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)

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

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"

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

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"

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;

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

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)

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)

Frequency Distribution

[image]

Has zero excess kartosis; ex: normal distribution

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

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

Variability: Deviation, Standard Deviation, Sum of Squares

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

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

σ=√SS/N

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

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

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]

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

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