Chapter 1: Statistical Analysis Fifteen Summary Facts

Worksheet 1.1

Chapter 1: Statistical analysis – fifteen summary facts

1Statistics is a branch of mathematics which allows us to sample small portions from habitats, communities or biological populations and draw conclusions about the larger population.

2Error bars are a graphical representation of the variability of data in the habitat, community or biological population. Error bars can be used to show the range of data or the standard deviation on a graph.

3The mean is an average of the data points.

4You must be able to calculate the mean and standard deviation of a set of data using a calculator.

5Standard deviation is used to summarize the spread of values around the mean; 68% of values fall within one standard deviation of the mean.

6Standard deviation tells us how tightly the data points are clustered around the mean. When the data points are clustered together, the standard deviation is small. When the data points are more variable and spread apart, the deviation is large.

7A high standard deviation results from a wide spread of data around the mean. This data is less trustworthy than data with a low standard deviation.

A low standard deviation results from data which is clustered around the mean. This data is more trustworthy.

8If two sets of data have the same means, it may appear that there is no significant difference between the two groups. If we only looked at the means, we may miss the variability in the data. Looking at the standard deviation forces us to recognize the variability which exists in each set of data.

9The t-test utilizes the standard deviations of both sets of data to deduce the significance of the difference. For example, does fertilizer applied to a group of plants really make a difference when compared with the plants that do not have fertilizer applied?

10When comparing two sets of data, the t-test helps scientists determine if the difference between the sets is significant (real) or not.

11Scientists are never completely certain but they like to be 95% certain of their findings before drawing conclusions. 95% certain indicates that there is a 95% chance that the difference between the two sets of data is significant. It also indicates that there is only a 5% probability that chance alone can produce this difference. For example, it is 95% certain that fertilizer makes a difference in the growth of the plants and there is only a 5% probability that the difference in growth is due to chance.

12When given a calculated value of t, use the table of t values (page 7) that you will be given to help find the chance that the difference between the values is significant. In the table of t values, look in the left-hand column headed ‘Degrees of freedom’. Degrees of freedom are the sum of the sample size of each of the two groups minus 2. For example, if two groups of 10 plants each are being looked at, then 10 plus 10 is 20 minus 2 is 18. Thus, the number to look at in the ‘Degrees of freedom’ column is 18.

13Since you will be given the value of t, go to the right of the Degrees of freedom (18 in this case) and find the box with the closest number to the t value you have been given. Now look to the bottom of the table and you will find the ‘Probability that chance alone could produce the difference’. If the t value given to you is the same or greater than 5% or 0.05, the difference is significant (real). Thus, there is a 95% chance that the fertilizer caused the difference in growth for the two groups of plants.

14Calculated value for t will always be given to you. You need only be able to use the table. Conditions which must be met for t-test to be applied are:

a)the population sampled must have a normal distribution

b)the variable measured must be continuous

c)the sample size must be at least 10.

15Observations without an experiment can only show a correlation between two variables. An experiment provides a test to show cause.