02 statistical tests

7/29/2019 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.

02 statistical tests

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