Second exam based on 7-10 Flashcards
What test does not require us to know the standard deviation population?
t-test
When can we conduct a z-test?
we know the population mean and standard deviation
Step 2 NHST t-test
comparison of distribution is still distribution if means, now it’s a t-distribution (thicker tails)
kurtosis
thickening of the tail in the t-distribution
How many distributions are apart of the t-distributions?
There are more than ine
What happens when our sample is smaller?
The more kurtotic the t-distribution is
What happens when the sample is bigger?
the more the t-distribution looks like a normal z-distribution
Why does the shape of our comparison distribution change from a z to a t distribution
We are estimating the variance of population 2
What happens when an estimate is wrong in science?
we have to build room for error, in case it is wrong
How do we build room for error?
we change the shape of our distribution, the room for error is done so by thickening the tails
What do thicker tails do?
Thicker tails make it harder to reject the null hypothesis, they push farther out from the mean, they help with the possibility if it is wrong
Rule 1 for t-distribution
u(m)=u(2)
the mean of the t-distribution is the same for the population 2
Step 2 of t-distribution
We use variance for the sample population 1 to pop 2, we assume they both have the same variance
S^2 = E (x-m) ^2 /N-1
=
SS/N-1 = variance
S^2
estimate of pop. 2 variance using our sample to estimate, instead of diving by N, we divide by N-1 to give room for error
What does a larger variance do?
it inflated the width of the distribution
In science we use what to estimate?
our sample
3rd rule of t-distribution
shape defined by degrees of freedom (df), our sample determines our distribution
what does a bigger sample size do?
it helps us to not have to estimate, instead it will give us a more accurate distribution
When do we not need more room for error or a kurtosis tail?
We do not when our sample is bigger
The bigger the sample the better estimate and the thinner tails can be?
True
what is df?
df = N-1
3 rules to determine t-distribution
1) Um = (variance)
2) S^2m= (SD)
3) Shape =t( ) (Degrees of freedom)
Step 3 of NHST
critical cutoff score .05, look at the table with df and match it with it, look for one or two tail
Step 4 of NHST
determine sample score on comparison distribution
t= M-ú/Sm
Step 5 of NHST
decide whether to reject the null hypothesis, present inferential stats
t-test for dependent means
comparing two means at two times, always dependent on each other
dependent means
measuring a sample of participants at time one and we measure the same sample for time two
mean of comparison distribution
standardized score of zero
What would the null represent in dependent t-tests?
represents no change between times
t test independent means
looking at two means from two separate groups, either naturally occurring or experimentally manipulated groups
naturally occurring groups
ex: people living in the u.s and people living in canada
experimentally manipulated groups
by researchers, one randomly group is assigned to receive some sort of treatment, the other is a control group with no treatment
null hypothesis for independent means
shows no difference between groups
degrees of freedom for independent means
df = N-2
one way anova
compares three groups
ex: clean record, dirty record & no info
anova
when we want to compare three or more groups we conduct an analysis of variance
In one way anova what variables do we have?
one categorical explanatory variable (A)
one continuous outcome variable (Y)
categorical variable
also called group membership, it explains variation in an outcome variable
outcome variable
the outcome of the study, a continuium
What does anova weigh?
b/w group variance vs. within group variance to see if the former outweighs the latter
between groups
captures the differences between group averages
within group variance
captures variance within the same groups
what anova weighs is what?
at the heart of understand variation in the social and behavioral sciences
what are the little x’s at the bottom of the anova graphs?
called sample means
What happens when the sample means are different from each other?
due to sampling error, because the sample was too big it will not match with population mean
what happens when there are wider distributions?
more variation within groups, also will create differences among sample averages
When the little x’s are spread out on a graph?
both within and between variances are influencing them with real differences within population means and reflected in sample means
F-ratio
between (estimate) / within (estimate)
filters out the fake differences seen in sample averages
What happens if the F-ratio is 1?
likely no real differences
F-ratio > 1 are there differences?
yes real differences
Anova Step 1 NHST
restate research question, H(0): u1 = u2 = u3
H(1): ~ (u1 = u2 = u3) (not the case that the three population means are the same)
Anova step 2 of NHST
comparison distribution is a f-distribution defined by two degrees of freedom F(df b, df w)
df b =a-1
df w= df(1)+df(2)+df(3)….
Anova NHST step 3
only one tail in a f-distribution, because it includes f-ratios with a lower limit of 0, critical cutoff is found on an f-table df b/ df w
NHST anova step 4
convert our data into f-ratio
Anova NHST step 5
decide whether to reject the null hypothesis
F(df b, df w) =X.XX, p < .05
What happens when rejecting a null hypothesis in a one-way anova?
it tells us the population means are not the same, but we want to know which subgroups are different from others
Significant Omnibus
gives us permission to probe for differences in follow up tests
follow up tests are both
comparisons & contrasts, they mean the same thing
follow up tests are either
pairwise or complex and a priori (planned) or a posteriori (post hoc)
pairwise
comparing two specific means from two specific groups
complex
tells us it’s not pairwise but we are always comparing two averages
What happens when one conducts more than one follow up test?
requires research’s to adjust for inflation of their alpha level using a multiple comparison procedure (MCP)
MCP
it is a procedure to show we are conducting multiple comparisons, to adjust our alpha level back to 0.05
MCP (dunn-bonferroni)
planned comparisons, pairwise or complex comparisons. divide overall target level / by comparisons
MCP (tukey)
planned or post hoc comparisons, pairwise comparisons
MCP (Scheffé)
planned or post hoc comparisons
pairwise or complex comparisons
How do you chose an MCP?
if more than one MCP is appropriate, it is acceptable to choose the MCP with best results
two-way anova
we break groups up in two different times, two categorical explanatory variables (A/B), one continuous outcome variable (Y)
What are the main effects in two way anova
main effect of factor A, B
interaction effects of A x B
How do we compare main effects?
using marginal means, they are margins of the table
A x B interaction effect
when comparing factor A & B it is called moderation, it shows whether factor B changes factor A
When is there an interaction effect in cell means?
when they go in different directions such as top row goes up and bottom row goes down
When graphing for a two way anova what does parallel lines tell us?
tells us there is no interaction
How are main effects tested?
through marginal means, the averages of the cell means
in two way anovas how many f-ratio or f-tests
3 for each because there are 3 effects (2 main & 1 interaction)
two-way anova step 1 NHST
main effect of factor A
pop 1: jurors told they have record
pop:2 jurors told they have no record
H(0): u(1) = u(2)
H(1): ~ (u 1 = u 2)
main effect of factor B
pop 1: no legal experience
pop 2: legal experience
AxB (2x2) interaction
the effect of factor A on Y varies as a function of factor B
two way anova step 2 NHST
df A =a-1 (a is the number of groups (2)
df B= b-1
df AxB = Ncells -df (a)-df (b)- 1
df w =df(1) +df(2) + df(3)….
two way anova NHST step 3
main effect of A -> F(1,df)
main effect of B -> F(1,df)
Interaction effect -> F(1,df)
two way anova step 4 NHST
calculate 3 f ratios
two way anova step 5 NHST
1) present inferential stats
2) present a statistical interpretation
3) present a substantial interpretation
what reveals complexity and conceals it?
interaction effects (reveal it)
main effects (conceal it)
