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Descriptive Statistics
Procedures for describing data
Mean, median, and mode
Inferential statistics
Procedures for drawing conclusions about data
Correlation, regression, t-tests, f tests
Population
The complete set of events in which you are interested.
All Pysch 60 students at UCSD.
Parameters
Numerical values summarizing population data.
The average final grade of all PSYCH 60 students at UCSD.
Sample
A set of actual observations: subset of a population
A section of PSYCH 60 students at UCSD.
Statistics
Numerical values summarizing sample data
The average final grade of this section of PSYCH 60 students at UCSD
Random Sample
A sample in which each member of the population has an equal chance of inclusion.
Why is random sampling important?
It increases the chance that the sample will be representative of the population.
How do you get random samples?
Random number generator Table of random numbers Records, locations, processes, etc. that provide representative samples.
What are the two kinds of data?
Measurement(quantitative) data and Categorical(frequency or count data)
Measurement (quantitative) data
Data obtained by measuring objects or events.
Numbers that represent aggression, height, working memory capacity, etc.
Categorical (Frequency or count data)
Data representing counts or numbers of observations in each category.
"23 instructors were in favor of the new curriculum and 27 were not"
Nominal Scale
Numbers used only to distinguish objects
An athlete's # or label Gender, male, female, nonbinary. (1 = male)(2 = female)(3 = nonbinary)
Ordinal Scale
Numbers used only to place objects in order.
"Rank: 1st, 2nd, 3rd" More than labels, specific ranking Dawn, day, dusk, night. (sequence)
Interval Scale
A scale on which equal intervals between objects represent equal differences - differences are meaningful
Temperature: 0 degrees does not mean there's no temperature.
Ratio Scale
A scale where true zero point-ratios are meaningful
Length, weight, volume, speed, hormones, etc. All measured on ratio scales. A zero means no quantity A swimmer's lap/speed
Variables
Properties of objects or events that can take on different values.
Anything that can be measured is a variable Height, speed, gender, etc.
Discrete Variables
Variables that can take on a small set of possible values. Gender, marital status, number of TV's in your house.
Continuous Variables
Variables that can take on any value Height, speed, cortisol, working memory capacity
Independent Variables
Those variables controlled by the experimenter.
Dependent Variables
The variables being measured: the data or score. IV is manipulated, DV is measured
Random Assignment
The allocation of participants to groups by a random process.
Frequency Distribution
A distribution in which the values of the dependent variable are tabled or plotted against their frequency of occurrence.
Histogram
A graph in which a rectangle is used to represent frequencies of observations within each interval.
Y-axis
The vertical axis
X-axis
The horizontal axis
Stem-and-leaf display
A graphical display presenting original data arranged into a histogram.
Leading digits (most significant digits)
The leftmost digits in a number The 1 in 15
Trailing digits (less significant digits)
The digits to the right of the leading digits. The 5 in 15
Stem
Vertical axis of display containing the lead digits
Leaves
Horizontal axis of display containing the trailing digits.
Line graph
A graph in which the y values corresponding to different values of x are connected by a line.
Bar graph
A graph in which the frequency of occurrence of different values of x is represented by the height of a bar.
Symmetric
Having the same shape on both sides of the center.
Ex. IQ scores distribution
Unimodal
A distribution of having one distinct peak
Ex. IQ scores distribution
Bimodal
A distribution having two distinct peaks
Ex. Scores on an exam where there are a lot of Cs and As, but barely any Fs, Ds, and Bs.
Modality
The term is used to refer to the number of major peaks in a distribution.
Or mode. In distribution, it's represented in peaks.
Skewness
The degree to which a distribution is asymmetrical. No skew is perfectly symmetrical.
Negatively Skewed
A distribution that rails off to the left.
Ex. A distribution of exam scores when the exam is easy. Data is trailing off of the left
Positively Skewed
A distribution that trails off to the right.
Ex. Lots of scores on the left end and trails off to the right Low to High scores
Central Tendency
A measure of the center of a distribution. Often mean, median, or mode.
Mode
The most commonly occurring score.
Median
The score corresponding to the point having 50% of the observations below it when the observations are arranged in numerical order.
Median Location
The location of the median in an ordered series: (N + 1) / 2 It's the middle number in an odd set of ordered numbers
Mean
The sum of scores divided by the number of scores The mean is the average.
Dispersion (Variability)
The degree to which individual data points are distributed around the mean.
Refers to how much scores vary or differ from the mean
Range
The distance from the lowest to highest score.
Ex. highest is 5, lowest is 1 = 5 - 1 = 4
Outliers
An extreme point that stands out from the rest of the distribution.
Interquartile Range
The range of the middle 50% of the observations.
two inner 25% are the inner half = 50%
Σ
The Sum
N
The number of observations in a population
n
The number of observations in a sample
μ
Population mean
X̄
Sample Mean
s^2
Sample variance - The sum of the squared deviations from the mean, divided by N - 1
S
Sample Standard Deviation - The square root of the sample variance. Rough idea (The average deviation from the mean)
σ^2
Population variance
σ
Population standard deviation
Degrees of Freedom (df)
The number of independent pieces of information remaining after estimating one or more parameters.
Boxplot (box-and-whisker plot)
A graphical representation of the dispersion of a sample.
Normal distribution
A specific distribution having a characteristic bell-shaped form. Ex. IQ scores are normally distributed, they fall on a normal distribution.
Standard Normal Distribution
A normal distribution with a mean equal to 0 and variance equal to 1. Uses z scores!
z score
The number of standard deviations above or below the mean. z scores range from -4 to +4 if its a perfectly normal distribution.
Percentile
The point below which a specified percentage of the observations fall.
Note 
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