HC1: Recap RBMS
…
Retain the null hypothesis, but we don’t conclude it’s true because of the uncertainty of the
research
PICOS: population, intervention, comparison, outcome variables, study design
Two-sided hypotheses
Null hypotheses: H0: no effect
Alternative hypotheses: H1 or Ha: an effect (can go in either direction)
One-sided hypotheses only if the other way around is biologically implausible, or based on
other research (but that is not a sufficient argument to choose a one sided hypothesis)
Null hypotheses: smaller than/larger than
Alternative hypothesis: larger than or equal to/smaller than or equal to
Research design
- Research question causal effect or association?
- Dependent variable
o Measurement type (nominal, ordinal, discrete, continuous), how many?
- Independent variable
o Measurement type, how many?
o Manipulation compare groups or conditions? How many?/ are
measurements/manipulations dependent/within-subjects/paired or
independent/between-subjects/not paired?
Biomedical research
- Observational conclusions on associations (no causation conclusion can be made)
o Cross-sectional: all measurements happen at the same time
o Case control: look all to the same outcome, look back in time to find possible
predictors
o Prospective: follow a sample over time to look at outcome
- Experimental allows conclusion on causal effect
o Randomized control design: people take part of 1 condition, 2 independent
groups
o Cross-over design: take part of all conditions, but the order is randomly
assigned
Descriptive statistics to present, organize and summarize data observed in the sample
- Measures of central tendency
o Mean
o Median
o Mode
- Measures of dispersion/variability
o Range, interquartile range
o Variance, standard deviation
- Graphs and figures
,Inferential statistics to draw conclusions about a population based on data observed in a
sample (by using statistical tests)
- P value = probability of the data to occur in a sample given that the H0 is true
o Very unlikely reject H0 and accept Ha
o Threshold alfa: 0.05 (5%)
o P-value < 0.05 is regarded as unlikely enough to reject the null hypothesis
- Statistical tests
o To what extent do the data we collected in the sample deviate from what we
would expect our sample to look like if the H0 is true
o TS = (point estimate – expected value) / SE
Point estimate: e.g. mean or proportion
Expected value: expected value under the null hypothesis (usually 0)
SE (standard error): precision of the point estimate
- Empirical probability distribution: sample distribution based on the 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
o If not, nonparametric statistics
- Normal distribution: continuous, bell-shaped symmetrical
o Defined by mean and SD
o Symmetrical around the mid-point of the horizontal axis
o Mid-point = mean = median = mode
o 95% of the observations fall between the mean – 1.96 SD and the mean + 1.96
SD
o 5% of the observations are < mean – 1.96 SD or > mean + 1.96 SD (2.5% each)
o Minus and plus 1SD = 68% and minus and plus 2SD = 95%
- From normal distribution to the standard normal distribution
o Standardizing: calculating Z-score
Z=(x-mean)/sd
o Compare two scores form two different normal distributions
o Probability calculate area under the curve OR calculate the value from the
standard normal table
o T-distribution strongly resembles a normal distribution but has higher tails
Apply the mathematical properties of the normal distribution to derive
probabilities
T statistic where on the t-distribution, probability of t: p-value
Critical t value mark the 5% cut off where we either reject or retain
or H0
- P value = the probability of finding the result you obtained, or a more extreme one,
given that the null hypothesis is true / the probability of finding the test statistic you
obtained, or a more extreme one, given that the null hypothesis is true
o If p-value < threshold alfa observed data are very unlikely given the null
hypothesis reject the null hypothesis – “significant result”
, o If p-value >= threshold alfa observed data are likely given the null
hypothesis retain the null hypothesis – “non-significant result”
o A p-value does not say anything about
Whether the null hypothesis is true failing to reject the null
hypothesis and retaining the null hypothesis does not mean that you
can accept the null hypothesis as true. It only means that there is not
currently enough evidence to conclude that it is untrue
The size of the effect
Small p-value indicates either a strong signal (reality is very
different from H0) or little noise (by large sample you
minimized the role of chance)
Test selection
- Does the research question involve
o A difference in means, in proportions or an association
o What level of measurement are the dependent variables and independent
variables?
o Is the DV normally distributed
o How many levels has the IV
o Are the measurements / manipulations
Dependent/within-subjects/paired
Independent/between-subjects/unpaired
, Hypothesis testing and errors
- Probability implies uncertainty errors possible
- Type 1 error: rejecting the null hypothesis, when you should have retained the null
hypothesis
- Type 2 error: retaining the null hypothesis, when you should have rejected the null
hypothesis
The process of null hypothesis testing
- A statistical test is a procedure to decide whether a hypothesis about the population
may or may not be supported by the results of the sample
- Confidence intervals: check whether the hypothesized estimate falls in an interval
around the sample parameter of which we are very confident that it contains the
population parameter
Confidence intervals: an interval of which the confidence is very high that it contains the
population mean
- Structure CI: point estimate +- margin of error
o Point estimate: mean or proportion
o Margin of error: critical test statistic value * SE
o SE: precision point estimate, dependent on sample size
o CI95%(u) = mean (x) +- t95% * se
o Se = sd*vn
- Meaning: if we sample a large number of times, and compute the CI for each sample,
95% of Cis would contain the true population parameter or we are 95% confident
that the population parameter lies within the CI
- One sample t-test
…
Retain the null hypothesis, but we don’t conclude it’s true because of the uncertainty of the
research
PICOS: population, intervention, comparison, outcome variables, study design
Two-sided hypotheses
Null hypotheses: H0: no effect
Alternative hypotheses: H1 or Ha: an effect (can go in either direction)
One-sided hypotheses only if the other way around is biologically implausible, or based on
other research (but that is not a sufficient argument to choose a one sided hypothesis)
Null hypotheses: smaller than/larger than
Alternative hypothesis: larger than or equal to/smaller than or equal to
Research design
- Research question causal effect or association?
- Dependent variable
o Measurement type (nominal, ordinal, discrete, continuous), how many?
- Independent variable
o Measurement type, how many?
o Manipulation compare groups or conditions? How many?/ are
measurements/manipulations dependent/within-subjects/paired or
independent/between-subjects/not paired?
Biomedical research
- Observational conclusions on associations (no causation conclusion can be made)
o Cross-sectional: all measurements happen at the same time
o Case control: look all to the same outcome, look back in time to find possible
predictors
o Prospective: follow a sample over time to look at outcome
- Experimental allows conclusion on causal effect
o Randomized control design: people take part of 1 condition, 2 independent
groups
o Cross-over design: take part of all conditions, but the order is randomly
assigned
Descriptive statistics to present, organize and summarize data observed in the sample
- Measures of central tendency
o Mean
o Median
o Mode
- Measures of dispersion/variability
o Range, interquartile range
o Variance, standard deviation
- Graphs and figures
,Inferential statistics to draw conclusions about a population based on data observed in a
sample (by using statistical tests)
- P value = probability of the data to occur in a sample given that the H0 is true
o Very unlikely reject H0 and accept Ha
o Threshold alfa: 0.05 (5%)
o P-value < 0.05 is regarded as unlikely enough to reject the null hypothesis
- Statistical tests
o To what extent do the data we collected in the sample deviate from what we
would expect our sample to look like if the H0 is true
o TS = (point estimate – expected value) / SE
Point estimate: e.g. mean or proportion
Expected value: expected value under the null hypothesis (usually 0)
SE (standard error): precision of the point estimate
- Empirical probability distribution: sample distribution based on the 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
o If not, nonparametric statistics
- Normal distribution: continuous, bell-shaped symmetrical
o Defined by mean and SD
o Symmetrical around the mid-point of the horizontal axis
o Mid-point = mean = median = mode
o 95% of the observations fall between the mean – 1.96 SD and the mean + 1.96
SD
o 5% of the observations are < mean – 1.96 SD or > mean + 1.96 SD (2.5% each)
o Minus and plus 1SD = 68% and minus and plus 2SD = 95%
- From normal distribution to the standard normal distribution
o Standardizing: calculating Z-score
Z=(x-mean)/sd
o Compare two scores form two different normal distributions
o Probability calculate area under the curve OR calculate the value from the
standard normal table
o T-distribution strongly resembles a normal distribution but has higher tails
Apply the mathematical properties of the normal distribution to derive
probabilities
T statistic where on the t-distribution, probability of t: p-value
Critical t value mark the 5% cut off where we either reject or retain
or H0
- P value = the probability of finding the result you obtained, or a more extreme one,
given that the null hypothesis is true / the probability of finding the test statistic you
obtained, or a more extreme one, given that the null hypothesis is true
o If p-value < threshold alfa observed data are very unlikely given the null
hypothesis reject the null hypothesis – “significant result”
, o If p-value >= threshold alfa observed data are likely given the null
hypothesis retain the null hypothesis – “non-significant result”
o A p-value does not say anything about
Whether the null hypothesis is true failing to reject the null
hypothesis and retaining the null hypothesis does not mean that you
can accept the null hypothesis as true. It only means that there is not
currently enough evidence to conclude that it is untrue
The size of the effect
Small p-value indicates either a strong signal (reality is very
different from H0) or little noise (by large sample you
minimized the role of chance)
Test selection
- Does the research question involve
o A difference in means, in proportions or an association
o What level of measurement are the dependent variables and independent
variables?
o Is the DV normally distributed
o How many levels has the IV
o Are the measurements / manipulations
Dependent/within-subjects/paired
Independent/between-subjects/unpaired
, Hypothesis testing and errors
- Probability implies uncertainty errors possible
- Type 1 error: rejecting the null hypothesis, when you should have retained the null
hypothesis
- Type 2 error: retaining the null hypothesis, when you should have rejected the null
hypothesis
The process of null hypothesis testing
- A statistical test is a procedure to decide whether a hypothesis about the population
may or may not be supported by the results of the sample
- Confidence intervals: check whether the hypothesized estimate falls in an interval
around the sample parameter of which we are very confident that it contains the
population parameter
Confidence intervals: an interval of which the confidence is very high that it contains the
population mean
- Structure CI: point estimate +- margin of error
o Point estimate: mean or proportion
o Margin of error: critical test statistic value * SE
o SE: precision point estimate, dependent on sample size
o CI95%(u) = mean (x) +- t95% * se
o Se = sd*vn
- Meaning: if we sample a large number of times, and compute the CI for each sample,
95% of Cis would contain the true population parameter or we are 95% confident
that the population parameter lies within the CI
- One sample t-test
