what is usually displayed on the X axis?
the measured variable
what is usually displayed on the Y axis?
the frequency
what are the characteristics of a normal distribution graph?
- Naturally Occurring
- Asymptotic (theoretically)
- Symmetrical
what is always in the middle of a distribution curve?
The mode, median and mean
what percentage of data is in the 1st SD?
68.56% (34.13% either positive or negative)
what percentage of data is in the 2nd SD?
34.13% (13.59% either positive or negative)
what percentage of data is in the 3rd SD?
4.3% (2.15% either positive or negative)
how do you determine the Z score?
average+SD
characteristics of Non-Normal distribution graphs
asymmetrical
mode, median and mean are all in different areas of the graph
can either have a positive or negative skew
why is distribution important?
- Determines which measure of central tendency to use
- Determines which measure of variability to use
- Provides ‘Z-score’ for standardised comparisons
- Determines further statistical analysis
- Parametric (assumes ND, random sample-more powerful)
- Non-parametric (simply calculated, distribution free-less powerful).
probability can scale from either
0-1
or
0%-100%
why do we need to understand probability?
- p-values are used in research and statistics!
- in order to determine how likely it is that:
- there is NO difference between groups /samples
- there is NO correlation between two variables
why do we use inferential stats?
- objectively interpret data
- Make an ‘inference’ about a population from our research sample
- draw conclusions
sample means can either be:
•‘real’:
-indicative of a difference between the 2 populations
•numerical only
-a ‘chance’ finding
-there is no difference between the 2 populations, just between the 2 samples
what does the null-hypothesis state?
•there is no difference in the population
•If H0 is correct:
- i.e.: no real difference between the two populations
* any observed NUMERICAL difference is coincidental
what will happen to the probability if the null-hypothesis is true?
We can calculate the probability (p): of finding a result as big or bigger as the one we observed, if the null hypothesis is true
why test the null-hypothesis?
- Null hypothesis is always exact (i.e.: REAL difference = 0)
- We are rarely able to exactly predict how big the difference should be for the experimental hypothesis
- Statistically we can work out the probability of finding a difference similar to or larger than we observed if H0 is correct
- If this probability is low enough, we reject H0 and accept that there is (probably) a real difference
when do we reject the probability?
We reject the null hypothesis if the probability of finding a similar or larger difference by chance is less than 5%
procedure: if p<0.05 we conclude that:
- the probability of finding a similar or larger difference is low enough to reject H0
- there is a SIGNIFICANT difference
procedure: if p>0.05 we conclude that:
- the probability of finding a similar or larger difference is too high to be able to reject H0
- there is no SIGNIFICANT difference
