Chapter 7 Flashcards
Parametric Tests:
-I__ statistical test based on a__ about a population.
Assumption: c__ about a population that we are sampling necessary for accurate i__
Inferential, assumptions
characteristic, inferences.
Nonparametric Tests:
-I__ statistical test NOT based on a__ about the population.
Inferential, assumptions
3 Assumptions for Hypothesis Testing:
1) DV assessed with s__ measure.
- if you break, it is usually ok if data are not clearly n__ or o__.
2) Participants are r__ s__.
- OK to break if we are cautious about g__.
3) Population must have an approximately n__ distribution.
- Usually is samples is > __ it’s ok.
If these aren’t met?
-Hypothesis tests are fairly r__, still very a__.
scale
nominal, ordinal
randomly selected
generalizing
normal
30
robust, accurate.
6 Steps of Hypothesis Testing:
1) Identify the p__, d__, and a__. Then choose the appropriate h__ test.
2) State n__ & r__ hypotheses in words &
notation
3) Determine c__ of c__ distribution.
4) Determine c__ v__ (cut-offs)
5) Calculate the t__ s__.
6) Make d__ and i__ result.
populations, distribution, assumptions, hypothesis
null, research
characteristics, comparison
critical values
test statistic
decision, interpret
Breakdown of Hypothesis Testing Steps:
IQ scores are designed to have a mean of 100 and a standard deviation of 15. A school psychologist is convinced that the mean IQ score of the high school seniors in her district is different from 100. She administered an IQ test to random sample of 50 seniors in her district and found their mean IQ was 104.
1) Identify the populations, distribution, and assumptions. Then choose the appropriate hypothesis test.
Identify population mean, SD, sample mean, and sample size (Number of elements)
populations represented by 2 groups
•All HS seniors in her district
•All HS seniors (in US?)
ID comparison distribution
•Distribution of means
ID hypothesis test & check assumptions
•One sample z test (because we know population mean & std deviation)
•Assumptions: DV scale? Random selection? Distribution/sample size?
Pop mean (μ)=100 SD (σ)=15 Sample Size (N)=50 Sample mean (M)=104
Breakdown of Hypothesis Testing Steps:
IQ scores are designed to have a mean of 100 and a standard deviation of 15. A school psychologist is convinced that the mean IQ score of the high school seniors in her district is different from 100. She administered an IQ test to random sample of 50 seniors in her district and found their mean IQ was 104.
2) State null & research hypotheses in words &
notation
-In regard to the p__.
- Two-tailed test: “n__” test (“d__”)
- One-tailed test: “d__” test
population
nondirectional, difference
Words: 2 tailed test.
•NULL: There is no difference between the average IQ of HS seniors in our district and the average IQ of HS seniors in the US.
•RESEARCH: There is a difference between the average IQ of HS seniors in our district and the average IQ of HS seniors in the US.
Notation: 2 tailed test.
null: H0:μ1 = μ2
research: H1:μ1 ≠ μ
directional
- Words: 1 tailed test
- NULL: The average IQ of HS seniors in our district is not greater than the average IQ of HS seniors in the US.
•RESEARCH: The average IQ of HS seniors in our district is greater than the average IQ of HS seniors in the US.
Notation: 1 tailed test
null: H0: μ1 ≤ μ2
research: H1: μ1 > μ2
Breakdown of Hypothesis Testing Steps:
IQ scores are designed to have a mean of 100 and a standard deviation of 15. A school psychologist is convinced that the mean IQ score of the high school seniors in her district is different from 100. She administered an IQ test to random sample of 50 seniors in her district and found their mean IQ was 104.
- Determine characteristics of comparison distribution
-•based on n__.
•z test: m__ & s__ e__ of distribution
null
mean, standard error
- μM = μ = 100
- σM = 15/√50 = 15/7.07 = 2.12
so:
mean: μM = 100 (aka: the population mean)
standard error: σM = 2.12
Breakdown of Hypothesis Testing Steps:
IQ scores are designed to have a mean of 100 and a standard deviation of 15. A school psychologist is convinced that the mean IQ score of the high school seniors in her district is different from 100. She administered an IQ test to random sample of 50 seniors in her district and found their mean IQ was 104.
- Critical values & rejection region how to
determine & interpret p values.
•critical values: t__ s__ needed to reject n__.
- _ statistic(s) needed to reject null
- may have o__ critical value (one-tail) or t__ critical values (both tails) depending on our null hypothesis
•critical region: area b__ critical values (t__); r__ the null if test statistic in this region
•p level (alpha) (α): p__ used to determine c__ values
-typically . (may sometimes see .):
•reject most e__ 5%(or 1 %) of distribution
•there is a 5% (or l__) chance we would find results this extreme if the null were t__.
•__-tailed or __-tailed matters here
Two tailed tests:
-rejection region divided between 2 tails (.%)
-In z table look at what’s closest to this percent.
what would it be for a 0.05 (5%) p level.
One tailed tests:
- cut off __ tail of distribution
- if the p level is .05, put all _% in one tail.
- so critical z=
- less c__ than 2 tail.
test statistics, null
z
one, two
beyond, tails, reject
probability, critical
0.05, 0.01
extreme
less, true
one, two
2.5%
critical z for 0.05= +1.96, -1.96
one, 5
1.65
conservative
- Calculate test statistic
- based on your d__
- Remember: we typically test m__, NOT i__ scores
zobs= (M - μM)/σM
Calculate for:
IQ scores are designed to have a mean of 100 and a standard deviation of 15. A school psychologist is convinced that the mean IQ score of the high school seniors in her district is different from 100. She administered an IQ test to random sample of 50 seniors in her district and found their mean IQ was 104.
What is actual P value?
data
means, individual
zobs= (104-100) * 104/2.12 = 1.89
actual P value: 2.94% (percent in tail)
- Make decision & interpret result
- Reject or fail to reject null?
- Compare t__ s__ to c__ v__
•If test statistic is more extreme -> r__
aka: the test statistic exceeds +1.96 or -1.96
•If test statistic is NOT more extreme -> __ to reject
aka: the test statistic stays within the tails.
test statistic, critical values
reject
fail
•Statistically significant: data differ from what we would expect by c__ if there were no actual d__ (if null were t__)
chance, difference, true
Make decision and interpret:
IQ scores are designed to have a mean of 100 and a standard deviation of 15. A school psychologist is convinced that the mean IQ score of the high school seniors in her district is different from 100. She administered an IQ test to random sample of 50 seniors in her district and found their mean IQ was 104.
zobs= (104-100) * 104/2.12 = 1.89
actual P value: 2.94% (percent in tail)
critical z for 0.05= +1.96, -1.96
Fail to reject
•zobs = 1.89 < 1.96 = z crit
p = 2.94% LOOKING FOR LESS THAN 2.5% in two-tailed test (or 5% - SPSS - over both tails - “as extreme as” -)
•No evidence from this study to support the research hypothesis that there is a difference in average IQ scores between the students at this district and the general population of students
