testing hypotheses i lesson 9. descriptive vs. inferential statistics n descriptive l quantitative...
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Descriptive vs. Inferential Statistics
Descriptive quantitative descriptions of
characteristics Inferential Statistics
Drawing conclusions about parameters ~
Hypothesis Testing
Hypothesis testable assumption about a parameter should conclusion be accepted? final result a decision: YES or NO qualitative not quantitative
General form of test statistic ~
Hypothesis Test: General Form
error
effect
chance todue difference
groupsbetween difference statistictest
X
obs
Xz
variationicunsystemat
variationsystematic statistictest
Two Hypotheses Testable predictions Alternative Hypothesis: H1
also scientific or experimental hypothesis there is a difference between groups Or there is an effect Reflects researcher’s prediction
Null Hypothesis: H0
there is no difference between groups Or there is no effect This is hypothesis we test ~
Conclusions about Hypotheses
Cannot definitively “prove” or “disprove” Logic of science built on “disproving”
easier than “proving” State 2 mutually exclusive & exhaustive
hypotheses if one is true, other cannot be true
Testing H0
Assuming H0 is true, what is probability we would obtain these data? ~
Hypothesis Test: Outcomes
Reject Ho accept H1 as true
supported by data statistical significance
difference greater than chance Fail to reject
“Accepting” Ho data are inconclusive ~
Hypotheses & Directionality
Directionality affects decision criterion Direction of change of DV
Nondirectional hypothesis Does reading to young children affect
IQ scores? Directional hypothesis
Does reading to young children increase IQ scores? ~
Nondirectional Hypotheses
2-tailed test Similar to confidence interval Stated in terms of parameter
Hypotheses H1 : 100
Ho : = 100 Do not know what effect will be
can reject H0 if increase or decrease in IQ scores ~
Directional Hypotheses
1- tailed test predict that effect will be increase
or decrease Only predict one direction
Prediction of direction reflected in H1
H1: > 100 Ho: < 100 Can only reject H0 if change is in
same direction H1 predicts ~
Errors
“Accept” or reject Ho
only probability we made correct decision
also probability made wrong decision Type I error ()
incorrectly rejecting Ho e.g., may think a new antidepressant is
effective, when it is NOT ~
Errors Type II error ()
incorrectly “accepting” Ho e.g., may think a new antidepressant is not
effective, when it really is Do not know if we make error
Don’t know true population parameters *ALWAYS some probability we are wrong
P(killed by lightning) 1/1,000,000 p = .000001
P(win powerball jackpot) 1/100,000,000 ~
Actual state of nature
H0 is true H0 is false
Decision
Reject H0
Correct
CorrectType I Error
Type II Error
Errors
Accept H0
Definitions & Symbols
Level of significance Probability of Type I error
1 - Level of confidence
Probability of Type II error
1 - Power ~
Steps in Hypothesis Test
1. State null & alternative hypotheses
2. Set criterion for rejecting H0
3. Collect sample; compute sample statistic & test statistic
4. Interpret resultsis outcome statistically significant? ~
Example: Nondirectional Test
Experimental question: Does reading to young children affect IQ scores?
= 100, = 15, n = 25 We will use z test
Same as computing z scores for ~X
Step 1: State Hypotheses
H0: = 100 Reading to young children will not
affect IQ scores. H1: 100
Reading to young children will affect IQ scores. ~
2. Set Criterion for Rejecting H0
Determine critical value of test statistic defines critical region(s)
Critical region also called rejection region
area of distribution beyond critical value in tails
If test statistic falls in critical regionReject H0 ~
2. Set Criterion for Rejecting H0
Level of Significance () Specifies critical region
area in tail(s) Defines low probability sample means
Most common: = .05 others: .01, .001
Critical value of z use z table for level ~
3. Collect data & compute statistics Compute sample statistic
Observed value of test statistic
Need to calculate ~
X
X
X
obs
Xz
3. Collect sample & compute statistics
3
1005.105 83.1
15100 ,
nX
25
15 3
3
5.5
n = 25 : 105.5assume X
X
obs
Xz
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