Distributions and Variables

Essential in statistics - provide information on data-set composition

Normal distributions (Gaussian distributions) = bell curves, symmetrical distribution around mean, 68.2% values fall in 1 SE around mean

• Bimodal distributions - two peaks, two modes
• Truncated distributions - cut offs at 0 and 100 e.g. %
• Uniform distributions - same for each value
• Skewed distributions - right or left tail is longer
• Exponential distributions - continuous distirbutions when there is a constant probabilty of increase or decrease

Small sample sizes are often not representative of the real distribution

If all possible data should follow a normal distribution while your data follows a uniform distribution = sample doesn't reflect population e.g. too small size

In experiments - don't know population distribution

• Only have sample distribution
• Hope this reflects population distribution

Shows importance of replication and large sample sizes

Parametric statistics - assume data comes from normal distribution

• Allows further calculations and makes data more powerful
• Violating assumptions = unreliable conclusions

Data analysis:

• Test wether sample differs from normal distribution
• If not different = parametric test
• If different
  • Transform data - check before this tough
  • Non-parametric statistics - less powerful

Parametric statistics - assumes normal distribution and equal variance

• Uses actual data = more powerful

Non-parametric statistics - assumes no specific distribution

• Uses ranks of data = information lost = less powerful

Response variable = dependent variable, varies in response to explanatory variable

Explanatory variable = independent variable, you think plays a role in value of response

EXPLANATORY VARIABLE ON X-AXIS AND RESPONSE VARIABLE ON Y-AXIS

Categorical variable - can only take 1 of a few unordered values/categories e.g. sex, location, colour

Discrete variable - can take one of unlimited number of specific values (no decimals) e.g. hairs, population size, no. cells

Continuous variable - can take any value e.g. size, weight, temp, volume

Derived variables - usually calculated from two (or +) other variables e.g. ratios, %, rates