benchmark quiz pbsi 301

tamu-alwood

statistics

statistics

a set of tools and techniques used for describing, organizing, and interpreting information or data

three basic goals of science

description, prediction, explanation

description

how people behave

rule-based vs rule free play behavior among children

prediction

identifying the factors that influence behavior

when a group has more boys than girls, rule based play is more likely

explanation

identifying the underlying causes of a behavior

boys are competitive? rule based games allow for more competition

how does statistics help science?

help scientists accomplish the three goals

descriptive statistics

used to organize and describe data (counts, means, percentages

inferential statistics

next step after descriptive

used to make inferences about a larger group from a smaller group

allow you to infer the truth about the larger group based on information you at her from smaller group people

sample

the group you are actually collecting data from

(smaller group/subset of the larger group you are interested in)

population

the group you are actually interested in drawing conclusions abou

variable

something that can vary or change or have different values for different individuals

data

information collected from the sample on the variables we are interested in

the actual numbers, measurements, or characteristics that represent the ideas we are interested in

continuous data

data measured on a continuum

all numbers between two endpoints are possible scores

categorical data

data that sorts people into categories (only so many options for the variables)

central tendency

a single number that represents a group of scores

mean, median, mode

mean

the average, sensitive to extreme scores

median

midpoint in set scores, point at which half the scores are bigger and half the scores are smaller, not influenced by extreme scores

mode

the value occurs most frequently in the data set, used for categorical data (not the number)

bimodal

when there is more than one mode

variability

how different scores are from each other

represent the spread or dispersion in the dataset

helps us to understand the nature of our sample and the nature of our variables

range, standard deviation, variance

range

how far apart the scores are from each other, subtract lowest score from highest score, considers only the most extreme values

standard deviation

average amount of variability in a set of data

variance

if you know sd, you know this, rarely reported as a descriptive statistic

how many standard deviations away from the mean is a potential outlier?

anything more than 2 (3 is likely a outlier)

histogram

allows us to see the distribution of our data
- the height of each bar is the number of times each value occurs in our data sat

skewness

lack of symmetry

kurtosis

peaked vs flat distribution

platykurtic

low kurtosis, flat so more variability

leptokurtic

high kurtosis, peaked so less variability

bar graph

show frequency of categorical responses

correlations

how do changes in the value of one variable relate to changed in the value of another variable
- compute when we have scores on two variables

scatterplot

plots one variable on the x-axis and the other on the y-axis
- useful for looking at relationship between two variables

correlation coefficients

assign a single number to describe the relationship between two variables

direction

positive or negative
- the sign
- positive signs indicate positive relationships(scores on the variables move in the same direction)
- neg sign indicates negative relationships (variables move in opposite directions)

strength

magnitude of the coefficient (how far it is from zero)
- if r is 0 then there is no relationship but if r is 1/-1 then there is a perfect relationship

limitations of correlation coefficients

can only be used to identify linear relationships
- restriction of range- occurs when most subjects have similar scores on one of the variables being correlated
- outliers have a big influence on correlation coefficients

correlation matrix

simple way to report a bunch of correlations at one time

coefficient of determination

represents how much variation 2 variables share

coefficient of alienation

the variance left over

reverse causation

the causal direction may be opposite from what has been hypothesized

reciprocal causation

two variables cause each other

measurement

the act or process of assigning numbers to phenomena according to a rule

measurement scales

the type of scale we use has important implications for what kind of statistics we use

nominal scales

measures that split people into categories
- categories must be mutually exclusive
- data is in the form of counts/percentages
=namable

ordinal scales

the number is a ranking
=ordering
- class ranking, candidates for a job, top 10 lists
- not clear how much distance separates the data points on the scale

interval scales

ordering events with equal spacing (based on an underlying continuum
- most common type of scale in psychology
- equal intervals

ratio scale

- similar to interval scale but zero has a specific meaning 0
- zero=ratio

reliability

how do we know that the measure we use works consistently

validity

how do we know that the measure we use measures what it is suppose to

observed score

the score you actually got

true score

true reflection of what you really know

error score

discrepancy between observes score and true score

test retest reliability

does the same person get a similar score when they complete the measure at two different time points

parallel forms reliability

are different forms of the measure equivalent

inter item reliability

internal consistency reliability
- how similar are a person's answer to different items meant to measure the same thing

inter rated reliability

how consistent are the observations made by two or more people

cronbachs alpha

single number that reflects the degree of internal consistency of the items on a scale

content validity

is the measure a good sample of the universe of items that could be used to assess this construct?

criterion validity

Does the measure reflect or relate to what it "should" right now and/or in the future?

construct validity

Is the measure related to other constructs it should be related to and not related to other constructs it should not be related to?

concurrent validity

Does the measure correlate with grades in PSBI 301? Class attendance? Etc.

predictive validity

Does the measure predict who will have a job using stats 10 years from now?

convaergent validity

Does the measure relate to other things it should?
Statistics and math proficiency
Self-esteem and depression

Discriminant Validity

Does the measure NOT relate to things it shouldn't?
Statistics and language proficiency
Self-esteem and political affiliation

null hypothesis

here will be no difference between your groups or no association between your variables

research hypothesis

level of the sample and directly linked to our method/measures

non directional research hypothesis

Reflects a difference between groups, but the direction is not specified

directional research hypothesis

direction of difference is specified

inferential logic

process of going from data to a universal truth about the world

what makes a good hypothesis?

based on scientific literature

concise

testable

normal cuve

bell shaped curved
- Mean, Median, and Mode are equivalent
- Perfectly symmetrical
-Asymptotic

z-scores

Uses the mean and the standard deviation to transform raw scores (x values) into a standard score (z-score)
- how far a point is from its mean and rely on standard deviations as the standardized unit

z-score and probability

All of these %'s represent the probability that a score would occur in the range you've defined

percentile rank

score that indicates the percentage of people who scores at or below a given raw score

alpha

The accepted cutoff for calling a result "statistically significant"

p value

probability of the observed results if the null hypothesis is true

statistical significance

Hypothesis testing is the process of determining this

type 1 error

Rejecting a null hypothesis that is actually true
Bad for science and the scientist
You may waste time trying to replicate the finding
Others may waste time trying to replicate it
May be discredited when study doesn't hold up to replication
Slows down the progress of science

type 2 errors

Failing to reject a null hypothesis that is actually false
- May stop studying something of interest
◦ Important research findings never make it to light
◦ Truth may never be uncovered

file drawer effect

Studies that reject Ho are more likely to get published than studies that fail to reject H0

effect size

The absolute difference has to also be considered

confidence intervals

Another way to apply probability via the Z table.
An estimated range for a population mean, given the descriptive stats from a sample
- use the Z table and the descriptive statistics from a sample to calculate a range in the population associated with a certain level of confidence.

one sample z test

When we want to test the difference between a sample and a population

independent samples t test

Use when comparing scores from two separate groups of people
- Also referred to as a between-subjects t-test

degrees of freedom

the number of scores in a sample that are free to vary once the mean is known
- n-2

effect size

A measure of how different two groups are from one another
INDEPENDENT of sample size
Related directly to the magnitude (size) of the difference between groups

paired samples t test

dependent samples t-test
- Same group of participants tested more than once

dependent pros

Need fewer participants to get to the same degrees of freedom/power
◦ Each participant serves as his/her own control

dependent cons

Order/learning effects
◦ Can't always have same person do both things(control condition and experimental condition)
◦ May increase potential for alternative explanations

dependent degrees of freedom

n-1

one way anova

Used when you have ONE factor with more than 2 levels

factor

variable that designates the groups to be compared (aka independent variables)

levels

the different groups within a factor

Sum of Squares Between

The differences between the group means and the "grand mean"

sum of squares within

sum of the differences between each score and the mean of the group it came from

factorial anova

used when you have more than one factor
- two or more independent variables

repeated measures anova

used when you test multiple groups multiple times