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

by OC1140114

School

University at BuffaloDepartment

PsychologyCourse Code

PSY 207Professor

Erica GoddardStudy Guide

MidtermThis

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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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