1.1 Statistical Analysis

Click4Biology - online resource about IB and Statistics

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

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.

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

Mean and Standard Deviation

Calculate Mean

Calculate Standard Deviation of the Mean 

Means and Standard Deviations

The standard deviation tells you how all the numbers (x₁, x₂, x₃, etc) are distributed around the mean.

• A small standard deviation tells you that most of the numbers are close to the mean.
• A large standard deviation tells you that most of the numbers are not close to the mean.

  What exactly is "most of the numbers"?

• 68% of the numbers are within one standard deviation of the mean. 

A bell curve shows the mean and standard deviation

• This graph shows test scores
• The mean was 100
• The standard deviation was 15
• 68% of people scored between 85 and 115

Comparing Means from Two Samples 

Often in labs, data is collected and compared.

The means and standard deviations of the two sets of data can be calculated

• A small standard deviation tells you that most of the numbers are close to the mean and there is less variation in the data and more reliability of the measurement.
• A large standard deviation tells you that most of the numbers are not close to the mean and there is more variation in the data and less reliability of the measurement.

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

Note: variability of range of data or standard deviation.

Making Graphs (see Click4Biology for great graphs about this topic)

Data that is collected from an experiment should be processed - find the mean and standard deviation. The processed data should be presented in a graph.

Error bars can show the variability of the data in three ways:

• range: shows the maximum and minimum values
• standard deviation: shows the spread of the data around the mean
• standard error: shows the possible error in the mean due to the size of the sample

Standard Error

Calculate standard error by dividing the standard deviation by the square root of the number of values. 

When comparing two sets of data, a graph showing the means with the standard error as error bars can tell you if the data is significantly different or not.

If the error bars overlap, the two means are not significantly different.

If the error bars do not overlap, the two means may be significantly different.

    Graphs showing overlapping error bars and not overlapping error bars. 

Graphs from Click4Biology

If the error bars do not overlap, a t-test can prove that the two sets of data are significantly different.

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

• Calculating a t value shows the difference or similarity of two sets of data.
• The t value has to be compared to a t-test table to determine the probability (p) that the difference is due to random chance.
• The degrees of freedom on the table are the total number of values from both sets of data minus 2.

Using the t table

• Find the t value on the table for the correct degrees of freedom.
• Find the corresponding p value.
•  

Understanding the t test 

In biology, the acceptable probability that the difference is due to random chance is 5% (0.05).

This means that there is a 95% chance that the difference is significant.

• If the p value is smaller than 5%, then the sets of data are significantly different.
• If the p value is greater than 5%, then the sets of data are not significantly different.

PowerPoint about t tests

Example calculations and analysis using Excel

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

Correlation and Causation

Define: strong, weak, postive, negative correlation

Identify difference between correlation and causation