02 Statistical Tests
Transcript of 02 Statistical Tests
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PENGENALAN ALAT-ALAT UJI STATISTIK
DALAM PENELITIAN SOSIAL
Tatang A Gumanti
2010
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Choosing the right test: 3
DV is Dichotomous Categorical Continuous
IV is/are:
Dichot-omous Chi-square Chi-square t-test
Cate-
goricalChi-square Chi-square ANOVA
Contin-
uous
Discriminant
function
analysis
Discriminant
function
analysis
Correlation or
regression
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Type of Scale and
Appropriate Statistical Test
Type of Scale Measure of
Central Tendency
Measure of
Dispersion
Statistical Test
Nominal Mode None Chi-Square
Ordinal Median Percentile Chi-Square
Interval or Ratio Mean StandardDeviation
T-test, ANOVA
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Measurement scales
Nominal Scale
numbers assigned to the object serve as labels foridentification i.e. gender (male, female); store type;accommodation type
(mode, frequency, percentage)
Ordinal Scale
a scale that arranges objects or alternatives
according to their magnitude in an orderedrelationship i.e. preference ranking for a product;social class
(median, semi-interquartile range)
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Measurement scales
Interval Scale a scale that both arranges objects according to their
magnitude and also distinguishes this orderedarrangements in units of equal intervals i.e. attitudes,
opinions (5 point likert scale) (mean, standard deviation, variance, range)
Ratio Scale a scale that has absolute rather than relative quantities
i.e. income, sales, costs, market share possess an absolute zero point and interval properties
(mean, standard deviation, variance + all lower leveldescriptive statistics)
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Parametric versus non -
parametric statistics
Statistical techniques can be classified as -
Parametric statistics the use is based on the assumption that the
population from which the sample is drawn isnormally distributed and data are collected on aninterval or ratio scale.
Non-Parametric statistics
makes no explicit assumptions regarding thenormality of distribution in the population (lessstringent requirements) and are used when the dataare collected on a nominal or ordinal scale.
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Methods of scaling
Response scales
rating scales: estimates magnitude of a
characteristic
ranking scale: rank order preference
sorting scales: arrange or classify concepts
choice scales: selection of preferred
alternative
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Testing Statistical Hypotheses
example
Suppose
Assume and population is normal, so samplingdistribution of means is known (to be normal).
Rejection region:
Region (N=25):
We get data
Conclusion: reject null.
75:;75: 10 HH10
3210-1-2-3
Z
Z
Z
1.96-1.96
Don't reject RejectReject
Likely OutcomeIf Null is True
79;25 XN
92.7808.7125
1096.175
X
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Tests of Normality
.246 93 .000 .606 93 .000TOTAL TIME SPENT
ON THE INTERNET
Statistic df Sig. Statistic df Sig.
Kolmogorov-Smirnova
Shapiro-Wilk
Li lli efors Signifi cance Correctiona.
The test of normality
Problem 1 asks about the results of the test of normality. Since the samplesize is larger than 50, we use the Kolmogorov-Smirnov test. If the samplesize were 50 or less, we would use the Shapiro-Wilk statistic instead.
The null hypothesis for the test of normality states that the actualdistribution of the variable is equal to the expected distribution, i.e., thevariable is normally distributed. Since the probability associated with the
test of normality is < 0.001 is less than or equal to the level of significance(0.01), we reject the null hypothesis and conclude that total hours spent onthe Internet is not normally distributed. (Note: we report the probability as
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Confidence intervals in z
For large samples (N>100) can use z.
Suppose
Then
If
M
Mest
yz
.
)(
N
N
yy
N
sest
y
M1
)(
.
2
200;5;10:;10: 10 NsHH y
35.
14.14
5
200
5.
N
sest
y
M
05.96.183.2;83.235.
)1011(11
pzy
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Difference Between Means (2)
We can estimate the standard error of
the difference between means.
For large samples, can use z
2
2
2
1 ... MMdiff estestest
diffest
yy
diffz 2121 )(
3;100;12
2;100;10
0:;0:
222
111
211210
SDNy
SDNy
HH
36.100
13
100
9
100
4. diffest
05.;56.5
36.
2
36.
0)1210(
pzdiff
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Independent Samples t(2)
21
21
21
2
22
2
11
2
)1()1(. NN
NN
NN
sNsNest diff
diffest
yy
difft 2121 )(
7;83.5;20
5;7;18
0:;0:
2222
1
2
11
211210
Nsy
Nsy
HH
47.135
12
275
)83.5(6)7(4.
diffest
..;36.147.1
2
47.1
0)2018(sntdiff
tcrit
= t(.05,10)=2.23
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Confidence Intervals in t
With a small sample size, we compute the same numbers
as we did forz, but we compare them to the tdistribution
instead of thezdistribution.
25;5;10:;10: 10 NsHH y
125
5.
N
sest
y
M1
1
)1011(11
ty
064.2)24,05(. t 1
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Rejection Regions (1)
1-tailed vs. 2-tailed tests.
The alternative hypothesis tells the tale
(determines the tails).
If 100:0 H
100:1 HNondirectional; 2-tails
100:1 H 100:1 H Directional; 1 tail
(need to adjust null forthese to be LE or GE).
In practice, most tests are two-tailed. When you see
a 1-tailed test, its usually because it wouldnt be
significant otherwise.
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Rejection Regions (2)
1-tailed tests have better power on the
hypothesized side.
1-tailed tests have worse power on the
non-hypothesized side.
When in doubt, use the 2-tailed test.
It it legitimate but unconventional to usethe 1-tailed test.