I'd be really appreciative if anyone might be able to help me. I'm studying biology at a foundation level and have recently been introduced to statistical tests for the first time as means of analyzing biological data from experiments. Because I've no previous statistics experience, I am finding it a bit of a struggle to get my head around how the basic Standard Error test works. What I specifically would like to understand is how the results of a simple Standard Error test with 95% confidence (95% confidence limits) can be analyzed. I know that you calculate the equation of Standard Error by dividing the standard deviation of the data by the square root of the number of samples. I also know that to calculate Standard Error with 95% confidence I must subsequently multiply the product of the Standard Error equation by 1.96.

At my level of biology I am then required to draw a bar chart with a bar for each sample being compared. Each bar should show the sample mean and error bars either side of the mean that represent the Standard Error of that sample. I then need to see whether or not the Standard Errors/error bars of the samples overlap. How should I interpret my results/findings?

If I calculate the standard errors for 2 mean values and then multiply each answer by 1.96 to get a value for each that is of 95% confidence (95% confidence limits) and then draw a bar chart depicting error bars for each of the 2 means, how would I then analyze these error bars? If the error bars overlap, would I say 'there is a 95% probability that the two means are not statistically different and that any differences between the two means are due to chance. Therefore the probability that the means are different is 5%?' If the error bars don't overlap, would I say 'there is a 95% probability that the means are statistically different and any similarities between the two means are due to chance with a percentage of 5%?'

Or would I perhaps express these ideas with different wording - for example by saying: 'if the error bars overlap there is a greater than 0.05 probability that any differences between the 2 means are due to chance' and 'if the error bars do not over lap there is a greater than 0.05 probability that any similarities between the means are due to chance' ?

Am I correct or incorrect with either of these?

Please might anyone be able to tell me if I'm on the right track?

Thank you very much - I'd be hugely grateful for any help!