STATISICAL ANALYSIS HLIB BIOLOGY TOPIC 1:

Why statistics? __________________ “Statistics refers to methods and rules for organizing and interpreting quantitative observations.” ( torial.asp)

1.1.1 State that error bars are a graphical representation of the variability of data. ___________________ Error bars can be used to show either the range of the data or the standard deviation.

Use of Error Bars Descriptive error bars. Means with error bars for three cases: n = 3, n = 10, and n = 30. The small black dots are data points, and the column denotes the data mean M. The bars on the left of each column show range, and the bars on the right show standard deviation (SD). M and SD are the same for every case, but notice how much the range increases with n. Note also that although the range error bars encompass all of the experimental results, they do not necessarily cover all the results that could possibly occur. SD error bars include about two thirds of the sample, and 2 x SD error bars would encompass roughly 95% of the sample Cumming, G. et al. J. Cell Biol. 2007;177:7-11

Definitions Mean Median Mode Range Standard deviation

MEAN Arithmetic mean is commonly called as average. Mean or Average is defined as the sum of all the given elements divided by the total number of elements.

MEDIAN Median is the middle value of the given numbers or distribution in their ascending order. Median is the average value of the two middle elements when the size of the distribution is even.

MODE Mode is the most frequently occurring value in a frequency distribution.

RANGE Range is the difference between the highest and the lowest values in a frequency distribution. Formula = largest number - smallest number

STANDARD DEVIATION Standard Deviation :

1.1.2 Calculate the mean and standard deviation of a set of values. __________________________ Specify the standard deviation(s), not the population standard deviation. It is not expected that you know the formula for calculating the standard deviation, but you are expected to use the standard deviation function of a graphic display or scientific calculator.

1.1.2 (Continued) Consider using the standard deviation calculation on a spreadsheet program.

1.1.3 State that the term standard deviation is used to summarize the spread of values around the mean, and that 68% of the values fall within one standard deviation. _________________________________ + 1 standard deviation = 68% + 2 standard deviations = 95%

1.1.4 Explain how the standard deviation is useful for comparing the means and the spread of data between two or more samples. __________________________________ A small standard deviation indicates that the data is clustered closely around the mean value. Conversely, a large standard deviation indicates a wider spread around the mean.

EXCEL and Standard Deviation

EXCEL Tutorial Statistics: excel/stats.html General: excel/index.html

1.1.5 Deduce the significance of the difference between two sets of data using calculated values for t and the appropriate tables. ___________________________________ For the t -test to be applied, the data must have a normal distribution and sample size of at least 10. The t -test can be used to compare two sets of data and measure the amount of overlap.

1.1.6 Explain that the existence of a correlation does not establish that there is a causal relationship between two variables. ___________________________________ When looking at correlation, you are trying to see if there is a cause and effect relationship between two variables.

EXAMPLE: 1.A person’s income seems related to the number of years of education. 2.However, the education may or may not cause the extra income. (Meaning from Data: Statistics Made Clear THE TEACHING COMPANY) Point: Statistics may show a correlation but there may be other factors at work.