Summary
Z Test ....................................................................................................................................................... 3
Assumptions - Test statist for μ when σ is known .................................................................................. 3
Z test statistic for p (=proportion) ........................................................................................................... 4
T test / Student t statistic / one simple T test ........................................................................................ 5
F-test (to test population variances) ....................................................................................................... 6
Independent t-test = 2T-test ................................................................................................................... 7
Paired simple T test / (T test and estimator of μD) .................................................................................. 8
Chi-Squared Goodness-of-fit Test Statistic (Nominal)............................................................................. 9
Chi-Squared test of a contingency table (Nominal) .............................................................................. 10
Wilcoxon Rank Sum Test (Data is ordinal or interval – nonparametric / Independent samples) ......... 11
Wilcoxon Signed Rank Sum Test (Data is interval – nonparametric / Matched Pair) ........................... 12
Sign test (Binomial matched pair) ......................................................................................................... 13
Spearman Rank Correlation Coefficient (Ordinal or Interval – Nonparametric)................................... 14
Regression analysis (multiple and single) .............................................................................................. 15
Pearson coefficient of correlation (normal Interval)............................................................................. 17
Multiple regression testing the validity................................................................................................. 18
Multiple regression testing the Coefficients (β0, β1, β2, etc.) ................................................................ 19
1 1
,2 2
, Z Test
Hypotheses
H0 = μ = the mean is equal to ..(invullen wat in de tekst staat…)
H1= μ = the mean is <>≠(invullen wat in de tekst staat)
Test Statistic
Test statistics Degrees Confidence Rejection p-value
of interval region
freedom
Right P(Z>…) = 1-
None P(Z< …)
Left P(Z< …) =
Note: zα/2
by a 2- Different 2P(Z>…) =
tailed 2* 1-P(Z<…)
test! =…
Computations
1. Look up the rejection region in table 3 (veld).
2. Do the test statistic
3. Draw a picture
Interpret
If the computed z-value falls in the rejection region we can reject the H0. So we do have enough
evidence to reject the null hypothesis. We assume that … (repeat H1 in words).
If the computed z-value is falls outside the rejection region we cannot reject the H0. We do not have
enough evidence to reject the null hypothesis. We assume that … (repeat H0 in words).
Assumptions
- Test statist for μ when σ is known
Interpretation confidence interval
If we repeatedly draw samples of sizes … (n) from the population of … , 95% of differences between
… and … would lie between … (LCL) and … (UCL)
3 3
, Z test statistic for p (=proportion)
Hypothesis
H0 : p = .5
H1 : p = </>/≠ .5
p = the proportion of (……)
Test statistic
Test statistics Degrees of Confidence interval Rejection p-value
freedom region
zα,n Right P(Z>…) =
None 1-P(Z<
…)
-zα,n Left P(Z< …)
=
Note: Different 2P(Z>…)
zα/2 by a =
2-tailed 2* 1-
test! P(Z<…) =
…
Computations
1. Look up the rejection region in table 3.
2. Fill in the formula for .
2. Fill in the formula.
3. Draw a picture
Interpret
If the computed z-value falls in the rejection region we can reject the H0. So we do have enough
evidence to reject the null hypothesis. We assume that We assume that … (repeat H1 in words).
If the computed z-value falls outside the rejection region we cannot reject the H0. We do not have
enough evidence to reject the null hypothesis. We assume that … (repeat H0 in words).
Interpretation confidence interval
If we repeatedly draw samples of sizes … (n) from the population of … , 95% of differences between
… and … would lie between … (LCL) and … (UCL)
4 4
, T test / Student t statistic / one simple T test
Hypothesis
H0 = μ = (invullen wat in de tekst staat…)
H1= μ = <>≠(invullen wat in de tekst staat)
μ = the mean of ……
Test Statistic
Test statistic Degrees of freedom Confidence interval Rejection region
tα,v
v=n–1 α = table 4.
Computations
1. Look up the rejection region in table 4
2. Do the test statistic
3. Draw a picture
Interpret
If the computed t-value falls in the rejection region we can reject the H0. So we do have enough
evidence to reject the null hypothesis. We assume that … (repeat H1 in words).
If the computed t-value is falls outside the rejection region we cannot reject the H0. We do not have
enough evidence to reject the null hypothesis. We assume that … (repeat H0 in words).
Assumptions
- Test statist for μ when σ is unknown
- Population = normal
- Data: interval/ ratio
- Doel: test population mean je vergelijkt een steekproefgemiddelde met een theoretisch
gemiddelde.
Interpretation confidence interval
If we repeatedly draw samples of sizes … (n) from the population of … , 95% of differences between
… and … would lie between … (LCL) and … (UCL)
5 5
, F-test (to test population variances)
Hypothesis
H0 :
H1 :
Test statistic
Test statistics Degrees of freedom Confidence interval Rejection region
F>
V1 = n1 – 1
V2 = n2 – 2
F<
Computations
1. Look up rejection region in table 6
2. Fill in the formula
3. Draw a picture
Interpret
If the computed F-value falls in the rejection region we can reject the H0. So we do have enough
evidence to reject the null hypothesis. We assume the population variances to be different.
If the computed F-value falls outside the rejection region we cannot reject the H0. We do not have
enough evidence to reject the null hypothesis. We assume the population variances to be equal.
Interpretation confidence interval
If we repeatedly draw samples of sizes … (n) from the population of … , 95% of differences between
… and … would lie between … (LCL) and … (UCL)
6 6
Z Test ....................................................................................................................................................... 3
Assumptions - Test statist for μ when σ is known .................................................................................. 3
Z test statistic for p (=proportion) ........................................................................................................... 4
T test / Student t statistic / one simple T test ........................................................................................ 5
F-test (to test population variances) ....................................................................................................... 6
Independent t-test = 2T-test ................................................................................................................... 7
Paired simple T test / (T test and estimator of μD) .................................................................................. 8
Chi-Squared Goodness-of-fit Test Statistic (Nominal)............................................................................. 9
Chi-Squared test of a contingency table (Nominal) .............................................................................. 10
Wilcoxon Rank Sum Test (Data is ordinal or interval – nonparametric / Independent samples) ......... 11
Wilcoxon Signed Rank Sum Test (Data is interval – nonparametric / Matched Pair) ........................... 12
Sign test (Binomial matched pair) ......................................................................................................... 13
Spearman Rank Correlation Coefficient (Ordinal or Interval – Nonparametric)................................... 14
Regression analysis (multiple and single) .............................................................................................. 15
Pearson coefficient of correlation (normal Interval)............................................................................. 17
Multiple regression testing the validity................................................................................................. 18
Multiple regression testing the Coefficients (β0, β1, β2, etc.) ................................................................ 19
1 1
,2 2
, Z Test
Hypotheses
H0 = μ = the mean is equal to ..(invullen wat in de tekst staat…)
H1= μ = the mean is <>≠(invullen wat in de tekst staat)
Test Statistic
Test statistics Degrees Confidence Rejection p-value
of interval region
freedom
Right P(Z>…) = 1-
None P(Z< …)
Left P(Z< …) =
Note: zα/2
by a 2- Different 2P(Z>…) =
tailed 2* 1-P(Z<…)
test! =…
Computations
1. Look up the rejection region in table 3 (veld).
2. Do the test statistic
3. Draw a picture
Interpret
If the computed z-value falls in the rejection region we can reject the H0. So we do have enough
evidence to reject the null hypothesis. We assume that … (repeat H1 in words).
If the computed z-value is falls outside the rejection region we cannot reject the H0. We do not have
enough evidence to reject the null hypothesis. We assume that … (repeat H0 in words).
Assumptions
- Test statist for μ when σ is known
Interpretation confidence interval
If we repeatedly draw samples of sizes … (n) from the population of … , 95% of differences between
… and … would lie between … (LCL) and … (UCL)
3 3
, Z test statistic for p (=proportion)
Hypothesis
H0 : p = .5
H1 : p = </>/≠ .5
p = the proportion of (……)
Test statistic
Test statistics Degrees of Confidence interval Rejection p-value
freedom region
zα,n Right P(Z>…) =
None 1-P(Z<
…)
-zα,n Left P(Z< …)
=
Note: Different 2P(Z>…)
zα/2 by a =
2-tailed 2* 1-
test! P(Z<…) =
…
Computations
1. Look up the rejection region in table 3.
2. Fill in the formula for .
2. Fill in the formula.
3. Draw a picture
Interpret
If the computed z-value falls in the rejection region we can reject the H0. So we do have enough
evidence to reject the null hypothesis. We assume that We assume that … (repeat H1 in words).
If the computed z-value falls outside the rejection region we cannot reject the H0. We do not have
enough evidence to reject the null hypothesis. We assume that … (repeat H0 in words).
Interpretation confidence interval
If we repeatedly draw samples of sizes … (n) from the population of … , 95% of differences between
… and … would lie between … (LCL) and … (UCL)
4 4
, T test / Student t statistic / one simple T test
Hypothesis
H0 = μ = (invullen wat in de tekst staat…)
H1= μ = <>≠(invullen wat in de tekst staat)
μ = the mean of ……
Test Statistic
Test statistic Degrees of freedom Confidence interval Rejection region
tα,v
v=n–1 α = table 4.
Computations
1. Look up the rejection region in table 4
2. Do the test statistic
3. Draw a picture
Interpret
If the computed t-value falls in the rejection region we can reject the H0. So we do have enough
evidence to reject the null hypothesis. We assume that … (repeat H1 in words).
If the computed t-value is falls outside the rejection region we cannot reject the H0. We do not have
enough evidence to reject the null hypothesis. We assume that … (repeat H0 in words).
Assumptions
- Test statist for μ when σ is unknown
- Population = normal
- Data: interval/ ratio
- Doel: test population mean je vergelijkt een steekproefgemiddelde met een theoretisch
gemiddelde.
Interpretation confidence interval
If we repeatedly draw samples of sizes … (n) from the population of … , 95% of differences between
… and … would lie between … (LCL) and … (UCL)
5 5
, F-test (to test population variances)
Hypothesis
H0 :
H1 :
Test statistic
Test statistics Degrees of freedom Confidence interval Rejection region
F>
V1 = n1 – 1
V2 = n2 – 2
F<
Computations
1. Look up rejection region in table 6
2. Fill in the formula
3. Draw a picture
Interpret
If the computed F-value falls in the rejection region we can reject the H0. So we do have enough
evidence to reject the null hypothesis. We assume the population variances to be different.
If the computed F-value falls outside the rejection region we cannot reject the H0. We do not have
enough evidence to reject the null hypothesis. We assume the population variances to be equal.
Interpretation confidence interval
If we repeatedly draw samples of sizes … (n) from the population of … , 95% of differences between
… and … would lie between … (LCL) and … (UCL)
6 6
