Lecture 1
Distribution
SPSS syntax
FREQUENCIES
VARIABLES=X
/HISTOGRAM
/ORDER= ANALYSIS
Central tendency = most characteristic score of a distribution.
N
o Mean:
∑ Xi
i=1
X=
N
o Median
o Mode
Dispersion = how much do scores deviate from the most characteristic score.
o Range
N
o Variance: SS
∑ (X i− X)2
S2 = = i=1
N−1 N−1
o Standard deviation s= √ s2
Hypothesis testing
In hypothesis testing, you examine whether the mean of the population is equal to a certain
value or not.
o Hypothesis are exclusive and exhaustive
Two-sided test (H1: ≠), one-sided test (H1 contains < or >).
o SPSS output is always two-sided, so convert two-
sided Sig. to correct p-value.
Rules of thumb for creating hypothesis:
o H0 contains ‘=’ – always the case.
o H1 contains expectations of researcher – often.
Steps:
1. Formulate hypothesis.
2. Determine decision rule to decide when a result is
statistically significant: ρ ≤ 𝛼.
3. Determine p-value based on SPSS output.
4. Decision on significance and conclusion.
SPSS syntax
T-TEST
/TESTVAL= …
/MISSING=ANALYSIS
/VARIABLES=X
/CRITERIA=CIN (.95) .
Logic hypothesis testing
o Step 1: Make an assumption about the value of a parameter.
o Step 2:
Given that the value is true, you determine the possible values the sample
statistics can take in a simple random sample of N cases.
Using that sampling distribution, you determine the p-value that the value of
X or a more extreme value occurs.
, o Step 3: You determine the position of X in the sample distribution.
o Step 4:
If p-value is lower than 𝛼, you reject H0
If p-value is larger than 𝛼, you do not reject H0.
Point estimation = which values lies closest to the population value.
Confidence interval
With CIs, you answer the question: “What is the interval in which the value of the parameter
lies with …% confidence?”
X ± t cv × s / √ N
Relation CIs and testing
o Decision rule: two-sided test with significance level 𝛼
o D
o D
o D
o D
o D
o Assume H0 is true:
95% of all possible samples will produce a CI 95 in which μ H falls.
0
Correctly not reject H0
5% of all possible samples will produce a CI95 in which μ H does not fall.
0
Incorrectly rejecting H0 = type I error.
Testing means
One population:
D
D
Two populations
D
When using independent samples test in SPSS use Levene’s test (sig.) to determine whether to use
sig. (2-tailed) of equal variances assumed or equal variances not assumed.
Not significant first row – equal variances assumed.
Significant second row – equal variances not assumed.
Lecture 2
Power of a test
Power = probability of correctly rejecting the null
hypothesis if this is indeed the correct decision.
o Small alpha, large power.
Steps for determining power:
o Determine the Z for the given H0
o Determine sample mean that belongs with Z
for the given H0.
, o Convert the critical value X to the Z-value for the
given H1.
o The power is equal to the change:
P( Z ≥ Z H 1 ⎸ H 1 )
Four factors that influence power:
o Alpha
Lower alpha, means smaller critical value.
Higher alpha, means larger critical value – higher statistical power
o The sample size
The larger the sample size, the smaller the standard error and the larger Z-
score higher statistical power.
o σ (= SD)
The smaller the SD, the smaller the standard error and the larger Z-score
higher statistical power.
o The ‘true 𝜇’ in the alternative hypothesis
Larger effect size.
Effect size
When H0 is rejected based on a hypothesis test significant.
o But does not mean that is has definitively been proven that there is a systematic
effect.
o Does also not mean that the effect is practically/clinically relevant.
Because
If N is small, power is small, statistically not significant, even if effect
is large.
If N is big, power is larger, statistically significant, even if effect is
small.
Two important measures of effect size when comparing means:
o Cohen’s D – how large is the relative difference in the groups?
o (Partial) explained variance η2 – how much of the variance is explained by group
membership?
Rules of thumb interpretating effect size:
oSmall effect: a lot of overlap between the two distributions.
50% of experimental group scores higher than average of control group.
o Large effect: not much overlap between the two distributions.
80% of experimental group scores higher than average of control group.
Formulas:
o One group:
o
d=t
Two groups:
√ 1
N
d=t
√ 1 1
+
n1 n2
Distribution
SPSS syntax
FREQUENCIES
VARIABLES=X
/HISTOGRAM
/ORDER= ANALYSIS
Central tendency = most characteristic score of a distribution.
N
o Mean:
∑ Xi
i=1
X=
N
o Median
o Mode
Dispersion = how much do scores deviate from the most characteristic score.
o Range
N
o Variance: SS
∑ (X i− X)2
S2 = = i=1
N−1 N−1
o Standard deviation s= √ s2
Hypothesis testing
In hypothesis testing, you examine whether the mean of the population is equal to a certain
value or not.
o Hypothesis are exclusive and exhaustive
Two-sided test (H1: ≠), one-sided test (H1 contains < or >).
o SPSS output is always two-sided, so convert two-
sided Sig. to correct p-value.
Rules of thumb for creating hypothesis:
o H0 contains ‘=’ – always the case.
o H1 contains expectations of researcher – often.
Steps:
1. Formulate hypothesis.
2. Determine decision rule to decide when a result is
statistically significant: ρ ≤ 𝛼.
3. Determine p-value based on SPSS output.
4. Decision on significance and conclusion.
SPSS syntax
T-TEST
/TESTVAL= …
/MISSING=ANALYSIS
/VARIABLES=X
/CRITERIA=CIN (.95) .
Logic hypothesis testing
o Step 1: Make an assumption about the value of a parameter.
o Step 2:
Given that the value is true, you determine the possible values the sample
statistics can take in a simple random sample of N cases.
Using that sampling distribution, you determine the p-value that the value of
X or a more extreme value occurs.
, o Step 3: You determine the position of X in the sample distribution.
o Step 4:
If p-value is lower than 𝛼, you reject H0
If p-value is larger than 𝛼, you do not reject H0.
Point estimation = which values lies closest to the population value.
Confidence interval
With CIs, you answer the question: “What is the interval in which the value of the parameter
lies with …% confidence?”
X ± t cv × s / √ N
Relation CIs and testing
o Decision rule: two-sided test with significance level 𝛼
o D
o D
o D
o D
o D
o Assume H0 is true:
95% of all possible samples will produce a CI 95 in which μ H falls.
0
Correctly not reject H0
5% of all possible samples will produce a CI95 in which μ H does not fall.
0
Incorrectly rejecting H0 = type I error.
Testing means
One population:
D
D
Two populations
D
When using independent samples test in SPSS use Levene’s test (sig.) to determine whether to use
sig. (2-tailed) of equal variances assumed or equal variances not assumed.
Not significant first row – equal variances assumed.
Significant second row – equal variances not assumed.
Lecture 2
Power of a test
Power = probability of correctly rejecting the null
hypothesis if this is indeed the correct decision.
o Small alpha, large power.
Steps for determining power:
o Determine the Z for the given H0
o Determine sample mean that belongs with Z
for the given H0.
, o Convert the critical value X to the Z-value for the
given H1.
o The power is equal to the change:
P( Z ≥ Z H 1 ⎸ H 1 )
Four factors that influence power:
o Alpha
Lower alpha, means smaller critical value.
Higher alpha, means larger critical value – higher statistical power
o The sample size
The larger the sample size, the smaller the standard error and the larger Z-
score higher statistical power.
o σ (= SD)
The smaller the SD, the smaller the standard error and the larger Z-score
higher statistical power.
o The ‘true 𝜇’ in the alternative hypothesis
Larger effect size.
Effect size
When H0 is rejected based on a hypothesis test significant.
o But does not mean that is has definitively been proven that there is a systematic
effect.
o Does also not mean that the effect is practically/clinically relevant.
Because
If N is small, power is small, statistically not significant, even if effect
is large.
If N is big, power is larger, statistically significant, even if effect is
small.
Two important measures of effect size when comparing means:
o Cohen’s D – how large is the relative difference in the groups?
o (Partial) explained variance η2 – how much of the variance is explained by group
membership?
Rules of thumb interpretating effect size:
oSmall effect: a lot of overlap between the two distributions.
50% of experimental group scores higher than average of control group.
o Large effect: not much overlap between the two distributions.
80% of experimental group scores higher than average of control group.
Formulas:
o One group:
o
d=t
Two groups:
√ 1
N
d=t
√ 1 1
+
n1 n2
