# 1.1 Statistical Analysis

Statistical test 1: Mean and Standard deviation

1.1.1 State that error bars are a graphical representation of variability of data.

Error Bars: Graphical representation of Bars showing the standard deviation (one S.D. above and one below the mean value) by extending above and below the mean value.

1.1.2 Calculate the mean and standard deviation (σ) of a set of values.

Mean:

The sum of all values in data divided by the total frequency of data.

Standard deviation:

Measurement of the spread of data above and below the mean.

(by calculating the deviation of each measurement from the mean of the set of data, value of standard deviation can be obtained.)

where:

σ=standard deviation of sample

∑= summation of

= difference between x value and mean

N= number of values

(Formula is expected to be memorized)

7 steps to find standard deviation:

Step 1. Find the mean and number of samples

Step 2. Calculate   for all sets of values

Step 3. Find for all values

Step 4.    (Adding up all  )

Step 5. (Divide answer in step 4 by total no. of value -1)

Step 6. (Square root the answer in step 5)

Step 7. Done, sit back and relax.

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 of the mean.

Standard deviation:

• Used to summarize the spread of values around the mean
• 68% of the values fall within one standard deviation (±1SD)
• 95% of the values fall within 2 standard deviation (±2SD)
• A  sample with a small standard deviation suggests that the set of data has a narrow variation
• A sample with a large standard deviation suggests that the set of data has a wide variation

1.1.4 Explain how the standard deviation is useful for comparing the means and the spread of data between two or more samples.

• One way to measure the variability in the set of data is to compare results with error bars.
• Error bar shows the range  of  ±1 SD from the mean, and is drawn above (+1 SD) and below (-1 SD) from mean.
• Therefore, 68% of the data fall within this range

If the error bars between data overlap, it can be concluded that there is no significantly difference.

In contrast, if the error bars do not overlap, we CANNOT said that the two set of data are significant different. Therefore, we must proceed to another statistical test: t-test.

Statistical test 2: t-Test

1.15 Deduce the significance of the difference between two sets of data using calculated values for t and the appropriate tables.

t-Test:

Measurement for testing the reliability on whether two sets of data are significantly different.

• Takes into account ofSo that we can be certain whether the two sets of data are significantly different or not.
• Means
• Amount of overlap

Where:

=Mean value of set 1 of the data

│=Positive difference between the means (larger mean value-lower mean value)

S= Standard deviation

n= Number/frequency of measurements

(Formula is expected to be memorized)

How to use t-Test

• The calculated value of t is used to compare with critical value in the t-Test table.
• There will be two conditions:
• if t value is larger than critical value: Significant difference between two sets of data (little overlap)
• if t value is smaller than critical value: No significant difference between two sets of data (a lot of overlap)

Table 1: t-Test table

Significance level:

• P=0.05 (5%) is being widely used in Biology.
• Meaning it is 95% sure that there is significant different/no significant different

Degrees of freedom= number of classes – 1

In scientific investigation, statistical tests are usually carried out with a hypothesis.

• Null hypothesis (H0): There is no significant difference between two samples.
• t value ≥ critical value, null hypothesis can be rejected. Therefore there is no significant difference

t-Test in excel (video guide): http://www.youtube.com/watch?v=JlfLnx8sh-o

1.1.6 Explain the existence of a correlation does not establish that there is a causal relationship between two variables.

• First we need to know what correlation is.
•  Correlation is not proof of cause, it is a statistical way to prove
• whether two variables are associated not.
• or will the variable change if the other changes.
• Two variables can have positive, negative or no association.