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PSY 207 Study Guide - Spring 2019, Comprehensive Midterm Notes - Standard Deviation, Normal Distribution, Statistical Inference


Department
Psychology
Course Code
PSY 207
Professor
Erica Goddard
Study Guide
Midterm

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PSY 207

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Ch 1: Statistics for Psychology: An Introduction
What’s a Statistic?
A set of tools used to organize, describe, and analyze numerical observations
Why are they important?
These tools are used to describe and analyze numerical observations derived from populations and
samples
Populations and Samples
Population : The set of all individuals of interest
Sample: A subset of a population
We use different terms to refer to the statistics used for populations and samples
Parameter: A numerical description of a characteristic of a population
average # of hours of sleep for entire population of depressed individuals
Statistic: A numerical description of a characteristic of a sample
average # of hours of sleep for those in our study
Parameters and Statistics
The term statistics is used to refer to the whole set of tools we use to describe and analyze numerical
observations
A statistic refers to a specific tool applied to samples
E.g., an average for a sample
A parameter refers to a specific tool applied to populations
E.g., an average for a population
Statistic describes Sample
Parameter describes Population
Descriptive vs Inferential Statistics
Descriptive statistics: Statistical procedures used to summarize, organize, and simplify the data
Examples: Arithmetic Average (statistical mean), standard deviation, Quartiles, etc.
Inferential statistics : Techniques to study samples and make use of generalizations about the population from
which they were selected
T-statistic, F-Statistic, Chi-Square, correlation coefficient ®
Inferential Statistics
Tools for making inferences from observations
Tools for generalizing beyond the available observations
Allows for inferences about populations based on samples
Sampling Error
There may be discrepancies between the sample and the population
A sample is not a perfect picture of a population
The discrepancy between the sample statistic and the population parameter is sampling error
For example: Average # of hours depressed people sleep
For sample = 12 hrs/per night
population 11.25 hrs/per night The .75 difference can be attributed to sampling error
Data
Collection of numerical observations from a survey or experiment
a single datum is a raw score
Qualitative versus Quantitative Data
Qualitative data : A single observation which represents a class or category (sometimes referred to as
categorical data)
Marital status, religious affiliation, etc.
Quantitative Data : A single observation is an amount or a count
Reaction time, height, performance accuracy, etc
Discrete versus Continuous Data
Discrete data consist of a countable number of possible values
e.g., number of cars in a parking lot
countable with integers
Continuous data consist of an infinite number of possible values on a scale in which there are no gaps or
interruptions
heights: 72.5 inches, 72.55 inches, 72.575 inches . . . .
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weights: 160.00 pounds, 160.5 pounds . . .
number of hours of sleep: 8.6 hours, 6.4 hours, 10.2 hours . . .
Qualitative data are always discrete
there’s no gray area with categories
But, Quantitative data are not always continuous:
number of cars in parking lot is discrete and quantitative
Experimental Design and Other Considerations
Experimental Design
Variable: A characteristic or property of organisms, events, or objects that can take on different values
height, weight, IQ, mood, degree of anxiety, personality type, etc.
Can be identified by letters such as X, Y, or Z
Constant: A characteristic or property that does not change
π is a constant : 3.1416 . . .
– to convert proportions to percentages, you multiply by a constant: .5 X 100 = 50%
Independent Variable (IV): a variable that is manipulated by the investigator
Dependent Variable (DV): a variable that is measured by the investigator
We conduct an experiment to determine if a new antidepressant drug is effective
We have two groups of depressed participants
Importance of Random Assignment in controlling for extraneous variables
We give one group an antidepressant drug
Experimental or treatment condition
We give the other group a placebo
Control condition (i.e., no treatment)
We measure symptoms of depression over the course of a month for both groups
Other Relevant Study Designs
Quasi-Experimental (“non-experimental”): Cases where researcher has no control of group assignment
Example, when comparing pre-existing , categorical groups
(E.g. gender)
Inability to rigorously control for extraneous variables
Example:
Pre- and Post-Test studies
Changes observed in DV may be a product of the passage of time.
Non-Equivalent Groups
Inability to control assignment to group due to previously established membership
Correlational study: Investigator measures two DVs and looks for a relationship
Is there a relationship between vocabulary size and age?
Key limitation: CORRELATION DOES NOT DETERMINE CAUSATION
Scales of Measurement
The answers to the following three questions appear to be the same:
What number did you wear in the race? 10
What place did you finish? 10
How many minutes did it take you to finish? 10
Are these answers equivalent?
No, because each answer of piece of data represents a different scale of measurement
Scales of Measurement are . . .
The methods of assigning numbers to objects or events
There are four scales of measurement:
Nominal: Refers to data that consist of names, labels, or categories - “nominal” from Latin for “name”
Numeric associations with labels are arbitrary and are used only to identify an object or event
Data cannot be meaningfully arranged in order
There is nothing in particular that requires use of numbers -- any label would suffice
Ordinal: Refers to data or scores that can be arranged in some order
Numbers are used to identify an object or event (nominal) and to tell us the rank order of each
object or event
NAME + ORDER
Interval
Refers to data that have meaningful differences between scores
Numbers are used to identify an object or event (nominal) and to tell us the rank order of each
object or event (ordinal)
NAME + ORDER + INTERVALS
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Two defining principles: 1.) Equidistant scale
2.) no true zero
Equidistant Scales: Those values whose intervals are distributed in equal unit
The differences or distances (intervals) between the scores are meaningful, unlike nominal or ordinal
data
However, a zero point may be lacking or it may be arbitrary
Celsius and Fahrenheit temperature scales are both interval scales
Zero degrees in both is determined “arbitrarily”
That is, zero does not mean the absence of heat
Ratio: Refers to data on a scale with a true zero point
Has all properties of nominal, ordinal, and interval scale
Is an interval scale with a true zero
True zero point: Complete absence of data being measured
NAME + ORDER + INTERVALS + TRUE 0
Note on Statistical Notation
read as “the sum of”
X means to add all the scores for variable X
X^2 means first square each value of X, then add all of those squared values
(X+1) means first add 1 to each value of X, then add all of those new values
(X+1)^2 means (1) add 1 to each value of X, (2) square each of those new values, (3) add all of those squared
values
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