STATISTICAL ANALYSIS

WHY DO WE NEED STATS?

•To understand results of an experiment

•Make effective conclusions

•To be informed consumers

What does this graph show us?

This graph shows that people over 80 are the safest group of drivers. Drivers under 20 are safer than those between 20 and 24. Right?

The problem with that assumption is that number of accidents does not account for how much driving each of the groups do. Consider this other graph.

• Mile for mile, people over 80 have the most accidents followed by those under 20. This graph suggests that up until age 44, a person’s driving improves. After that, there is a decline in safety per mile driven. Over 74, there is a huge jump in accidents per mile driven.

• Neither graph prove that age is what causes the incident of accidents.

STANDARD DEVIATION

• There is almost always variation in biological data

•This variation can be shown using a frequency distribution graph

•The mean value is in the middle of the distribution

•Mean- the average of the values (the sum of the values divided by the number of values

Normal Distribution

Standard Deviation- The computed measure of how much the values vary around the mean score (above and below)

• 68% of the data is within 1 SD from the mean•95% of the data is within 2 SD from the mean•99% of the data is within 3 SD from the mean

Starter Questions

Which Sx represents a set of data that is very similar to the mean?

A. 4.5 B. 23.6 C. 0.6 D. 19.6

What percentage of data falls within +/-1Sx of the mean?

If the mean of a set of data is 55, and the SX=6 what is the value of data? +/- 1Sx +/-2Sx +/-3Sx

Draw a normal distribution graph. Include a mean, and the percentage of data that fall with in +/-1 Sx +/-2 Sx +/-3 Sx

•A low standard deviation indicates that the data points tend to be very close to the mean, whereas

•A high standard deviation indicates that the data are spread out over a large range of values.

A set of length measurements are taken with a mean of 2.5 cm and the standard deviation of 0.5cm. Which of the following is true?

1. 68% of all data lie between 2.5cm and 3.5cm

2. 68% of all data lie between 1.5cm and 3.5cm

3. 95% of all data lie between 1.5cm and 3.5cm

4. 95% of all data lie between 2.0cm and 3.0cm

95% of all data lie between 1.5cm and 3.5cm

•1 SD=0.5cm•68% of data is +/- 1SD, so 68% are between 2.0cm and 3.0cm

•95% of data are within +/- 2SD, so 95% are between 1.5cm and 3.0cm

Error Bars

2 Types of Error Bars Range of Data Standard Deviation

In a population of men the systolic blood pressure shows a normal distribution. The mean of the population is 125 (measured in mm and Hg) and the standard deviation is 10. If the population was 1000, how many of them have a blood pressure between 115 and 135mm Hg?

680 men have blood pressure between 115 and 135mm Hg.

If the mean is 125, and the standard deviation is 10, then +1 Sx is 135, and -1 Sx is 115, and we know that 68% of your data (in this case the men) are +/-1 Sx from the mean.

Starter

Using Excel

•Create your data•Find the mean of your data•Calculate the Standard Deviation (Sx) of your data

•Graph your mean•Insert Graph (Scatter)•Then go to layout

In layout choose the Error Bars Tab

Choose the More Error bars Options

Select Custom

For Standard Deviation Error Bars select your Sx for both Positive and Negative Values

For Max/Min Error Bars select your max and your min. •Take the difference from your mean, and input that as your value

Now Label Your Graph!

MeansA = 10B = 20

MeansA = 10B = 20

Is there a significant difference between the means?

MeansA = 10B = 20

Is there a significant difference between the means?

MeansA = 10B = 20

Is there a significant difference between the means?

Would knowing the standard deviations help?

What if both had “large” standard deviations?

MeansA = 10B = 20

Is there a significant difference between the means?

Would knowing the standard deviations help?

What if both had “small” standard deviations?

MeansA = 10B = 20

Is there a significant difference between the means?

Would knowing the population size help?

What if one had a large population size and the other a small size? What if both were large or both small?

The t-test takes from both samples:

the means, the standard deviations and the population size

into account and will give you a t-value which you can use with a t-test table to determine if there is a statistically significant difference between the means. DO NOT learn the formula. The t-value will be given to you.

•0.05 column is our Critical value

•Calculated Value of t > critical value it has is <0.05 which means there is a significant difference

•Calculated Value of t < critical value it has is >0.05 which means there is NO significant difference

•α significance level

Calculate Degrees of Freedom

N= Population N1 + N2 -2

NO YES

H0 Null Hypothesis states that there is no significant difference between the two groups

Never want to assume there is a difference

The null hypothesis typically corresponds to a general or default position. For example, the null hypothesis might be that there is no relationship between two measured phenomena or that a potential treatment has no effect.