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Statistics
Statistics Test 1: Standard deviations, z scores, and sample means
50
Mathematics
Undergraduate 3
02/20/2010

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Term
Variable
Definition
Somehing that can change or have different values
Term
Data (raw score) (X)
Definition
The measurement obtained for each individual
Term
Parameter
Definition
a characteristic that describes a POPULATION
Term
Statistic
Definition
a characteristic that describes a SAMPLE
Term
Descriptive Statistics
Definition
consist of statistical procedures that are used to simplify and summarize data
Term
Inferential Statistics
Definition
are methods that use sample data to make general statements about a population
Term
Sampling Error
Definition
Samples are expected to be REPRESENTATIVE of the population but they are not perfect. There is usually some discrepancy between the sample and the population
Term
The Correlational Method
Definition

Measuring two variables as they exist naturally for a set of individuals. The results can demonstrate of a relationship between two variables but CANNOT PROVIDE AN EXPLANATION FOR THE RELATIONSHIP

 

Ex: The relationship between student wake up time and school grades (the wake up time is not manipulated)

Term
The Experimental Method
Definition
The researcher MANIPULATES oen variable by changing its value from one level to another and excercises CONTROL over the research situation being examined. The goal is to demonstrate a cause and effect relationship between two variables
Term
Three techniques to control other variables
Definition

Random Assignment: each participant has an equal chance of being assigned to each of the treatment conditions

     Matching: ensures equivalent groups or equivalent environments

    Holding constant: ex: using only 10 year old children

Term
Independent Variable
Definition
Variable that is manipulated by the experimenter (the treatment condition to which subjects are assigned)
Term
Nonexperimental Methods
Definition

These are not true experiments but measure the relationship between variables by comparing groups of scores

The experimenter has no control over the assignment of participants to groups because these groups are pre-existing. Variable is often called "quasi-experimental"

Term
Discrete Variable
Definition
Consists of separate. indivisible categories. Commonly restricted to whole numbers (the number of children in a family, students in a class)
Term
Continuous variable
Definition

Not limited to separate indivisible cateogires because they can be divided into an infinite number of fractional parts. When measuring these variables it should be rare to obtain identical measurements in each individual and each measurement category is actual an INTERVAL that must be defined by boundaries

Ex: Time, weight, height etc

4 and 5 really mean 3.5-4.5 and 4.5-5.5

Term
Real Limits
Definition

The upper and lower boundaries which designate intervals on a continuous variable

Ex: 3.5 is the lower real limit of 4 and 4.5 is its upper real limit. All scores between 3.5 and 4.5 are considered to be "4"

Term
The Nominal Scale
Definition

Classifies individuals into categories with different names but only allow us to tell that the individuals are different, not whether one is better than the other or how big the difference is

ex: female, male; team 1, team 2; black, blue;

Term
The Ordinal Scale
Definition

Individuals placed on an ordinal scale have different names and also have a fixed order that can relay rank. However, even though you can tell that two individuals are different and the direction of the difference (better or worse, faster, or slower) you cannot tell by how much

ex: placement in a race, food preferences, etc

Term
Interval Scale
Definition

A series of ordered categories that are exactly the same size. You can not only tell that the individuals are different and which direction the difference is but also by how much (the distance between 1 and 2 place is the exact same as the difference between 2 and 3 and so on)

Contains an arbitrary zero point (there is no real zero except for convenience)

Term
Ratio Scale
Definition

The exact same as an interval scale except that the zero point has a meaningful value

ex: you have 0 pizzas, 0 pencils

With interval 0 is representative such as 0 degrees farenheit (it doesn't mean there is no temperature)

Term
N and n
Definition
N represents the number of people in a POPULATION, while "n" represents the number of people in a SAMPLE
Term
[image]x
Definition
Sum of all scores...the expression means to add all the scores together for the variable X
Term
IMPORTANT: We assume that all survey or questionnaire TOTAL SCORES are interval-scaled (this does not mean each individual question but the summation of the answers to those questions)
Definition
Term

Frequency Distribution

Definition
Descriptive statistics; takes a disorganized set of scores and places them in order from highest to lowest and groups together people with like scores
Term
[image]f=N (n)
Definition
Sigma(frequency) or sum of all frequencies is equal to the number of subjects in the population or sample
Term
The Sum of All Scores in a Distribution Table
Definition
[image]fX
Term
Mesokurtic
Definition

[image]

Has zero excess kartosis; ex: normal distribution

Term
Platykurtic
Definition
Has a negative excess of kurtosis; has a lower, wider peak around the mean and thinner tail[image]
Term
Leptokurtic
Definition
Has a more acute peak above the mean and fatter tails[image]
Term
Cumulative Frequency
Definition
Gives you the reverse of rank...gives you the number of people with THAT SCORE OR BELOW
Term
Percentile Rank
Definition
The porportion of people with a certain score or below that is associated with the upper real limit
Term
Sample Mean (X bar)
Definition
[image]
Term
Population Mean (mew)
Definition
[image]
Term
Mode
Definition
Easiest to calculate, can be used with any kind of variables THE ONLY ONE THAT CAN BE USED WITH NOMINAL-SCALED DATA
Term
Median
Definition
Useful when there are OUTLIERS or the distribution is SKEWED, used to determine OPEN-ENDED values and most appropriate for ORDINAL data
Term
Mean
Definition
Most commonly used, good indicator of an actual average bc all of the numbers are used; when there are outliers in the distribution the mean is heavily influenced by their values
Term
Weighted Mean
Definition

Sometimes  we need to combine two sets of scores and then find the overall mean

Add the sum of scores for sample 1 to the sum of scores for sample 2 and divide by the sum n1+n2

Term
When to Use What
Definition

Descriptive Statistics: Mean, Median, Mode, Shape, Kurtosis, Frequency Distribution

Variability: Deviation, Standard Deviation, Sum of Squares

Term
Deviation
Definition

Simply X - mu

The deviation scores will add up to 0 so the average deviation will not work as a measure of variability

The solution? To get rid of the plus and minus signs by squaring each deviation score and then square root the answer

Term
the Sum of Squared Deviations (Population)
Definition
[image]
Term
Population Standard Deviation
Definition

lowercase sigma (standard deviation) is equal to the square root of the Sum of Squared Devations divded by the population size

σ=√SS/N

Term
Standard Deviation vs Sum of Squares
Definition
The sum of squares is an unscaled measure of variability or dispersion; standard deviation is the scaled version which allows you to calculate variance
Term
Biased Sample
Definition
Samples are less variable than their population counterparts which means that sample results will UNDERESTIMATE the population value
Term
Subtracting/Adding-Multiplying/Dividing: σ from a constant
Definition

Subtracting/Adding to all the scores in a sample will NOT affect the standard deviation becase the distanc between scores does not change

 

Multiplying all scores by a constant causes the standard deviation to be multiplied by the same constant because the distance between scores is getting larger/smaller

Term
The Range
Definition

The highest minus the lowest scores (including upper and lower real limits)

While simple to calculate the range gives too much weight to extreme scores/outliers and does not take into account distribution

Term
The Interquartile Range
Definition

The range of the middle 50% of scores

The 75th percentile score minus the 25th percentile score (the top 25 and the bottom 25)[image]

Term
The Semi-Interquartile Range
Definition

Provides you with the range of approximately the middle 25%

 

The problem with the Interquartile and SemiIQ range is that THEY DO NOT USE INFORMATION FROM ALL OF THE SCORES

Term
σ2 vs. σ
Definition

σ is standard deviation and is represents distance from the mean in units the same as the original scores

σ2 is the population VARIANCE or how spread apart each score will be (is there high variance or low variance)

Variance units are always squared

Term
z scores
Definition
Offer a standardized view of a distribution of scores. The new distribution will always have the same shape as the old one (positively/negatively skewed or normal),a mean of 0 and a standard deviation of 1
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