Topic 1: Statistical Analysis

Introductory link:

Statistics [1]

1.1 Error bars: graphical representation of the variability of data

Error bars show the distribution of a set of values around a mean.
Large error bars show the data values to be less reliable.
When the error bars between two different sets of data overlap, a comparison or conclusion concerning the two data sets is said to be less significant. Since error bars may refer to different statistical measurements, a key should be provided with their use.
Uncertainty is the doubt that you might have in a measurement. Usually in biology this refers to the uncertainty of the instrument with which you are measuring your data. For most measuring instruments, the uncertainty is half of the smallest value that you are using to make your measurements. An exception is the ruler and digital instruments, in which case the uncertainty is the smallest value that you are using to make your measurements. In biology, the uncertainty is usually not expressed in an error bar.
Standard error determines the difference of the lowest value from the mean and the highest value from the mean.
Mean = average = total counts/number of sets (trials) counted

1.2 Standard Deviation (SD) determines the accumulated differences of all the values from the mean

The SD measures the spread of data of a Normal Distribution. The bigger the SD, the wider and lower the distribution curve – thus the data is spread out widely from the mean. The smaller the SD, the taller and narrower the distribution curve – thus, the data is closely cluttered around the mean.
Statistically, for a normal distribution of data, about 68% of all values lie with in +/- 1 SD from the mean; while 95% of the values lie within +/- 2 SD from the mean.

Be able to calculate from a set of values. For directions on how to calculate SD with a TI- 86 or a TI 83 calculator go to p. 5 in Damon et al. for web address. Otherwise follow -

STAT/ edit enter; STAT/calc enter/ AV-1 or AV-2 (depending on number of data sets)/ sX = SD

Determining the standard deviation (SD) through equation:
external image S_equation.gif

1.3 For a normal distribution , 68% of all measurements fall within one standard deviation of the average, or mean. 95% of all measurements fall within two standard deviations of the mean.

external image f8-1.jpg

1.4 SD is used for comparing the means and spread of values between two or more samples

When comparing 2 means between two data sets, if the SDs are smaller than the differences between the 2 means you can say the data is probably significant, relevant and not just due to chance.

1.5 Significance of data between two sample sets :

To be able to say that there is a statistically significant difference (that is not just due to chance) between two sets of data, a t test needs to be done. This assumes the data has a normal distribution and a sample size of at least 10.

Be able to deduce the significance of the difference between two sets of data using calculated values for t and the appropriate tables.

1.6 Correlations

Although two data sets may look like cause and effect, wiithout evidence, you can only say their is a positve or negative correlation but not that there is a causal relationshipbetween two variables. For example, the data taken from the Mauna Loa observatory in Hawaii shows a positive correlation between rising levels of atmospheric carbon dioxide and earth's temperature, but it does not show a causal relationship between the two.