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TT2 Flashcards

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1
Q

hypothesis test steps

A
  1. state hypothesis and select alpha level
  2. locate crit. region boundaries (t or z value)
  3. collect data and calculate sample stats (t ot z score)
  4. make decision based on criteria (is it in the crit region? reject or retain?)
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1
Q

characteristics of a distribution of sample means

A
  1. normal if variable is normal OR n>30
  2. the larger the sample size, the closer the sample means should be to the population mean, therefore lower n = more widely scattered (larger variance)
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2
Q

standard deviation for a distribution of sample means

A

standard error of M
how much distance to expect between a sample mean and the population mean
σ sub M
= σ/square root of n

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3
Q

mean for a distribution of sample means

A

expected value of m
= population mean

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4
Q

law of large numbers

A

as n increases, the error between the sample mean and the population mean should decrease
this is bc as n increases, samples should be more accurate to the population, reducing variance and therefore the standard error of M

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5
Q

when is standard error of M identical to standard deviation

A

when n = 1
bc when n = 1, the distribution of sample means is the same as just the distribution of scores

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6
Q

what is the “starting point” for standard error?

A

standard deviation, bc standard error = SD when n = 1, as n increases standard error decreases from there

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7
Q

central limit theorem

A
  1. law of large numbers
  2. standard error = SD when n = 1
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8
Q

the standard error can be viewed as a measure of the ____ of a sample mean

A

reliability
If the standard error is small, all the possible sample means are clustered close together and a researcher can be confident that any individual sample mean will provide a reliable measure of the population.

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9
Q

the expected value of M (when n = 100) will be ____ the expected value of M (when n = 25), because

A

equal to
they should both be equal to the population mean

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10
Q

the standard error of M (when n = 100) will be ____ the standard eror of M (when n = 25) because of ___

A

less than
the law of large numbers

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11
Q

random sampling criteria/assumptions for a z test

A

sampling with replacement, selections must be independent (each selection is not influenced by the last, gambler fallacy)

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12
Q

type 1 error

A

reject the null hypothesis when in fact the treatment has no effect

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13
Q

probability of type 1 error

A

alpha level
ex. if 0.05, there is a 5% that the sample is extreme by chance and therefore a 5% chance of a type 1 error

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14
Q

type 2 error

A

retains/fails to reject the null hypothesis, when in fact there is a treatment effect

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15
Q

level of confidence

A

chance that we will correctly retain the null aka say there isnt an effect when there isnt
= 1- alpha
if alpha is 0.05, there is a 5% chance of a type 1 error and 95% chance there isnt

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16
Q

chance of a type 2 error

A

function represented by beta

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17
Q

When does a researcher risk a Type I error?

A

when null is rejected

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18
Q

When does a researcher risk a Type 2 error?

A

when null is retained

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19
Q

In general, increasing the variability of the scores produces a larger ___ and a z score ____.

A

standard error
closer to 0

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20
Q

the ____ the variability, the lower the likelihood of finding a significant treatment effect.

A

larger

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21
Q

increasing the number of scores in the sample produces a ___ standard error and a ___ value for the z-score

A

smaller
larger

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22
Q

the ___ the sample size is, the greater the likelihood of finding a significant treatment effect.

A

larger

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23
Q

selections are not independent when…

A

ppts were sourced from the same place and are more likely to have similar responses
and if sampling was done without replacement and each person had a higher likelihood of being picked than the last

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24
does the hypothesis use M or μ?
μ because we are making predictions on the population
25
statistical hypotheses for positive directional hypothesis
Null: μ ≤ (μ value) Alt: μ > (μ value)
26
z score boundary for alpha level 0.05 for one tailed test vs two tailed test
1.65 vs 1.96
27
APA description
mean and sd after each group, test value (z or t(DF)), p value, one vs two tailed
28
statistical hypotheses for non directional hypothesis
Null: μ = (μ value) Alt: μ ≠ (μ value)
29
d = 1 means...
the treatment changed the mean by a full standard deviation
30
evaluating effect size of cohens d
0.2 - small effect (0.2 of an SD) 0.5 - medium effect 0.8 - large effect
31
The power of a test
the probability that the test will correctly reject the false null hypothesis if the treatment really has an effect aka the test will identify a treatment effect if one really exists = 1 - beta
32
as effect size increases, ___ increases
power
33
___ sample produces greater power of a test
larger
34
____ alpha level reduces the power of a test
reducing
35
___ tailed test increases the power of a test
one
36
type 1 error is ___ ___ null hypothesis
rejecting, true
37
type 2 error is ___ ___ null hypothesis
failing to reject, false
38
use t test when...
population SD/variance is unknown
39
estimated standard error
used in t tests when population SD/variance is unknown, uses sample SD/variance instead unbiased stat s sub m = s/square root of n = square root of (s^2/n)
40
z statistic vs t statistic
z score formula with standard error (σ sub M) or estimated standard error (s sub M) instead of SD
41
In general, the ____ the sample size (n) is, the ____the degrees of freedom are, and the ____the t distribution approximates the normal distribution.
greater larger better
42
the t distribution has more ___than a normal z distribution (distribution of sample means), especially when df values are ___. Because....
variability small t scores are more variable bc the sample variances changes for each sample while the population variance doesnt, this effect lessens with larger sample sizes
43
SS to variance
SS/n-1
44
steps to t test
1. SS/n-1 = s^2 2. square root of (s^2/n) = s sub M 3. (M - mu)/s sub M = t
45
for t tests, large variance means that you are ____ to obtain a significant treatment effect
less likely
46
large samples tend to produce ___ t statistics
bigger
47
r^2
percentage of variance accounted for by the treatment
48
r^2 interpretation
0.01 small effect 0.09 medium effect 0.25 large effect
49
confidence interval
interval around the sample mean in which the population mean likely resides
50
___ sample size leads to smaller confidence intervals
bigger
51
larger sample sizes lead to ___ cohens d and r^2 values
the same
52
A researcher rejects the null hypothesis with a regular two-tailed test using . If the researcher used a directional (one-tailed) test with the same data, then what decision would be made?
Definitely reject the null hypothesis if the treatment effect is in the predicted direction.
53
estimated value of d
cohens d with sample SD instead of population SD unbiased
54
As df increases, the shape of the t distribution ____ a normal distribution.
approaches
55
hypotheses for independant
Null: μ1 - μ2 = 0 Alt: μ1 - μ2 ≠ 0
56
For the independent-measures t formula, the standard error measures the amount of error that is expected when ...
you use a sample mean difference to represent a population mean difference. When the null hypothesis is true, however, the population mean difference is zero. In this case, the standard error is measuring how far, on average, the sample mean difference is from zero. However, measuring how far it is from zero is the same as measuring how big it is.
57
the standard error for the sample mean difference
s sub dif It measures the standard, or average size of m1 -m2 if the null hypothesis is true. That is, it measures how much difference is reasonable to expect between the two sample means. = square root of SE1 + SE2 - biased if sample sizes are different
58
if two samples are exactly the same size, the pooled variance is simply the ___ of the two sample variances.
average
59
steps for independent samples t test
0. find crit region based on POOLED df 1. pooled variance (USE DF) 2. estimated standard error (use n) 3. calc t value
60
assumption of homogeneity of variance
for an independent samples t test, the two samples being compared must have the same theoretical population variance
61
find cohens d for independent samples t test
1. pooled variance (USE DF) 2. sqaure root pooled variance for SE 3. put in formula
62
s^2 sub p
pooled variance - weighted mean of sample variances
63
s sub dif
estimated standard error for independent sample test
64
s sub p
pooled SD use for cohens d
65
why is repeated better than individual?
individual differences - ind has more variance bc of difference and so harder to see a treatment effect, cost of more participants
66
related sample t-test steps
SS, s^2, Smd, T
67
d=?
n x/2
68
related null hypothesis directional and nondirectional
mew d = 0 mew d greater than or equal to 0
69
related samples assumptions
1. observations within a group must be independent 2. distribution of d scores must be normal
70
cons of repeated measures design
other factors like time may affect scores, practice effects/order effects solution: counterbalance order
71
for repeated measures, null hypothesis assumes...
that mean population difference is 0
72
for anova, null and alt. hypothesis
mew condition 1 = mew condition 2 = mew condition 3 At least one of the treatment means is different
73
denominator of f ratio is called
the error term bc it represents the random unsystematic errors you can expect is null is true
74
k
number of levels of the factor/treatment groups
75
n in ANOVA
number of scores in each treatment group
76
N in ANOVA
number of total scores in the study = kn
77
T
Treatment total; sum of all the scores in a treatment group = sum of X for sample 1
78
G
Grand total sum of all the scores across all treatments = sum of X for all scores = sum of T
79
what to put on an ANOVA summary table
SS, df, and MS for bw, within, and total also F
80
ANOVA assumptions
observations within groups must be independant, populations from which samples are selected must be normal, homogeneity of variance of populations
81
what happens to pearson r if constant is added or pos constant is multiplied? what is neg constant is multiplied?
nothing sign flips
82
uses of correlation
predications, test validity (compare against another feature), test reliability (compare two scores at different times, they should have a strong pos correlation), theory verification
83
r^2 in correlation
coefficient of determination % of the variability in the Y scores can be predicted from the relationship with X. ie r^2= 0.36, 36% of the variance in GPA can be explained by IQ. same cut offs as regular r ^2
84
correlation null and alt hypotheses
p = 0 there is no population correlation p doesn't not = 0 there is a population correlation or directional
85
r vs p
sample correlation vs population correlation
86
df for correlation
n-2 bc 2 points always make a perf correlation
87
spearman correlation
when x and y are ordinal or when you're looking for consistency in a not linear relationship
88
if you want to measure the consistency of a relationship for a set of scores, you can simply
convert the scores to ranks and then use the Pearson correlation formula to measure the linear relationship for the ranked data
89
point biserial correlation
used when one variable is dictonomous (only has two values)
90

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