tuesday, april 8 n inferential statistics – part 2 n hypothesis testing n statistical significance...
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Tuesday, April 8
Inferential statistics – Part 2Inferential statistics – Part 2 Hypothesis testingHypothesis testing Statistical significanceStatistical significance continued….continued….
What you want to know is What you want to know is
what is going on in the population?what is going on in the population? All you have is sample dataAll you have is sample data
Your research hypothesis states there is a Your research hypothesis states there is a difference between groups difference between groups
Null hypothesis states there is NO difference Null hypothesis states there is NO difference between groupsbetween groups
Even though your sample data show some Even though your sample data show some difference between groups, there is a chance difference between groups, there is a chance that there is no difference in populationthat there is no difference in population
Sample Population
?Male GPA= 3.3
Female GPA = 3.6 Inferential
N=100
Parameter
Ha: Female students have higher GPA than Male students at UH
Three Possibilities Females really have higher Females really have higher
GPA than MalesGPA than Males
Females with higher GPA Females with higher GPA are disproportionately are disproportionately selected because of selected because of sampling biassampling bias
Females’ GPA happened to Females’ GPA happened to be higher in this particular be higher in this particular sample due to sample due to random random sampling errorsampling error
Male GPA= 3.3
Female GPA =3.6
Logic of Hypothesis Testing
Statistical tests used in hypothesis testing deal with the probability of a particular event occurring by chance.
Is the result common or a rare occurrence
if only chance is operating?
A score (or result of a statistical test) is “Significant”
if score is unlikely to occur on basis of chance alone.
The “Level of Significance” is a cutoff point for determining significantly rare or unusual scores.
Scores outside the middle 95% of a distribution are considered “Rare” when we adopt the standard
“5% Level of Significance”
This level of significance can be written as:
p = .05
Level of Significance
P < .05Reject Null Hypothesis (H0)
Support Your Hypothesis (Ha)
Decision Rules
Reject Ho (accept Ha) when
sample statistic is statistically significant at
chosen p level, otherwise accept Ho (reject Ha).
Possible errors:
• You reject Null Hypothesis when in fact it is true,
Type I Error, or Error of Rashness.
B. You accept Null Hypothesis when in fact it is false,
Type II Error, or Error of Caution.
Correct
Correct
Ho (no fire) Ha (fire)
Ho = null hypothesis = there is NO fire
Ha = alternative hyp. = there IS a FIRE
Accept Ho
(no fire)
Type IIerror
Type I errorReject Ho
(alarm)
True State
What Statistics CANNOT do Statistics CANNOT THINK or reason.Statistics CANNOT THINK or reason. It’s It’s
only only youyou who can think.who can think. Something can be statistically significant, yet Something can be statistically significant, yet
be meaningless. be meaningless.
Statistics - about probability, thus canStatistics - about probability, thus canNOT NOT prove prove your argument. Only your argument. Only supportsupport it. it.
Reject null hypothesis if probability is Reject null hypothesis if probability is <.05<.05 (probability of Type I error < than .05)(probability of Type I error < than .05)
Statistics Statistics can NOT show causalitycan NOT show causality; can show ; can show co-occurrence, which only co-occurrence, which only impliesimplies causality. causality.
When to use various statistics
ParametricParametric Interval or ratio dataInterval or ratio data
Non-parametricNon-parametric Use with non-Use with non-
interval/ratio data (i.e., interval/ratio data (i.e., ordinal and nominal)ordinal and nominal)
Parametric Tests
Used with data w/ mean score or standard Used with data w/ mean score or standard deviation.deviation.
t-test, ANOVA and Pearson’s Correlation r.t-test, ANOVA and Pearson’s Correlation r.
Use a Use a t-testt-test to compare mean differences to compare mean differences between two groups (e.g., male/female and between two groups (e.g., male/female and married/single).married/single).
Parametric Tests
use use ANalysis Of VArianceANalysis Of VAriance (ANOVA) to (ANOVA) to compare more than two groups (such as compare more than two groups (such as age and family income) to get probability age and family income) to get probability scores for the overall group differences. scores for the overall group differences.
Use a Use a Post Hoc TestsPost Hoc Tests to identify which to identify which subgroups differ significantly from each subgroups differ significantly from each other.other.
When comparing two groups on MEAN SCORES use the t-test.
t =
+1 2
M ean - M ean
2SD
n
2SD
n 2
2
1
1
When comparing more than two groups on MEAN SCORES,
use Analysis of Variance (ANOVA)
The computer will do all the work!
T-test
If If pp<.05<.05, we conclude that two groups are , we conclude that two groups are drawn from populations with different drawn from populations with different distribution (distribution (reject Hreject H00) at 95% confidence ) at 95% confidence levellevel
Product RecognitionBest Recognized Shapes
VAS-J SCOPE J&J-P OLAY J&J-S JERGNS TUMS VAS-L SECRT MENN ARID0
20
40
60
80
100Percent
Product RecognitionLeast Recognized Shapes
SEL-B CREST M.O.M. CHLOR. SKIN-B VITAL BARBI RT.GRD. KAO DESE S&S-L0
20
40
60
80
100Percent
Product RecognitionComparison of Total Scores
Male Female 17-26 27-33 34+ Single Married 0-15 16-35 36+9
10
11
12
13
14Mean Score
Gender Age Marital Status Family Incomep=.02 p=.001 p=.91 p=.004
Is there a meaningful difference between subgroups?Question:
Answer:Use Inferential Statistics to help you decide if differences could be due to chance, or are they likely a true difference between groups.
If differences are too large to be due to chance, then there is a Significant Difference between the groups.
We know the probability that our conclusions may be incorrect.
Males:
Mean = 11.3
SD = 2.8
n = 135
Females:
Mean = 12.6
SD = 3.4
n = 165
11.3 12.6
12
Mean scores reflect real difference
between genders.
Mean scores are just chance differences from
a single distribution.
** Accept Ha
Accept Ho
p = .02
Married:
Mean = 11.9
SD = 3.8
n = 96
Single:
Mean = 12.1
SD = 4.3
n = 204
Mean scores reflect real difference
between groups.
Mean scores are just chance differences
from a single distribution.
Accept Ha
**Accept Ho
p = .9111.9 12.1
12
Decision Making2 ways you can be “right”
Your inference based onsample data:
Reject H0
Accept H0
RealityH0 true H0 false
Decision Making2 ways you can be wrong
XType IIerror
XType IerrorYour inference
based onsample data:
Reject H0
Accept H0
RealityH0 true H0 false
Rating the importance of the reason for purchasing clothing "You need that piece
of clothing" in a 7-point scale
4.92
5.52
1
2
3
4
5
6
7
Female
Male
Most Important
Neutral
Least Important
p=0.038
Correlation - Measures of Association
Pearson’s Correlation CoefficientPearson’s Correlation Coefficient
both variables interval / ratio databoth variables interval / ratio data
one variable interval and other nominalone variable interval and other nominal
Non-parametric:Non-parametric: Spearman’s Rank Order CorrelationSpearman’s Rank Order Correlation
with ordinal datawith ordinal data Phi coefficientPhi coefficient
Both variables are dichotomous (2 choices Both variables are dichotomous (2 choices only)only)
Measures of Association Measures of associationMeasures of association examines the examines the
relationship between two variables = relationship between two variables = bivariate analysisbivariate analysis
Measures of association involves Measures of association involves the the significance testsignificance test
Significance test examines Significance test examines the probability the probability of TYPE I errorof TYPE I error
Conventionally we reject the null Conventionally we reject the null hypothesis if probability is hypothesis if probability is <.05<.05 (probability (probability of TYPE I error is smaller than .05)of TYPE I error is smaller than .05)
Measures of Association
Ordinal Intervl/Ratio
Nominal
Ordinal
Intervl/Ratio
Correlation (Spearman)
Correlation (Spearman)
Correlation (Pearson)
Measures of association to use depends on which level your variables are measured
Nominal
Phi coefficient
HEIGHT SMART
Men Women Men Women
Very Unimportant Very Unimportant
Unimportant Unimportant
Neutral Neutral
Important Important
Very Important Very Important
Total Total
TEETH
Men Women Men Women
Very Unimportant Very Unimportant
Unimportant Unimportant
Neutral Neutral
Important Important
Very Important Very Important
Total Total
When selecting a potential dating partner, how important are the following characteristics?
HEIGHT F>M p=.001
Men Women
Very Unimportant 0 2 1
Unimportant 22 2 12
Neutral 23 12 18
Important 47 58 53
Very Important 6 26 16
Total 100 100
Importance of HEIGHTBy Gender
p = .001
Very Unimportant Unimportant Neutral Important Very Important0
10
20
30
40
50
60Percent
Men Women
SMART F>M p=.05
Men Women
Very Unimportant 0 0 0
Unimportant 0 0 0
Neutral 10 6 8
Important 58 38 48
Very Important 32 56 44
Total 100 100
Importance of SMARTBy Gender
p = .05
Very Unimportant Unimportant Neutral Important Very Important0
10
20
30
40
50
60Percent
Men Women
TEETH F=M p=.88
Men Women
Very Unimportant 0 0 0
Unimportant 8 12 10
Neutral 26 28 27
Important 44 38 41
Very Important 22 22 22
Total 100 100
Importance of TEETHBy Gender
p = .88
Very Unimportant Unimportant Neutral Important Very Important0
10
20
30
40
50Percent
Men Women