Exam 1 Flashcards
(148 cards)
1
Q
Statistics
A
Mathematical technique by which data are organized, treated and presented for interpretation and evaluation.
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Research
A
A systematic investigation which includes research, development, testing and evaluation designed to develop or contribute to generalized knowlege.
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Historical Research
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A search through record to establish a possible how and why explaining an event or phenomenon
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Observational Research
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(descriptive research) involves describing events or conditions that the researcher does not actively manipulate
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Experimental Research
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involves manipulating and controlling events or variables to solve a problem
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Measurement
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The process of comparing a value to a standard
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Data
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the result of a measurement
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Dimensions
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physical quantities that can be measured (M,L,T,Te)
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Units
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A single quantity or individual isolated component that may be part of a more complex structure, function or system.
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Validity
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The soundness or the appropriateness of the test in measuring what it is designed to measure.
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Types of Validity
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Internal and External
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Internal Validity
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A measure to control within the experiment, (the study itself), results are due to the treatment that was applied
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Threats to Internal Validity
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Research Design
Extraneous Variables
Instrument Error
Investigator Error
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External Validity
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The ability to generalize the results of the experiment to the population from which they were drawn.
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Reliability
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The consistency and reproducibility of data (test-retest value)
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Variable
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A characteristic of a person place or object that can assume more than one value.
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Intervening Variable
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Extraneous Variable: Confouding variable that may reduce internal validity
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Continuous Variable
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A variable that can assume any value (distance, force etc)
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Discreet Variable
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A variable that is limited to certain numbers, usually whole numbers or integers. (ticket sales, gymnast scores)
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Constant
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A characteristic that can only assume one value, never changes.
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Classificaiton of Data or Scales Acronymn
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No Oil in Rivers
Nominal
Ordinal
Interval
Ratio
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Nominal Scale
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Mutually exclusive categories, assigned number does not indicate an amount of something.
Numbers assigned to runners
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Ordinal Scale
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Gives quantitiative order to the variables, but does not indicate how much better one score is than another, rank.
Rank order of winners
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Interval Scale
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Has equal units, or intervals of measurement but has no absolute zero point (zero is arbitrary)
Performance rating on a scale of 1 to 10
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Ratio Scale
Quantitative, based on order has equal distance between scale points and uses zero to represent the absence of value, negatives are not possible.
Time to finish`
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Frequency Data
Data which indicates the number of occurences of a given value or event.
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Hypothesis
An educated guess or logical assumption that is based on prior research or known facts and that can be tested.
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Research Hypothesis
( H1 or Ha) The hypothesis that prompts the reserach, typically a statement, usually predicts a relationship or differences between or among groups.
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Null Hypothesis
(Ho) Prediction that there is no relationship or no difference between groups
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Independent Variable
In Experimental Studies: The variable that is manipulated or controlled by the researcher
In observational Studies: The "predictor variable" this is measured only not controlled.
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Dependent Variable
In experimental studies: The variable that is measured
In observational studies: The criterion variable
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Population
Any group of persons, places, or objects that ahve at least one common characteristic.
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Sample
A subset of a population (Samples are representative of the population of intrest)
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Statistical Inference
The process of generalizing from a sample to a population
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Parameter
A characteristic of the population
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Statistic
A characteristic of a sample that is used to estimate the value of the population parameter
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Theory
A belief regarding a concept or a series of related concepts
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Rank Order Distribution
ordered listing of the data in a single column, quick view of spread or variableity in the group, easily identifies outliers qualitatively
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Range
Distance from HIghest to lowest value
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Types of Frequency Distribution
Simple and Complex
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Simple Frequency Distribution
Ordered listing of the variable being studied (x) with a frequency colun (f) that indicates the number of cases at each given (x) value.
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Grouped Frequency Distribution
Ordered listing of, in one column, a variable (x) in groups and in a second column (f).
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Frequency Histogram
Bar graph, displays a frquency distribution, frequency on y axis and groups on X
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Frequency Polygon
Line Graph of scores plotted against frequency
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Cumulative Frequency Graph
Curve:
- Line Graph
-Ordered scores on X axis
- Number of subjects at or below that value on Y axis
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Dot Plot
Scatter Plot: one categorical axis and one continuous axis. Each point represents the score of a dependent variable for each subject.
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Normal Curve
Bell or Gaussian Curve: Assumes a symmetrical distribution of values abou thte center of the curve. Mean, Median, Mode are all located at the center point of the curve. ( z = 0)
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Central Limit Theorem
A sum of random numbers becomes normall distributed as more and more of the random numbers are added together.
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Bimodal Curve
Curve which contains multiple values occuring with the highest frequency
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Skewed Curve
Nonsymmetrical curve, number of subjects or values shifted to one side.
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Ceiling Effect
Limit on the upper value of scores causing high scores to be clustered around the limit.
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Floor effect
Opposite of ceiling, when the lower limit causes cluster of values around it.
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Percentile
Represents a fraction (in hundreths) of the ordered scores that are equal to or fall below a given raw score.
Standard Score
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Uses of Standard Scores
Evaluate Raw Score
Compare two sets of scores that have different units
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Standard Score
A score that is derived from raw data that has a known basis for comparison.
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Quartile
Precentile Scores divided into four equal parts.
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Q1
First quartile: 0-25%
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Q2
Second Quartile: Q1 ato 50th percentile
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Q3
Third Quartile: Q2 to 75th Percentile
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Q4
Fourth Quartile: Q3 to 100th Percentile.
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Quintile
Similar to quartile but uses 20% divisions
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Steps to calculate percentile
Create a fraction: Number of values at or below value of interest / N
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Steps to determine score from percentile
Convert percentile to decimal
Multiply deceimal by number of score (N)
Count that many scores from the bottom
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Mean
Arithmetic average of the sample (Sum/n)
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Median
The middle number, score associated with 50th percentile
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Mode
The most frequent or common score in a distribution
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Mode Disadvantages
Unstable: Varies depending on grouping methods
Terminal: Not useful for other calculations
Ignores extreme scores
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Variability
Measure of the spread or dispersion of the data set
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Indices of Dispersion
Describes the scatter of scores in a distribution
Describes the spread of data
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IQR
Interquartile Range: The difference between the 75th and 25th Percentile (3rd and 1st quartile)
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SIQR
Semi Interquartile Range: Half of the IQR: (Q3-Q1)/2
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Variance
The average of the squared deviations from the mean
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Sum of Squares
Measures the deviation of data points away from the mean
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Σ
Sigma : The sum of
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𝛔
Population Standard Devation
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V or 𝝈²
Population Variance
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SD or s
Sample Standard Deviation
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s²
Sample Variance
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Describe SD in relation to the normal curve
When N is large and the distribution is normal ther are typically 5 or 6 SDs within the range.
Does not apply if range is small
Does not apply in skewed data
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Degrees of Freedom
The number of values in a data set that are free to vary
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CoV
Coefficient of Variation: A normalized SD measure, normalized to mean,
Percentage
(SD/x) * 100
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x̄
Sample Mean
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𝝁
Population Mean
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Z-Score
Number of standard deviations away from the mean (x-x̄)/s
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T-score
Assigns the number 50 to a z-score of 0
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What proportion of scores fall +/- 1 SD away from the mean?
68.26
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What proportion of scores fall +/- 2 SD away from the mean?
95.44
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What proportion of scores fall +/- 3 SD away from the mean?
99.75
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Z score of 95% CI
1.960
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Z score of 99% CI
2.576
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Z score of 90% CI
1.645
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Stanine
Standard 9: 9 point scale of scores can be used to assign a test score a single digit number, always positive from 0-9
e.g. 1,2,3 normal, 4,5,6 average, 7,8,9 above average
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Probability
The liklihood of a particular outcome.
0 means it will definitely not happen
1 means it will definitely happen
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Odds
p/(1-p) where p is the probability of the outcome
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Skewness
Bilateral symmetry of the data
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Positive Skew
long tail to right
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Negative Skew
Longer tail to left
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Kurtosis
The relative peakedness (magnitude) of the curve
measure of heaviness of the tails
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Leptokurtic
more peaked
Kurtosis > 0
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Platycurtic
less peaked, flatter
Kurtosis < 0
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Raw Skewness formula
(ΣZ³)/N
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Raw Kurtosis formula
(ΣZ⁴/N)-3
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Standardized Skewness Score
Z score of the raw skewness calclulated by taking the raw skewness dividing it by the standard error
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Standardized Kurtosis Score
Z score of the raw kurtosis calculated by taking the raw skewness and dividing it by the standrard error
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Standardized Skewness Formula
Zskew = ((ΣZ³)/N)/SQRT((6/N))
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Standardized Kurtosis Formula
Zkurt = ((ΣZ⁴/N)-3)/SQRT(24/N)
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Conditional Probability
Probability of the outcoem given that another outcome has occured.
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Sampling Error
The amount of error in the estimate of a population parameter that is based on a sample statistic
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Standard Error of the Mean
An estimate of the amount of Sampling Error
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SEm formula
SEM = SD/ SQRT(N)
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Sampling Distribution of the Mean
Frequency Distribution of Means
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Level of Confidence
Degree to which it is believed that the IV has an effect on the DV. Opposite of the Probability of Error
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𝝰
The probability of commiting a type 1 error (Alpha Level)
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CI
Confidence Interval: Range of actual values associated with a level of confidence
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CI formula
Mu =x̄ +/- Z(SEM)
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Type 1 Error
𝝰 False Positive: Reject Null when Null is true
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Type 2 Error
𝜷 False Negative: Fail to reject Null when Null is false
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Region of Rejection
AUC either smaller than the lower critical value or larger than the higher critical value area where we reject alternate hypothesis and accept null.
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Two tailed test
H0: Xbar1 - Xbar2 = 0
Rejection area divided between the two tails of the sampling value, upper and lower critical values
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One tailed test
H1: Xbar1 > Xbar2
All rejection area in one tail of the sampling distribution
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Correlation
Used to quantify the degree of relationship or association between variables.
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r
Pearson Product Moment Correlation: Ranges from -1 to 1 , 1 = strong positive relationship -1 = strong negative relationship 0 = no relationship
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Best fit line
Line of Best Fit: the best linear estimate of the relationship between the two variables.
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Linear Relationship
Rate of change of variables is constant
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Curvilinear Relationship
Rate of change of variables is not constant
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Covariance
An index of how x and y vary together
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Bivariate Regression
Predict a score on y if we know a score on x
Simple linear regression
regression = prediction
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Residual
Error factor, the distance of the point from the line of best fit, difference between the predicted values of Y (DV) and the observed values of Y
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Regression
Statistical technique that relates a DV to one or more IVs
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"a" (correlation)
Y intercept: The value of y wehre the line crosses the y axis, the value of y when the value of x = 0
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"b" (correlation)
Slope: the change ofy for 1 unit increase in x, rise/run, y2-y1 / x2-x1
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r²
Represents the proportion of teh variance for a DV that is explaine dby and IV or variables in a regression.
Common variance
Shared variance
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How to find r squared
r = .8 , rsquared = .8*.8 = .64 = 36% unexplained
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Homoscedasticity
Assumption that the residuals do not vary, there is no apparent relationship between the size of the residuals and the size of X,
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Heteroscedasticity
Variance of the residuals is not constant
Inflates tyle 1 errors
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R
Multiple Correlation Coefficient:
Ranges from 0 to 1
Cant be negative
0 no relationship
1 perfect relationship
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R^2
Multiple correlation coefficient squared
More useful than R
Multivariate coefficient of determination
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Partial Correlation
Teases out the correlation between a single x variable and the y variable in a multiple regression.
i.e. Correlation of x1 and y with x2 removed (rsubYX2.X@) / correlation of x2 and y with x1 removed (rsubYX2.x1)
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b (multiple regression model)
slope coefficient: coefficients that give weight to the independent variables according to their relative contributions to the prediction of Y.
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k (multiple regression)
number of predictors, or IVs
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Beta Weights
Regression coefficeints for standardized data
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Multiple Regression Methods
Forward Selection
Stepwise
Backward Elimination
Hierarchical Multiple Regression
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Forward Selection Method Steps
1. Start with correlation matrix (pearson r table)
2. First X variable added has highest correlation with Y variable
3. Further additions of X variables are added in order of how much unique variance they can account for.
**Variables that add uniqueness**
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Stepwise Multiple Regression
Same process as forward selection
Each step considered the Rsquared
Each step the algorithm may remove a variabel that was previously added if it does not decrease the Rsquared
This occurs if ta variable no longer accounts for a significant portion of unique variance in the model
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Backward Elimination
All X variables forced into the model
Removes variables by which effects Rsquared the least.
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Hierarchical Method
Allows researchers to dictate the order in which X variables are added
Used to examine a specific modelor hypothesis
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Multicollinearity
When IVs are correlated with each other
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Singularity
An extreme form of multicollinearity, perfect linear relationship between variables.
