# Summary Introduction to Statistical Methods and Data Analysis

ISBN-10 0495109142 ISBN-13 9780495109143
52 Flashcards & Notes
10 Students

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• ## 1 Descriptive statistics for 1 sample

• Sample Mean?
Y=yi/n
• Sample Variance?
Sy square= (yi-y)square/(n-1)
• Standard deviation?
Sy= wortel Sy square
• Standard Error?
se= Sy/wortel n
• Steps in Testing?
1. Ho and Ha
2. TS
3. Behaviour of TS, e.g. under H0 a t distribution and ... values under Ha
4. Type of critical region (RR of P-value)
5. Value TS
6. P-value
7. P-value in comparison with alpha
8. conclude if H0 is rejected or not
9. Formulate conclusion in words
• ## 1.1 One Sample t-test

• Test statistic?
t= (y-mu)/(s/wortel n)
• Rejection Region (RR)?
Reject H0 if t is in the RR.
• Model assumptions?
• Independence of observations
• equality of variances
• Normality of observations
• ## 1.1.1 Inference for one or two sample situations

• The 8 steps testing for Rejection Region

1. H0 and Ha

2. Test statistic formula

3. The behaviour of the test under H0 and under Ha

4. Type of rejection region (left, right or two-sided RR)

5. Rejection region for a given alpha (mostly 0.05)

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6. Outcome of test statistic

7. Compare test statistic to rejection region, is it in the RR?

8. Draw conclusions, T.S. in RR? reject H0

• The 8 steps testing for p-value, use this when computer output is available.

1. H0 and Ha

2. Test statistic formula

3. The behaviour of the test under H0

4. The behaviour of the test under Ha

5. Type of p-value: left, right or two-sided?

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6. Outcome of test statistic

7. Compare p-value to alpha

8. Draw conclusions, p-value smaller than alpha? Reject H0.

• Bij een two-sided test (alpha=0.05) gebruik je in tabel 2,
0.05 of 0.025?

0.025

• Bij een one-sided test (alpha=0.05) gebruik je in tabel 2, 0.05 of 0.025?

0.05

• TS for one sample

• For (1-alpha)-CI, reject H0 if H0 is not in the CI

• Termonology

S = standard deviation

SE = Standard error

• ## 1.1.1.1 Two samples

• Two independent samples.

Equal variances assumed?

H0: u1-u2=0 Ha: u1-u2 is no 0

If H0 is true, t ~ t (n1+n2)-2

• How is it possible the two p-values are not the same?

df and approximate df are not the same.

• How is it possible t and t` ( values test statistic) are the same for two independent samples?

The sample sizes are the same

• Levene's test: H0: equal variances assumed Ha: not assumed.

So if Levene's test is smaller than 0.05, equal variances are not assumed.

In the example here Levene's test sig. = 0.25, which is bigger than 0.05, so equal variances are assumed.

• ## 1.2 two independent samples, equal variances

• Parameter of interest?
mu1-mu2
• se?
se(y1-y2)= sp*wortel((1/n1)+(1/n2))