Statistics Quiz #1

Type II error

we agree with null, when it is in fact false.

theorietical construct

thing you are taking measurement of (ex. age, gender, opinion).

scales of measurement

distinguishing between different types of variables.

ordinal scales

order different possibilities.

Variability

how spread our is the data, how far away from the median or mean are the values.

standard deviation

the square root of the variance

platykurtic data set

too flat.

mesokurtic data set

pointiness is just about perfect.

leptokurtic data set

too point

z-score

(raw score-mean)/standard deviation

boxplots

provide visual depiction of the median, the interquartile range and range of data.

inferential statistics

uses measurements from the sample of subjects in the experiment to compare treatment groups and make generalizations about large populations.

probability theory

how often different kinds of events will happen.

probability

how often something is too happen.

frequentist view

defines probability as a long-run frequency, objective, and unambiguous.

Bayesian view

subjectivist view, allows you to assign probabilities to an event you want, but we cannot be be purely objective.

Law of Probability

if we add up all the probabilites of the events, they sum to 1.

binomial distribution

The probability distribution of a binomial random variable, discrete.

normal distribution

bell curve distribution, use two parameters 1. mean of distribution 2. standard dev. of the distribution, continuous.

t distribution

arises in situations where you think that the data actually follow a normal distribution but you do not know the mean or the standard dev.

x squared deviation

seen in categorical data analysis.

sampling theory

specifies assumptions upon which your statistical inferences rely.

population

set of all possible people.

sampling method

relationship between two depends on the procedure by which the sample was selected.

stratified sampling

population is or can be divided into several different sub-populations.

snowball sampling

sampling from a "hidden" or hard to access population, gets data in situations that might be challenging otherwise.

convienence sampling

Samples are are chosen in a way that is convenient to the research and not randomly selected from the population of interest.

population parameters

characteristics of the entire population.

sample statistics

properties of my data set.

sampling distribution of the mean

replicating an experiment over and over again.

sampling distribtution of the maximum

keeping track of highest (max) number in each set of data taken.

Central Limit Theorem

tells us if the pop. distribution has mean μ and standard dev σ, then the sampling distribution of the mean also has mean μ and the standard error of the mean is SEM = σ/ square root N

σ

population standard deviation

σ (hat)

estimate of population standard deviation

s^2

sample variance

σ^2

population variance

σ hat^2

estimate of population variance.

hypothesis testing

researcher has theory about the world and wants to determine whether or not the data actually support that theory.

research hypotheses

fundamentally about psychological constructs,

statistical hypotheses

must be mathematically precise, and correspond to specific claims about the characteritiscs of the data generating mechanism.

type I error

reject null, when it is true.

critical region

corresponds to those values of X that would lead us to reject null hypothesis

effect size

how big the difference between the true population parameters and the parameter values that are assumed by null.

x^2 (chi-squared) goodness of fit test

use when you have a table of observed frequencies of different categories, and the null hypothesis gives you a set of "known" probabilities to compare them to.

x^2 (chi-square) test of independence

used when you have a contingency table of two categorical variables. the bull is that there is no relationship or association between variables.

Measurement

data collection.

self report

fast, cheap, easy, only works if people understand the question.

operationalism

taking meaningful but vague concept and turn it into a precise measurement.

measure

method or tool used to make observations.

nominal scale

categories, no particular realtionship between the different possibilities.

interval scales

difference between variables, number does not have a natural zero.

ratio scale

difference between two numbers gathered for data (ex. ryan took 2.1 sec to respond, and Carl took 3.1 seconds to respond

--> 3.1-2.1= 1.

continuous variable

between any two values, it is possible to a have another number in between.

discrete variable

no possible number in the middle. set value.

Likert Scale

choose between several options (strongly agree, strongly disagree...)

Reliability

consistency of measurement

validity

how accurate the measure is

internal validity

extent to which you are able to draw the correct conclusions about the relationship between two variables.

external validity

extent you see the same pattern of results in real life, that you saw in your study.

construct validity

if you are measuring what you want to measure.

confounder variable

additional, often unmeasured variable, that turns out to be related to both predictors and outcome.

descriptive statistics

summarizing data in compact, easily understood fashion.

central tendency

average or middle of where your data lies.

mean

average.

N

number of numbers.

median

middle value.

mode

most frequently occurring.

frequency table

A table that uses numbers to record data.

range

biggest value - smallest value

interquartile range

difference between the 25th percentile and 75th percentile is taken.

Variance

standard deviation squared

histogram

bars touching, interested in shape of distribution.

F distribution

compare two x squared distributions together.

μ / M_pop

population mean

μ w a hat

estimated population mean

x̄ / M

sample mean

σ / SD_pop

Population Standard Deviation

σ w a hat

estimated population standard deviation

S / SD

Sample Standard Deviation

S x̄ / SEM / SE

Standard Error

SD formula

CI formula

M + SE (times a critical value)

SE formula