The SPINE of statistics Flashcards
What should the author stop doing?
Talking about his little boy penis
What is the Spine of statistics?
Five key concepts to understand statistics:
- Standard error
- Parameters
- Interval estimates (confidence intervals)
- Null hypothesis significance testing
- Estimating the parameter
What is meant by the fit of a model?
The degree top which a statistical model represents the data collected
What is meant by parameters?
Parameters are the unknown values of an entire population, such as the mean and standard deviation
What does the little hat denote in an equation?
An estimate
What is meant by deviance/ error
The difference between a score and the mean
When is the mean a good fit for the data?
When there isn’t much deviance
What is a sampling distribution
Distribution showing the data of means ( or other parameters) from different samples
When is a t distribution formed?
When the sample is relatively small (under 30) so the sampling distribution is not normal
What value of t do we get for a 95% confidence interval?
Value of t for a two tails t test with a probability of 0.05, for the appropriate degrees of freedom
What is an error bar and how is it marked?
An error bar shows the confidence interval on a graph and looks like the capital letter I
What does it usually mean if two confidence intervals don’t overlap
they come from two different populations
What can we infer if they come from two different populations from the experimental condition?
The experimental condition has induced a difference in the examples
What two different approaches are there to the problem of how to use data to test theories?
1) Ronald Fishers idea of computing probabilities to evaluate evidence (P value)
2) Neyman and Pearsons idea of competing hypotheses (H0, H1)
What is meant by the alpha?
The error rate/ significance level (95% etc)
What is the difference between systematic and unsystematic variation?
Systemic variation is variation that can be explained by a model that we’ve fitted into the data (and therefore due to the hypothesis that we’re testing). Unsystematic variation is variation that cannot be explained by the model that we’ve fitted
What is a test statistic mathematically?
Size of parameter/ sampling variation in the parameter
What are type 1 and type 2 errors?
Type 1: Believing there is an effect in the population when there isn’t (false positive) (too small an interval)
Type 2: Believing there is no effect when there is (too wide an interval)
When should you use a one tailed test?
When the opposite direction would result in the same as a non significant result
What is meant by a and b levels?
a- The probability of type 1 error (0.05 in 95% significance level)
b- The probability of type 2 error
If you wanted to measure three constructs in an experiment at a 95% significance level, assuming they’re independent, what would the probability of no type 1 error be?
95^3= 0.857
How can we avoid this build up of error
Adjusting the level of significance so that it stays at 5%, this can be done by dividing a by the number of comparisons (tests)
What is meant by the power of a test?
The statistical power of a test is its ability to find an effect
How can the power of a test be described mathematically ?
1- B
What statistical power do we typically aim for?
1- 0.2 = 0.8 (80%)
What does the power of a test depend on?
- The effect size
- Level of significance (a level) - also recurring tests affect this
- Sample size
What can scientists do with this knowledge of calculating power?
- Check if they have enough statistical power
2. Measure the sample size required
What are the three guidelines regarding confidence levels and statistical significance?
- 95% confidence intervals that just about just end to end represent a p-value for testing the null hypothesis of no differences of approximately 0.01
- if there is a gap between the upper end of one 95% confidence interval and the lower end of another then p< 0.01
- A p value of 0.05 is represented by a moderate overlap between the bars
How is moderate overlap generally defined?
Half the length of the average margin of error (MOE is half the length of the confidence interval)
What effect does the sample size have on the confidence intervals and why?
As the sample size gets bigger the interval gets smaller by the sd is divided by the square root of the sample size
If we had a mean of 14 and the confidence interval ranged from 8-20 how would we report this?
M= 14, 95% Cl [8, 20] M= 14 [8, 20]
