The PENIS of Statistics (L2 & L3) Flashcards
What does PENIS stand for?
Parameters Estimation Null Hypothesis Statistic Testing Intervals [of confidence] Standard error.
What are parameters?
Every model has parameters, represented by ‘b’. Regardless of the model, parameters are estimated using the same principles.
All parameters have: standard error, confidence interval & p-value.
What makes the mean a statistical model?
The value ascertained by the mean is hypothetical; it is not observed in the data.
Does the mean have error?
Yes, as the value obtained will not be correct for every person in the population. However, it has the ‘least error’ due to the squared scores deviating the least.
What do we assess how well a model accurately represents data?
Sum of squared error (or variance).
How do we assess how well a model accurately represents the population?
Standard error and confidence intervals.
What do we use the mean for?
To make predictions about the population.
What is ‘error’?
The deviation from what a model predicts (eg. the mean) and the actual data point (the observed value).
How do we calculate the sum of squared error?
SS = the sum of (score - mean)squared.
How do we calculate mean squared error?
s[squared] = the sum of (score - mean)squared / n-1
Note: why n-1? Because we are calculating for the population (see degrees of freedom).
What is standard deviation?
Variance in squared units.
How do we calculate standard deviation?
SD = squared root of mean squared error.
What do sum of squared error, variance and standard deviation all represent?
- The fit
- The variability
- The representation of the population
- Error.
What are degrees of freedom?
The freedom the experimenter has to randomly sample people from the population, in order to keep calculating the same mean.
Note: why n-1? As last person sampled is chosen so the mean continues to calculate a stated value, -1 removes this ‘person’ from the equation.
What is estimation through the method of least squares error?
Based on minimising squared error whereby we keep estimation the value of the mean until we find the lowest error for the parameter (b value)
What is the sampling error?
The difference between the sample value and the value given to you by the population.
What is the standard error?
Tells us something of how a parameter differs from sample to sample (ie. how spread out our samples are)
Why is it important to know the spread of sampling distribution?
It can tell you how close to the true value you are.
What percentage of the sample fall within 1.96 standard deviations of the mean in a normal distribution?
95%, indicating that 95% of people in the same ‘contain’ the value we are interested in (relates to confidence intervals)
What are confidence intervals?
They ‘go around’ the mean.
If confidence interval doesn’t overlap with each other it could be chance, but equally could show that the manipulation has created a population difference (eg. good experimental significance)
If confidence interval doesn’t overlap with the mean, they don’t contain the desired value.
NOT RELATED TO PROBABILITY
What does the null hypothesis suggest about the parameter value?
That (b)=0, because the parameter represents the effect/relationship of the parameter and in a null hypothesis there is no effect.
How is significance testing related to sample size?
The bigger the sample is, the easier it is to ‘find’ significance (ie. the same experiment could be insignificant with a small but significant with a large sample)
What is Cohen’s ‘d’?
A way to quantify the differences between means by dividing by the control groups SD (see equation).
- 2 is a small value,
- 8 is a large value.
What does a Cohen’s ‘d’ value of ‘d’=1 mean?
That the means are 1SD apart and therefore there is an effect.
What does a Cohen’s ‘d’ value of ‘d’=0 mean?
That the means are the same and therefore there was no experimental effect.
