MAKING MEANING OUT OF DATA Statistics for IB-SL Biology

There are two types of data. Quantitative Qualitative

There are two types of data. Quantitative data Measured using a naturally occurring numerical scale Examples  Chemical concentration  Temperature  Length  Weight…etc. If you give a group of students a taste test and they have to rank drinks in order of 1-10 as to which one they like, would this be quantitative data?

There are two types of data. Qualitative data Information that relates to characteristics or description (observable qualities) Information is often grouped by descriptive category Examples  Species of plant  Type of insect  Shades of color  Rank of flavor in taste testing Qualitative data can be “scored” and evaluated numerically

Can you count EVERY ONE?!?!

Sampling Data Don’t have enough time or resources to measure every individual in a population. Choose and measure a representative sample from a population. Need to have a good SAMPLE SIZE in order to “believe” your data. (statistically significant)

Statistical analysis of a sample Mean: is the average of data points Range: range is the measure of the spread of data Standard Deviation: is a measure of how the individual observation of data set are dispersed or spread out around the mean

The standard deviation tells us how tightly the data points are clustered together. When standard deviation is small—data points are clustered very close When standard deviation is large—data points are spread out Statistical analysis of a sample

We will use standard deviation to summarize the spread of values around the mean and to compare the means and spread of data between two or more sample In a normal distribution, about 68% of all values lie within ±1 standard deviation of the mean. This rises to about 95% for ±2 standard deviation from the mean

Statistical analysis of a sample Confidence Intervals (CI) We will use a CI of 95%. How many standard deviations away from the mean is this? This 95% CI will be used to measure the “significance” of the data. We are 95% confident that the mean will be found within this interval. What do we call data that lies outside of this?

Statistical analysis of a sample

Let’s imagine a scenario… You are trying to find the average height of a 5 th grade student. You measure 15 students present in one 5 th grade class. You calculate the mean to be 1.6 m and the confidence interval to be +/- 0.5m. This +/- amount represents which value? You measure a second class of 5 th grade students, and then a third class of 5 th graders, etc. 95% of the time the mean should be between which two values?

Statistical analysis of a sample Your experiment leads you to a new question… Are 6 th graders the same height as 5 th graders? You should always assume the null hypothesis, or n 0. This is that there is no significant difference between the two variables. You use the same procedure to measure the height of 6 th graders. How will you know if there is enough of a difference between the average heights of the two groups to truly be different? Statistical significance: 95% of the data should not overlap So, CI’s should not overlap. If they do, it is not statistically significant (not different).

Statistical analysis of a sample To present your data for all IA’s, you MUST use MS Excel. CI’s will be represented on graphs through the use of error bars. These error bars represent the spread of data around the mean.

Statistical analysis of a sample

 What can you conclude when error bars do overlap?  No surprises here.  When error bars overlap, you can be sure the difference between the two means is not statistically significant.  Why?  Due to chance variations!

Statistical analysis of a sample  What can you conclude when error bars do not overlap?  When error bars do not overlap, you cannot be sure that the difference between two means is statistically significant.  The t-test is commonly used to compare these groups.  We WILL be learning about t-tests.

Statistical analysis of a sample  What if you are comparing more than two groups?  ANOVA is a statistical test commonly used for comparing multiple groups.  We will not be using ANOVA!

The t-test The t-test determines whether the difference observed between the means of two samples is significant The test works by considering the following:  The size of the difference between the means of the samples.  The number of items in each sample.  The amount of variation between the individual values inside of each sample…this is known as…? The t-test always assumes what is called the null hypothesis, or n 0. This always states that there is no significant different between the two pieces of data.

The t-test When a t-test is performed it returns a “p” value. We want p< 0.05 When p < 0.05 this means that less than 5% of the time the CIs of the two groups will overlap. 5%...why does this sound familiar? This means that the two groups ARE statistically different. When p > 0.05, there is a greater chance the CIs of the two groups will overlap. This means that the two groups ARE NOT statistically different. The difference is due to natural randomness.

The t-test Let’s go back to the height of the 5 th and 6 th graders… Using a calculator or Excel, you determined the following value: p = What question do you ask yourself? Is there a difference between the heights of the 5 th and 6 th graders?

Correlation Correlation is a measure of the association between two factors. The strength of the association between two factors can be measured. An association in which all the values closely follow the trend is described as being a strong correlation. An association in which there is much variation, with many values being far from the trend, is described as being a weak correlation. A value can be given to the strength of the correlation, r.  r = +1a complete positive correlation  r = 0 no correlation  r = -1a complete negative correlation

Correlation