Cogntive Testing and Statistics Flashcards
What is cognition?
The mental action or process of acquiring knowledge and understanding through thought, experience, and the senses
What are we interested in in scientific investigation of cognition?
The mechanisms of thought that drive a person’s mind
Can be impaired - cogntive deficits are distressing to patients
Cognition is driven by multiple processes and functions that work together to create a whole- highly complex
What is a caveat of measuring cognition?
Any measurement attempt we make is always a best guess- always caveats and a level of noise that come between us and the thing we want to measure
-affects ability to accurately quantify what we’re interested in
Why is measuring cognition hard?
Because the mind itself is a psychological theory - so we have to consider what a psychological theory is and also how accurate it is
We break down the mind into what we think its made up of but we are always one step away from measuring it- we’re dealing with a theoretical construct within a theoretical construct
What are cognitive tests if the mind is a psychological theory?
Cognitive tests are attempts at creating markers of something that only exists in a theory
What is a normal distribution?
A normal distribution is where there is a clear trend for the value of most points to cluster around a central mean, with equally increasing rarity on either side of this
Many things don’t follow this pattern but it’s used as a starting point to decide how to conduct statistics
Why is a normal distribution important?
The central issue is asking if the mean value is a fair way of representing what is “average”
-if we have a normal distribution then the mean of that is the most appropriate value to represent that data
What does it mean if something is parametric?
That is has a normal distribution
When does data violate parametric assumptions?
The moment it doesn’t follow a mathematically perfect normal distribution (when most data isnt perfect) it means it violates these assumptions
What happens when data distribution becomes more skewed?
Once data is skewed, the mean is increasingly pulled in one direction by extreme values.
The median and the mode become more representative of what is most expected.
When we have a normal distribution we want to know how variable it is, how do we work this out?
By calculating its variance - so how far away from the mean it is
What is variance?
The variance of a sample is the average difference of all individual data points from the mean. It quantifies how tightly clustered (or not) the data is around the mean
It is a slight overestimation, of the sum of squares, of the difference between each individual data point and the mean
What is standard deviation (SD)?
Because variance is a version of our data after we have squared everything, its value is greatly increased compared to our original units of measurement
The SD is just the square root of the variance, so it re-converts it back into proportion with our data.
What is the relationship between the mean and SD in a normal distribution?
SD has a consistent mathematical relationship with a normal distribution
What does it mean if we travel x SD’s away from the mean?
As we travel x SD’s away from the mean, the % of data points included in our range increases by set amounts.
e.g. 1 SD either side of the mean captures the results of about 68% of people
When do scientists attribute significance to something?
When it has less than 5% probability of happening by chance
This is often a single data point more than 2 SD’s from the mean (where 2 SDs covers 95% of people)
What are the number of points in the data (the sample size) referred to as?
N
What does a larger sample mean?
Means we have more confiedence that our means etc are representative of that variables’ true pattern
What is the p value?
The objective of stats tests is to summarise your experiment with a p value.
This is a number between 0 and 1, which is essentially the % probability (when multiplied by 100) that the data you have observed has happened by chance.
We are trying to work out if the data are so different that it can’t be caused by noise & there is a reason people are scoring differently
What does it mean if p<0.05 ?
That there is a less than 5% probability of it happening by chance alone, that it is “statistically significant”
We would reject the null at this point
What are two common statistical designs?
- Comparing a value between groups of participants , or before/after and intervention: groupwise tests
- Seeing how one value changes depending on another value: correlations
What is parametric groupwise testing?
Comparing a score between two groups
What statistical test do we use for parametric groupwise testing that looks at two groups e.g. healthy vs disease groups ?
Independent samples T-test
What makes the t value bigger?
Greater distance between means
Smaller SDs
Largers Ns
How to we go from a T value to a p value?
Statisticians know the thresholds for t values at different probabilities.
The last thing we need to convert a t statistic to a p value is the degrees of freedom, which is essentially our N but in a t-test we subtract 1 from it
How does a higher N affect t-tests?
Having a higher N makes the significance threshold on a t value “easier” to achieve.
What statistical test do we use for parametric groupwise testing that looks at a before and after score?
Paired samples t-test
What are parametric correlations?
Seeing if there is a relationship between two variables
What statistical test do we use for a parametric correlation?
Pearson’s correlation
What is a pearson’s correlation?
It calculates the covariance between your X variable and your Y variable
r value comes out between -1 and 1 where:
-1 = perfect negative correlation
0 = no relationship at all
1 = perfect positive correlation
What are the three types of correlation?
Perfect positive
Zero
Perfect negative
What do we do with skew?
We use non-parametric equivalent statistical tests
Because our parametric tests rely on mean values a skewed distribution becomes a problem for their validity.
We can still run the same experiments (groupwise or correlations) but we must substitute them with non-parametric test alternatives.
What does in independent t-test become in non-parametric testing?
Mann-Whitney U
What does a paired t-test become in non-parametric testing?
Wilcoxon signed-rank
What does a Pearson correlation become in non-parametric testing?
Spearman correlation
What is the main difference between parametric and non-parametric tests?
Non-parametric tests often just used a “ranked” version of the data
This is still representative of which samples are bigger than others, but massively reduces the disproportionate effect that extreme values have on the mean.
How do we examine multivariate models?
Often we want to look at how multiple variables affect an outcome, all at once.
It is possible (advisable!) to build a single multivariate model to test this.
This is called a multiple regression
What does the sig. column show in multivariate models?
Shows the individual p values for each variable
What are multiple regressions?
Multiple regressions are not the same as separately running single variable analyses and putting the results in a list. They consider how these variables relate to one another as well in determining the model significance.
Allows us to control for factors we want to exclude
What is the multiple comparisons problem?
The more tests we run in a study, the more likely we are to get a “significant” result by random chance
We need to be conscious of this in our study design, and in the way we approach our analyses
How can we correct for multiple comparisons?
Bonferoni correction
How do you calculate a Bonferoni correction?
Divide 0.05 by the number of comparisons we have run
This is our new significance threshold
