

Spurious Correlation

A correlation that is artificially high or low as the result of some confounding variable (words of caution)

Coefficient of Non-Determination

% of non-overlap (remember circles percent not shared)

Measures of Dispersion

(Measure of Spread) Measures the degree to which data points (Scores) are spread out to each other

Spearmans Rho

(Statistical test) Used at the oridinal level

True Experimental Research

*Must use control group *Must manipulate the Independant variable *Must have randomization

Discrete Variable

A (quantitive) variable whose values are countable

Scatterplot

A plot of paired oberservations. Tracks positive and negative correlations

Biased Sample

A sample in which some members of the population are less likely to be included than others No ability to generalize i.e a sample of volunteers

Statistic

A sample measure calculated for sample data.

Simple Linear Regression

A statistical technic used to predict Y from X as correlations get strong enough/are high enough

Population

All or a complete set of individuals (elements) under investigation

Confounding Variable

Any variable(s) highly related to the independant (IV) (treatment)/dependant variable that may effect the accuracy of our results...(IQ)

Mean

Arithematic average

Inferential Statistics

Collection of methods that help make decisions about a population based on sample results

Cross section Data

Data collected on different elements at the same point in time or for the same period of time

Raw Data

Data recorded in the sequence in which they are collected and before they are processed.

Operational Definitions

Define conceptual definitons in terms of how they are measured (scale)

Parameters

Describes populaton characteristics A statisical value that describes the population such as mean, mode,median,range,variance or standard deviation calculated for a population data set

Interval Scale

Equal distance between points on the scale (like thermometer) No true Zero (zero is not the absence of anything (very cold)

Areas Under the Curve

Equal segments (also called just areas) when added up will equal 100%

Correlation Matrix

Found in literature. Lists variables across the top and side.

Statistics

Group of methods used to collect, analyze, present, and interpret data and to make decisions

Positive Correlations

Has simultaneouus increase or decrease in the x and y. The strongest positive correlation we could have would be +1.00 Exampe (an increase in study time (x) it creates an increase in grades(y) OR a decrease in sleep (x) creates a decrease in energy(y)

Normal Distribution

In a normal distribution the mean, median and mode will be identical, will have shape of triangle. (Gaussion Dist, Symmetrical Dist. & Bell Curve) house prices ( 50k, 75k, 100k, 10,000,000) "extreme"

Variance

Indicate the degree to which scores are dispersed around the mean. The standard deviation is obtained by taking the positive square root of the variance. The variance calculated for population data is denoted by (read as sigma squared).

Correlation Research

Is always tentative

Range

Is the simplest measure of dispersion to calculate. Its obtained by taking the difference between the largest and smallest values in a data set.

Quasi-Experimental Research

Lack of randomization *Manipulates an independent variable *Uses a control group

Regression Line

Line of the best fit or best prediction

Measure of Central Tendency

Measures that describe the center of a distribution. The Mean, Median, Mode are three of the measures of central tendency

Mode

Most frequently occuring score, i.e. 1,2,3,3,3,4,4,5

Z Score

Most widely used, the distance from the mean to any score in the distribution in standard deviation units, ranging from -3 to +3 with a mean of 0 and a standard deviation of 1 RULES: If Z is positive we add 50% to our proportion between z and the mean If Z is negative we simply use the proportion that is greater than z

Ratio Scale

Most widely used.Equal distance between points on scale. Has TRUE ZERO. (Pulse, blood pressure weight etc..)

Language of Science

Natural & Physical behavior "Approach to gather Knowledge" Functions: Develope of theory & Testing of Hypotheses "We have Method"

Curvilinearity

Non-Linear, Pearson r is meaningless (words of caution)

Nominal Scale

Numbers represents categorical or classifications, used to identify i.e. social security numbers,home address, cell numbers No arithmetic operations can be performed w with them

Operationalization

Operational definitions define Conceptional definitions in terms of how they are measured We "Operationalize" headache pain and define it via a scale

Three measures of dispersion

Range, Variance, Standard Deviaton Both Variance & Standard Deviation measure the degree to which our data points are dispersed around the mean

Ordinal Scale

Rankings/Standings unequal distance between points on the scale (Percentile rank %le) (using names or #'s where only the comparison is relevant)

Randomization

Reduces (spread of risk) of the effects of any confounding variable(s) equally across all groups

Covariance

Relationship or the measure of the relationship that is non-standardized (sister measurement to correlation)

Replication

Repeating the essence of a research study,usually with different participants in different situations,to see whether the basic finding extend to other participants and circumstances

x-bar

Sample mean

r

Sample measure of bivariate relationship

s

Sample standard deviation

S (squared)

Sample variance

Descriptive Statistics

Set of procedures in which we organize, summarize, present data. This is done is 5 ways 1.Frequency distributions 2.Measures of central tendency 3.Measures of dispersion 4.Measures of position 5.Measures of relationship

Standardization

Set of procedures where we transform raw scores (grades,weight, height) to another score with a known mean and standard deviation with a purpose of determining "Percentile Rank" (%le)

Data

Sets of numbers we collected that represents some measurement/Information about individuals in a population

Y(1)=bx +a

Simple linear regression Y(1) is said to be Prime. This formula will give you the regression line. b=slope, a = intercept, y(1) Predicted variable (dependent variable) x= Predictor variable (independent variable)

Continuous Variables

Some variables can not be counted, and they can assume any numerical value between two numbers

Summation Notation

Sometimes a mathematical notation helps express a mathematical relationship concisely. Summation Notation is used to denote the sum of values The act of adding paticular data points and the meaning of E which we refer to as "sum". it means "add em up" greek symbol

Negative Skew

Tail points in negative direction

Positive Distribution (skew)

Tail points in the positive direction

Random Assignment

The act of taking those names from a bin & assigning them to respective groups in the case of experimental research, where we indeed manipulate the (IV) and measure for its effect on the (DV)

Standard Normal Distribution

The characteristics are identical. It has a bell shape curve and symmetrical distribution.It has a mid point that is the Mode and the Median and the Mean

Correlation

The extent to which two variables change together in a systematic way or "co-vary" (the relationship or association between two variables). This relationship is Linear. Does not infer causation!!

Samples

The selection of a few elements from the population (subsets of population)

Measurement

The value of a variable for an element, The act of assigning numbers to observations using a set of rules which we define as measurement scales (Nominial, Ordinal, Interval,Ratio)

Independant Variable

The variable we manipulate to measure for its effect on the dependent variable (treatment)

Dependent Variable

The variable we measure "Data" the observed outcome of interests, data, the effect in terms of cause and effect

Phi Coefficient

Used at nominal level

Point biserial Correlation

Used at nominal level

Empirical research (Scientific Research)

Uses observation, measurement and data analysis to help answer specific questions

Outliers or Extreme values

Values that are very small or very large relative to the majority of the values of the values in a data set. (words of caution) Can effect the magnitude of r..

Qualitative or Categorical Variables

Variables that cannot be measured numerically but can be divided into different categories (Nominal scale)

Coefficient of Determination

Variation over-lap (remember circles % which is shared)

Measure of position

Where does the score rank in relation to others or where does your score rank/fall in relation to all the others

Science

an approach to gathering knowledge

Negative Correlations

has opposing increase or decrease in x and y. The strongest negative correlation we could have is -1.00. Example ( an increase in alcohol consumption (x) creates a decrease in dexterity

Research Design/Method

is a plan for collecting and analyzing data that allows us to answer the specific questions

Standard Deviation

mostly used measure of dispersion. tells how closely the values of a data set are clustered around the mean

Sum of Squares

take each difference from the mean and square it. Then, add up these squared deviations. When you do this you have the sum of the squared deviations (which is then reduced to "Sums of Squares", or SS).

Statistics "The Language of Science"

the sciences, i.e. natural & physical behavioral Science " approach to gathering knowledge" Development of Theory testing of Hypotheses

Random Selection/Sample/Probabitlity Sample

whereby each memeber of the population we're investigating has an equal likelihood of being selected

Independent (predictor) Variable

x