RBMS recap
Hypothesis testing gives us an estimate of how likely it is to observe what we observe, given the
null hypothesis.
We never accept a null hypothesis as true, since we cannot prove a negative. You can only prove a
positive by rejecting a negative.
Study design
Research question: Population, Intervention, Comparison, Outcome variables, Study design.
H0 = no effect.
H1 = effect.
Two-sided: can go in either direction.
One-sided: smaller/ larger than.
You can only use a 1-sided effect when the 2-sided is biologically implausible of at no interest at all.
Dependent variables: how are we going to measure the outcomes we are interested in, in what way,
and how many?
- Type (nominal, ordinal, discrete, continuous).
Independent: how are we going to measure/ manipulate our variables
- Type (nominal, ordinal, discrete, continuous).
- Manipulation; within subjects > dependent/ paired.
between > independent/ unpaired.
Observational:
Without manipulation and without randomization.
Only allows conclusions on associations, and no causal inference can be made.
3 ‘options’
o Cross-sectional: all measurements happen at the same time.
o Case control: you measure the outcome and you look back in time to find possible
predicters.
o Prospective: you follow a sample over time for a certain period.
Experimental:
Manipulation and randomization.
Randomization: allows conclusions on causal effects.
2 ‘options’
o RCD: participants are randomly assigned to only 1 of more groups.
, o Cross-over: randomly assigned to an order of 2 or more conditions (order= random).
Design example with breathing is e.g. randomized cross-over.
Dependent: (para)sympathetic tone (ton/ responses).
Independent: breathing protocol (deep breathing or sham breathing) + time (pre vs post).
When you use the difference scores instead of pre and post breathing (so one measurement), this
results in only 1 independent variable.
Descriptive statistics
Goal: to present, organize and summarize data observed in the sample.
Inferential statistics
Goal: to draw conclusions about a population based on data observed in a sample.
P-value = probability of the data given that the null hypothesis is true.
Very unlikely: reject the null hypothesis, accept the alternative/ experimental hypothesis.
Very unlikely: threshold < α: 0.05 is regarded as ‘unlikely enough’ to reject the null hypothesis.
Test Statistic (TS) = (point estimate - expected value)/ SE.
(Point estimate = the mean, SE = sd/√n).
Test statistic= the deviation of the data from the data under null hypothesis.
Independent samples t-test: null hypothesis is ‘means from 2 groups are equal’.
Dependent samples t-test: null hypothesis is ‘means from 2 conditions in 1 sample are equal’.
Empirical sample distribution: based on empirical data in the sample.
Theoretical probability distribution: predicted/ approximated/ hypothetical population distribution.
If empirical distributions of data resemble the normal distribution, then the mathematical properties
of the normal distribution can be used to draw conclusions about the population based on the
sample using parametric statistics.
If not, nonparametric statistics are required.
Normal distribution: continuous, bell-shaped and symmetrical.
Mid-point = mean = median = mode.
95% of the observations fall between the mean –1.96 SD and the mean + 1.96 SD.
2.5% (0.025) of the observations are < mean –1.96 SD.
2.5% (0.025) of the observations are > mean + 1.96 SD.
, From normal to standard normal distribution: Z = (x – mean)/ sd.
Compare two scores from two different normal distributions.
Compare where the score of someone lies in two different distributions.
Z-score = ‘answer’ times higher (or lower is negative) than the mean.
Probability for this: use Z-table (or area under the curve).
o If probability in the table is 0.97128, then the probability student lies less than Fred
= 97.1%.
o Probability that a student lies more than Fred = 2.9%.
Blue zone: p > 0.05. If the observed t is not more extreme than the critical t:
Probability of observing the data given that the H 0 is true is likely > retain the H0.
Red zone: other way around. More extreme, very unlikely > reject H0. (SIGNIFICANT RESULT).
P-value = the probability of finding the result you obtained (or test statistic), or a more extreme one,
given that the null hypothesis is true.
A p-value does not say anything about whether the H 0 is true, or about the size of the effect.
Test selection
Does the research question involve;
o a difference in means
o a difference in proportions
o an association?
What level of measurement are the dependent variables (DV) and independent variables
(IV)? (nominal, ordinal, discrete, continuous)
Is the DV normally distributed?
How many levels has the IV?
Are the measurements / manipulations
o dependent/within-subjects/paired
o independent/between-subjects/unpaired?
Hypothesis testing gives us an estimate of how likely it is to observe what we observe, given the
null hypothesis.
We never accept a null hypothesis as true, since we cannot prove a negative. You can only prove a
positive by rejecting a negative.
Study design
Research question: Population, Intervention, Comparison, Outcome variables, Study design.
H0 = no effect.
H1 = effect.
Two-sided: can go in either direction.
One-sided: smaller/ larger than.
You can only use a 1-sided effect when the 2-sided is biologically implausible of at no interest at all.
Dependent variables: how are we going to measure the outcomes we are interested in, in what way,
and how many?
- Type (nominal, ordinal, discrete, continuous).
Independent: how are we going to measure/ manipulate our variables
- Type (nominal, ordinal, discrete, continuous).
- Manipulation; within subjects > dependent/ paired.
between > independent/ unpaired.
Observational:
Without manipulation and without randomization.
Only allows conclusions on associations, and no causal inference can be made.
3 ‘options’
o Cross-sectional: all measurements happen at the same time.
o Case control: you measure the outcome and you look back in time to find possible
predicters.
o Prospective: you follow a sample over time for a certain period.
Experimental:
Manipulation and randomization.
Randomization: allows conclusions on causal effects.
2 ‘options’
o RCD: participants are randomly assigned to only 1 of more groups.
, o Cross-over: randomly assigned to an order of 2 or more conditions (order= random).
Design example with breathing is e.g. randomized cross-over.
Dependent: (para)sympathetic tone (ton/ responses).
Independent: breathing protocol (deep breathing or sham breathing) + time (pre vs post).
When you use the difference scores instead of pre and post breathing (so one measurement), this
results in only 1 independent variable.
Descriptive statistics
Goal: to present, organize and summarize data observed in the sample.
Inferential statistics
Goal: to draw conclusions about a population based on data observed in a sample.
P-value = probability of the data given that the null hypothesis is true.
Very unlikely: reject the null hypothesis, accept the alternative/ experimental hypothesis.
Very unlikely: threshold < α: 0.05 is regarded as ‘unlikely enough’ to reject the null hypothesis.
Test Statistic (TS) = (point estimate - expected value)/ SE.
(Point estimate = the mean, SE = sd/√n).
Test statistic= the deviation of the data from the data under null hypothesis.
Independent samples t-test: null hypothesis is ‘means from 2 groups are equal’.
Dependent samples t-test: null hypothesis is ‘means from 2 conditions in 1 sample are equal’.
Empirical sample distribution: based on empirical data in the sample.
Theoretical probability distribution: predicted/ approximated/ hypothetical population distribution.
If empirical distributions of data resemble the normal distribution, then the mathematical properties
of the normal distribution can be used to draw conclusions about the population based on the
sample using parametric statistics.
If not, nonparametric statistics are required.
Normal distribution: continuous, bell-shaped and symmetrical.
Mid-point = mean = median = mode.
95% of the observations fall between the mean –1.96 SD and the mean + 1.96 SD.
2.5% (0.025) of the observations are < mean –1.96 SD.
2.5% (0.025) of the observations are > mean + 1.96 SD.
, From normal to standard normal distribution: Z = (x – mean)/ sd.
Compare two scores from two different normal distributions.
Compare where the score of someone lies in two different distributions.
Z-score = ‘answer’ times higher (or lower is negative) than the mean.
Probability for this: use Z-table (or area under the curve).
o If probability in the table is 0.97128, then the probability student lies less than Fred
= 97.1%.
o Probability that a student lies more than Fred = 2.9%.
Blue zone: p > 0.05. If the observed t is not more extreme than the critical t:
Probability of observing the data given that the H 0 is true is likely > retain the H0.
Red zone: other way around. More extreme, very unlikely > reject H0. (SIGNIFICANT RESULT).
P-value = the probability of finding the result you obtained (or test statistic), or a more extreme one,
given that the null hypothesis is true.
A p-value does not say anything about whether the H 0 is true, or about the size of the effect.
Test selection
Does the research question involve;
o a difference in means
o a difference in proportions
o an association?
What level of measurement are the dependent variables (DV) and independent variables
(IV)? (nominal, ordinal, discrete, continuous)
Is the DV normally distributed?
How many levels has the IV?
Are the measurements / manipulations
o dependent/within-subjects/paired
o independent/between-subjects/unpaired?
