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Research and Design Test 2
na
58
Psychology
Undergraduate 2
02/02/2013

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Term
Definitional Formula for Sum of Squares
Definition
SS = Sigma(X - mu)^2

Best to use if you have a small group of scores and the mean is a whole number.
Term
Three Steps of finding Sum of Squares - Definitional
Definition
1. Find each deviation score (X - mu)
2. Square each deviation score (X - mu)^2
3. Add the squared deviations.
Term
Computation Formula for Sum of Squares (population)
Definition
SS = SigmaX^2 - [(SigmaX)^2]/N

Use most of the time.
Term
Three Steps of finding Sum of Squares - Computational (population)
Definition
1. Square each score and then add the squared values. SigmaX^2
2. Find the sum of scores, then square this total and divide the results by N.
3. Subtract the second part from the first.
Term
Population Variation Equation
Definition
variance = SS/N
Term
Population Standard Deviation Equation
Definition
standard deviation = Square Root of: (SS/N)
Term
Three Steps to finding Sum of Squares for a Sample
Definition
1. Find the deviation for reach score: deviation = X - M
2. Square each deviation: squared deviation = (X - M)^2
3. Add the squared deviations: SS = Sigma(X - M)^2
Term
Definitional Formula for Sum of Squares for Sample
Definition
SS = Sigma(X - M)^2
Term
Computational Formula for Sum of Squares for Sample
Definition
SS = SigmaX^2 - [(SigmaX)^2/n]
Term
Sample Variance Formula
Definition
s^2 = SS/(n-1)
Term
Sample Standard Deviation Formula
Definition
s = Square Root of s^2 = Square Root of SS/(n - 1)
Term
Degrees of Freedom Formula
Definition
df = n = 1
Term
Error Variance
Definition
The sample variance represented unexplained and uncontrolled differences between scores. (In the context of inferential statistics).
Term
Variability
Definition
Measure the extent to which our observations are spread out or clustered together.
Term
Range
Definition
A type of variability, difference between highest and lowest value.
Term
Interquartile Range (IQR)
Definition
A type of variability, range of middle 50% (chop off top and bottom 25%)
Term
How to find IQR
Definition
1. Find overall median
2. Throw it away
3. Find median for upper/lower half
4. Subtract
Term
Variance
Definition
A form of variability, measures, on average how far away are our observations from the mean? What is the average deviation?
Term
z-score
Definition
Specifies the precise location of each X value within a distribution. (+ or -) signifies whether the score is above the mean (positive) or below the mean (negative).
Term
Standard Distribution
Definition
Composed of scores that have been transformed to create predetermined values for mu and sigma (o). Used to make dissimilar distributions comparable.
Term
Probability
Definition
Defined as a fraction or a proportion of all possible outcomes for a situation in which several different outcomes are possible.
Term
Formula for Probability
Definition
If the possible outcomes are identified as A, B, C, and D then:

Probability of A = (number of outcomes classified as A)/(total number of possible outcomes)
Term
Random Sample
Definition
Requires that each individual in the population has an equal chance of being selected. A second requirement, necessary for many statistic formulas, states that the probabilities must stay constant from one selection to the next if more than one individual is selected.
Term
Sampling Error
Definition
The natural discrepancy, or amount of error, between a sample statistic and its corresponding population parameter.
Term
Distribution of Sample Means
Definition
Collection of sample means for all the possible random samples of a particular size (n) that can be obtained from a population.
Term
Sampling Distribution
Definition
A distribution of statistics obtained by selecting all of the possible samples of a specific size from a population.
Term
Expected Value of M
Definition
The mean of a distribution of sample means is equal to the mean of population scores, and mu.
Term
Standard Error of M
Definition
Standard error provides a measure of how much distance is expected on average between a sample mean (M) and the population mean (mu)
Term
Law of Large Numbers
Definition
States that the larger the sample size (n), the more probable it is that the sample mean will be close to the population mean.
Term
Hypothesis Test
Definition
A statistical method that uses sample data to evaluate a hypothesis about a population.
Term
Null Hypothesis
Definition
States that in the general population there is no change, no difference, or no relationship. In context of an experiment, this predicts that the independent variable has no effect on the dependent variable for the population.
Term
Alternative Hypothesis
Definition
States that there is a change, a difference or a relationship for the general population. In the context of an experiment, this predicts that the independent variable does have an effect on the dependent variable.
Term
Alpha Level / Level of Significance
Definition
A probability value that is used to define the concept of "very unlikely" in a hypothesis test.
Term
Critical Region
Definition
Composed of the extreme sample values that are very unlikely (as defined by the alpha level) to be obtained if the null hypothesis is true. The boundaries for this are determined by the alpha level. If sample data fall here, the null hypothesis is rejected.
Term
Type I Error
Definition
Occurs when a researcher rejects a null hypothesis that is actually true. This means the researcher concludes that a treatment does have an effect when it in fact has no effect.
Term
Type II Error
Definition
Occurs when a researcher fails to reject a null hypothesis that is really false. In a typical research situation, this means that the hypothesis test has failed to detect a real treatment effect.
Term
Significant / Statistically Significant
Definition
A result is said to be this if it is very unlikely to occur when the null hypothesis is true. That is, the result is sufficient to reject the null hypothesis. Thus, a treatment has a significant effect if the decision from the hypothesis test is to reject the null hypothesis.
Term
Directional Hypothesis Test / One-Tailed Test
Definition
The statistical hypotheses specify either an increase or a decrease in the population mean. That is, they make a statement about the direction of the effect.
Term
Effect Size
Definition
The measure of this is intended to provide a measurement of the absolute magnitude of a treatment effect, independent of the size of the samples being used.
Term
Power
Definition
The probability that the test will correctly reject a false null hypothesis. That is, this is the probability that the test will identify a treatment effect if one really exists.
Term
Raw Scores
Definition
Original, unchanged scores that are the direct result of measurement.
Term
1. Each z-score tells the exact location of the original X value within the distribution.
2. The z-scores form a standardized distribution that can be directly compared to other distributions that also have been transformed into z-scores.
Definition
Two useful purposes of transforming X values into z-scores.
Term
Deviation Score
Definition
The distance in points between X and mu and indicates whether X is located above or below the mean.
Term
Shape of a z-score
Definition
Will be the same as the original distribution of raw scores.
Term
Mean of a z-score
Definition
The z-score distribution will always have a mean of zero.
Term
Standard Deviation of a z-score
Definition
The distribution of z-scores will always have a standard deviation of 1.
Term
Relabeling
Definition
z-score transformation
Term
p
Definition
probability
Term
Sampling with Replacement
Definition
The process of returning each individual to the population before you make the next selection.
Term
Unit Normal Table
Definition
This table lists proportions of the normal distribution for a full range of possible z-score values.
Term
Body
Definition
Larger section of the normal distribution separated by a vertical line.
Term
Tail
Definition
Smaller section of the normal distribution separated by a vertical line.
Term
1. If you know a specific location (z-score) in a normal distribution, you can use the table to look up the corresponding proportions.
2. If you know a specific proportion (or proportions), you can use the table to look up the exact z-score location in the distribution.
Definition
Two purposes of the unit normal table.
Term
1. Transform the X values into z-scores
2. Use the unit normal table to look up the proportions corresponding to the z-score values.
Definition
Two steps to answering probability questions about scores from a normal distribution.
Term
Percentile Rank
Definition
Defined as the percentage of the individuals in the distribution who have scores that are less than or equal to the specific score.
Term
Percentile
Definition
When a score is referred to by its percentile rank.
Term
Central Limit Theorem
Definition
For any population with mean mu and standard deviation sigma, the distribution of sample means for sample size n will have a mean of mu and a standard deviation of sigma divided by square root of n and will approach a normal distribution as n approaches infinity.
Term
1. The population from which the samples are selected is a normal distribution.
2. The number of scores (n) in each sample is relatively large, around 30 or more.
Definition
How to make the distribution of sample perfectly normal.
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