stat exam 3

sM

estimated standard error

Df

Degree of freedom

SS

Sums of squares

S2p

Pooled variance

R

Variance accounted for

M

Sample

μ

population mean

Most research studies compare how many sets of data?

two (or more) sets

between-subjects design

Data from two completely different

a within-subjects or repeated-measures design

Data from the same or related participant group(s)

Seek to prove null or alt

Null

Null there is or is not significant difference

There is

Estimated standard error

Measure of standard or average distance between sample statistic (M1-M2) and the population parameter

Pooled variance

Provides an unbiased basis for calculating standard error, correcting the bias in the standard error is to combine the two
sample variances into a single value

Degrees of freedom for t test w/ two samples

Just add them both

Steps for independent hypothesis

• State the hypothesis and select an alpha level
• Locate the critical region
• Collect data & compute the test statistic
• Make a decision

When to use one tail

When you know the direction

Assumptions underlying indp. measures tests

• Observations within each sample must be independent.
• The two populations must be normal (always assume normality unless told otherwise)
• The two populations must have equal variances (called homogeneity of variance)

How to test for homogeneity of variance

Use F max test

Do you want significancy with f max test?

No

Small value (1.00) indicates similar or different sample variances?

Similar

If the null hypothesis is rejected the effect size should be determined by using either

Cohen's d/percentage of variance explained

What is used to estimate the population mean difference?

M1-m2

Estimation can provide an indication of

Size of treatment effect/significance of effect

If interval contains 0

Not a significant effect

Does not contain 0

Was significant

Large variance leads to large/smaller error and what t value?

Larger error

Larger samples produce larger/smaller error and what t values?
Smaller error

larger t

What does cohen d need to be significant?

0.5

Variance accounted for that is best for studies

15-20% is the best

Hypothesis testing definition

a statistical method that uses sample data to evaluate the validity of a hypothesis about a population- most commonly used w/ inferential stats

process of hypothesis test

state hypothesis

steps of hypothesis test

state hypothesis/ set criteria/ collect data

symbol for null hypothesis

HO

Null hypothesis definition

states that the treatment has no effect: there is no change

alternative hypothesis symbol

h1

alternative hyp definition

states that there is a change

alpha level

α or significance level, a probability value used to define “very unlikely” outcomes.

critical regions consist of

extreme scores, sample outcomes that are very unlikely

how are boundaries of critical regions determined

by probility set by the alpha level

data is always collected after...

hypothesis is stated and establishing decision criteria

z score is the difference between what

the observed sample mean and the hypothesized population mean divided by the standard error of the mean

if sample stat is located in critical region

null hypothesis is rejected (above 1.96)

if sample is not located in critical region

researcher fails to reject null hypothesis

hypothesis testing is a what process?

inferential (makes a generalization)

type 1 errors

Researcher rejects a null hypothesis (H0) that is actually true.
Researcher concludes that a treatment has an effect when it has none

What is the probability that test will have type 1 error?

Alpha level

Type 2 error

Harder to identify
Researcher fails to reject a null hypothesis that is actually false.
Researcher has failed to detect a real treatment effect.

When is a result significant

if it is very unlikely to occur when the null hypothesis is true

larger discrepancies mean

larger z scores

more variability means

larger standard error

larger n or scores in sample

smaller standard error

assumption of hyp testing w/ z scores

Random sampling
Independent observation
Value of σ is not changed by the treatment
Normally distributed sampling distribution

Standard hyp is one or two tailed?

Two tailed

Directional or one tailed test

the researcher specifies either an increase or a decrease in the population mean as a consequence of the treatment.

one tailed rejects null with small or large difference

small provided the difference is in the predicted direction

two tailed tests need small or large difference

large regardless of direction of difference

should one or two tailed test be used

two unless there is a strong directional prediction

effect size measures

the absolute magnitude of a treatment effect

cohen's d measures

effect size simply and directly in a standardized way

standard error describes

how much difference is reasonable to expect between population and sample mean

cons of using z scores

The z-score requires more information than researchers typically have available
Requires knowledge of the population standard deviation σ
Researchers usually have only the sample data available

What can t b considered in relation to z?

The approximate z

The difference between the t test and z test?

Estimated standard error (sM) is used as in place of the real standard error when the value of σM is unknown

Estimated standard error

used as estimate of the real standard error when the value of σM is unknown

when computing the sample variance what do you need to do first?

calculate sample mean

t distribution

• Family of distributions

How does t distribution compare to normal dist.?

It's flatter more spread out and has more variability ("fatter tails") in t distribution

Assumptions of t test

• Values in the sample are independent observations.
• The population sampled must be normal
• With large samples

Larger the sample effect on error

Makes it smaller

Larger the variance effect on error

Makes it larager

Hypothesis tests determines what about the treatment effect?

If it's greater than chance

How does cohen's d differ from t test to z test?

In t test it is estimated

Percentage of variance explained

Determining the amount of variability in scores explained by the treatment effect is an alternative method for measuring effect size

How to know if you have small/medium/large effect

Small=0.01
Medium=0.09
Large=0.25

Factors affecting width of confidence interval

• Confidence level desired
• More confidence desired increases interval width
• Less confidence acceptable decreases interval width
• Sample size
• Larger sample smaller SE smaller interval
• Smaller sample larger SE larger interval

In research is 1 or 2 tailed z test used more often?

2 tailed

Analysis of variance (ANOVA) definition

Used to evaluate mean differences between two or more treatments
Uses sample data as basis for drawing general conclusions about populations

Advantage of ANOVA over a t test

can be used to compare more than two treatments at the same time (simultaneously)
between variance

low dose has more or less variance

more variance (more variety)

high dose (maximum dose)

less variance (less variety)

Factor

The independent (or quasi-independent) variable that designates the groups being compared

Levels

Individual conditions or values that make up a factor

Factorial design

A study that combines two or more factors

Null hypothesis

the level or value on the factor does not affect the dependent variable
In the population this is equivalent to saying that the group means do not differ from each other

Benefit of using ANOVA

ANOVA evaluates all mean differences simultaneously with one test—regardless of the number of means—and thereby avoids the problem of inflated experimentwise alpha

F ratio

Based on variance instead of sample means

Between-treatments variance

Variability results from general differences between the treatment conditions
Variance between treatments measures differences among sample means

Within-treatments variance

Variability within each sample
Individual scores are not the same within each sample

Sources of variability between treatments

Systematic differences caused by treatments
Random

Source of variability within treatments

No systematic differences related to treatment groups occur within each group
Random, unsystematic difference (individual)

In f ratio if h1 is true

Size of treatment effect is more than 0
F is noticeably larger than 1.00

Denominator of the F-ratio is called

error term

K

Number of treatment conditions (groups)

n1

n2

N

Total number of scores
T

GT

Grand total of all scores in study

What will value of f be if null hypothesis is true

1.00

F ratios are always -/+?

+

Measuring effect size for anova

Compute percentage of variance accounted for by the treatment conditions