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1

Descriptive Statistics

Procedures for describing data

Mean, median, and mode

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Inferential statistics

Procedures for drawing conclusions about data

Correlation, regression, t-tests, f tests

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Population

The complete set of events in which you are interested.

All Pysch 60 students at UCSD.

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Parameters

Numerical values summarizing population data.

The average final grade of all PSYCH 60 students at UCSD.

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Sample

A set of actual observations: subset of a population

A section of PSYCH 60 students at UCSD.

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Statistics

Numerical values summarizing sample data

The average final grade of this section of PSYCH 60 students at UCSD

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Random Sample

A sample in which each member of the population has an equal chance of inclusion.

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Why is random sampling important?

It increases the chance that the sample will be representative of the population.

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How do you get random samples?

Random number generator Table of random numbers Records, locations, processes, etc. that provide representative samples.

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What are the two kinds of data?

Measurement(quantitative) data and Categorical(frequency or count data)

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Measurement (quantitative) data

Data obtained by measuring objects or events.

Numbers that represent aggression, height, working memory capacity, etc.

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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"

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Nominal Scale

Numbers used only to distinguish objects

An athlete's # or label Gender, male, female, nonbinary. (1 = male)(2 = female)(3 = nonbinary)

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Ordinal Scale

Numbers used only to place objects in order.

"Rank: 1st, 2nd, 3rd" More than labels, specific ranking Dawn, day, dusk, night. (sequence)

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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.

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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

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Variables

Properties of objects or events that can take on different values.

Anything that can be measured is a variable Height, speed, gender, etc.

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Discrete Variables

Variables that can take on a small set of possible values. Gender, marital status, number of TV's in your house.

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Continuous Variables

Variables that can take on any value Height, speed, cortisol, working memory capacity

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Independent Variables

Those variables controlled by the experimenter.

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Dependent Variables

The variables being measured: the data or score. IV is manipulated, DV is measured

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Random Assignment

The allocation of participants to groups by a random process.

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Frequency Distribution

A distribution in which the values of the dependent variable are tabled or plotted against their frequency of occurrence.

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Histogram

A graph in which a rectangle is used to represent frequencies of observations within each interval.

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Y-axis

The vertical axis

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X-axis

The horizontal axis

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Stem-and-leaf display

A graphical display presenting original data arranged into a histogram.

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Leading digits (most significant digits)

The leftmost digits in a number The 1 in 15

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Trailing digits (less significant digits)

The digits to the right of the leading digits. The 5 in 15

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Stem

Vertical axis of display containing the lead digits

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Leaves

Horizontal axis of display containing the trailing digits.

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Line graph

A graph in which the y values corresponding to different values of x are connected by a line.

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Bar graph

A graph in which the frequency of occurrence of different values of x is represented by the height of a bar.

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Symmetric

Having the same shape on both sides of the center.

Ex. IQ scores distribution

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Unimodal

A distribution of having one distinct peak

Ex. IQ scores distribution

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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.

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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.

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Skewness

The degree to which a distribution is asymmetrical. No skew is perfectly symmetrical.

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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

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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

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Central Tendency

A measure of the center of a distribution. Often mean, median, or mode.

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Mode

The most commonly occurring score.

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Median

The score corresponding to the point having 50% of the observations below it when the observations are arranged in numerical order.

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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

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Mean

The sum of scores divided by the number of scores The mean is the average.

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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

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Range

The distance from the lowest to highest score.

Ex. highest is 5, lowest is 1 = 5 - 1 = 4

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Outliers

An extreme point that stands out from the rest of the distribution.

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Interquartile Range

The range of the middle 50% of the observations.

two inner 25% are the inner half = 50%

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Σ

The Sum

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N

The number of observations in a population

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n

The number of observations in a sample

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μ

Population mean

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X̄

Sample Mean

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s^2

Sample variance - The sum of the squared deviations from the mean, divided by N - 1

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S

Sample Standard Deviation - The square root of the sample variance. *Rough idea* (The average deviation from the mean)

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σ^2

Population variance

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σ

Population standard deviation

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Degrees of Freedom (df)

The number of independent pieces of information remaining after estimating one or more parameters.

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Boxplot (box-and-whisker plot)

A graphical representation of the dispersion of a sample.

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Normal distribution

A specific distribution having a characteristic bell-shaped form. Ex. IQ scores are normally distributed, they fall on a normal distribution.

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Standard Normal Distribution

A normal distribution with a mean equal to 0 and variance equal to 1. Uses z scores!

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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.

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Percentile

The point below which a specified percentage of the observations fall.

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