Test One - Chapters 1-6 Flashcards
Variability
The degree to which scores in a distribution are spread out
How much distance to expect between one score and another
Standard Deviation
The distance between each score and the mean
The average distance from the mean
Most commonly used measure of variability
Standard Deviation for Samples
Samples are consistently less variable than their population
Sample variability is a biased estimate of population variability
Consistently underestimates the population value
Descriptive Statistics
Organizes and summarizes info from a research study
Inferential Statistics
Determines what conclusions can be drawn from a research study
- use the sample data as the basis for answering questions about the population
> to accomplish this, typically built around the concept of probability
Statistics
A set of mathematical procedures for organizing, summarizing and interpreting info
Parameter
A value that describes a population
i.e. 65% are female
Statistic
A value that describes a sample
Sampling Error
Discrepancy between the sample and the population
Unpredictable, random differences that exist between samples
Operational Definition
A statement of procedures (operations) used to define research variables
Discrete Variable
Variable with separate, indivisible categories
Continuous Variable
Infinite number of value between two observed values
Deviation Score
x-u
u= mew
Sum of deviation scores should always be 0
Nominal Scale
classify individuals into categories that have different names
eg. gender, university, etc.
direction of difference = no
magnitude of difference = no
Ordinal Scale
set of categories organised in an ordered sequence
eg. t-shirt size, ranked place in a race, class, etc.
direction of difference = yes
magnitude of difference = no
Interval Scale
categories form a series of intervals all of the exact same size
eg. temperature or golf scores
- arbitrary zero point -> zero represents the presence of something
Ratio Scale
categories form a series of intervals all of the exact same size
eg. distance, time, weight
- absolute zero point -> zero represents the absence
N v.s. n
N = total number of scores in a population n = total number of scores in a sample
u (mew) v.s. M
u (mew) = mean of a population
i.e. Σx/N
M = mean of a sample
i.e Σx/n
Order of Operations
(1) parentheses (_____)
(2) squaring
(3) x or /
(4) Σ
(5) +/-
Central Tendency
single value that defines the average score
identifies the center of the distribution
no single measure will always produce a central, representative value in every situation
uses mean, median and mode to find “center”
Weighted Mean
combining two sets of scores to find the overall mean
*below the 1 and 2 represent the set
Σx1 + Σx2 / n1 + n2
Rules of the Mean
changing the value of any score will change the mean
Bimodal or Multimodal
two or more modes
The Mode is preferred when…
nominal scale of measurement
discrete variables
describing the shape of the distribution graph
The Mean is preferred when…
preferred measure of central tendency
The Median is preferred when…
few extreme scores
unknown or undetermined scores
no upper or lower limit for one category
Variability
the degree to which scores in a distribution are spread out
how much distance to expect between one score and another
Standard Deviation
most commonly used measure of variability
the distance between each score and the mean
the average distance from the mean
σ v.s. s
σ = standard deviation for a population s = standard deviation for a sample
σ²
variance
= SS/N
Computational Formula
SS = ΣX2 - (ΣX)2/N
Standard Deviation for Samples
samples are consistently less variable than their population
sample variability is a biased estimate of population variability
consistently underestimates the population value
to correct for this do n-1 i.e. sample variance is: s2 = SS/n-1 sample standard deviation is: s = square root of SS/n-1
z-Scores
- statistical technique that uses the mean and standard deviation to transform each x-value into a standardized score
- tells us exactly where x-values are located in a distribution
- sign tells whether the score is above (+) or below (–) the mean
- number tells distance (number of standard deviations) from the mean
Characteristics of a z-score distribution
- shape of z-score distribution will be the same as the original
- each individual score stays in the same position
- the mean is always = 0
- the standard deviation is always = 1
Probability
For a situation in which several different outcomes are possible, the probability for any specific outcome is defined as a fraction or a proportion of all the possible outcomes. If the possible outcomes are identified as A, B, C, D, and so on, then:
probability of A =
number of outcomes classified as A / total number of possible outcomes
- probability gives us a connection between populations and samples
The role of probability in inferential statistics
Probability is used to predict what kind of samples are likely to be obtained from a population.
Probability establishes a connection between samples and populations. Inferential statistics rely on this connection when they use sample data as the basis for making conclusions about populations.
Simple Random Sample
A simple random sample requires that each individual in the population has an equal chance of being selected.
Random Sampling
• each individual in the population has an equal chance of being selected for a sample.
p = 1/N
• the probabilities must stay constant from one selection to the next if more than one person is selected
- sampling with replacement
A sample produced by this technique is known as a random sample.
Probability and Normal Distribution
- highest frequencies are in the middle (close to the mean)
* lowest frequencies are in the tails (highest and lowest scores)
Probability and z-Score Distribution
- percent of scores that fall within each region
* regions on left side of 0 are the same as the right side (symmetrical)
