Data!

Scenario The Ministry of Education has come up with a newfangled education strategy based on patterning to teach math. They say that in a pilot program there was a 5% gain for all students and that all classes did better with patterning.

“There was a 5% gain for all students!”

You, being a student with critical thinking skills asked to see the data.

The data is now hosted at Biologymound.com They decline to give you the data so you file a freedom of information request and after paying a deposit on the processing fee you got your data. The data is now hosted at Biologymound.com Syllabus links / Data sets and reports / data assignment File name: ib_biology_data_assignment.xlsx note: More on F.O.I. requests can be found at: https://www.ontario.ca/page/how-make-freedom-information-request

Scenario: Apparently the Ministry of Education conducted their study on four classes of 30 students. 15 students got the regular math instruction in each class, and 15 students got an additional 15 minutes of class instruction on the same concept using “patterning”.

The data is in an excel file. Classes are numbered 1, 2, 3 and 4 BACKGROUND The data is in an excel file. Classes are numbered 1, 2, 3 and 4 Groups are: A (Control), B (Treatment) The students were allocated to the groups by last name (first 15 in alpha order were group A and last 15 in alpha order were group B) The numbers are the percent grade achieved by the students on the final test for the unit.

Consider the design Do you have any concerns about the design? Are there problems in the design which may bias the study and make you question the validity of the results? Try to think of a few problems.

Method You want to know if these numbers show what is claimed: Step 1: Open up the data set and save it to your home drive. Step 2: Copy all of your data so you have a working file separate from your raw data in case something goes wrong. Do this by: Clicking on the cell between the 1 And the A Right click and select copy Click on “Sheet 2” at the bottom of the page and paste.

Method Step 2: Calculate the average for class 1, group A in the appropriate box: Go to formula, more functions, statistics, average. You should get 71.26667

Once you have calculated the average for Class 1 group A, drag that calculation to all other classes and groups. Do this by: 1. move the cursor over the bottom right corner. 2. hold down your mouse button. 3. drag through the cells to the right. 4. delete error texts so that only the averages remain. Do the “patterning treatment” groups do better on average?

71.26667 is irritating Your averages are irritating, let’s fix it! Highlight all of the cells that include averages by holding down the left mouse button and dragon the cursor across the numbers Right click on the highlighted field In the menu that comes up click on format cells Click on “number” Set the decimal places to 1 That is better!

Note that changing numbers like 71. 2667 to 71 Note that changing numbers like 71.2667 to 71.3 makes the data better it also can hide small differences. So be careful when you do this. For example the difference in averages in class 4 will not be apparent after you do this.

You can see that some groups are different by different amounts and that all groups have variation in them. In the image on the next page the bell curves are different by the same amount on average but they have different amounts of variation.

In the previous slide you can see that the difference between the averages becomes more and more significant as the variation in the data goes down. A MAJOR assumption in a lot of statistics is that there is a normal distribution of data. This may or may not be a reasonable assumption but it is often used. The next image is a bell curve with a normal distribution and the standard deviation listed.

Notice that 1 standard deviation will be the value that includes 68% of the data.

An average of 20 with a standard deviation of 1 would mean that the average is 20 and 68% of the data is +/- 1 from 20. An average of 20 with a standard deviation of 5.6 would mean that the average is 20 and 68% of the data is +/- 5.6 from 20.

These are usually shown on a bar chart as error bars These are usually shown on a bar chart as error bars. The overlap makes it hard to say that these values are different.

The graph below shows a clear difference in age but no difference in gender.

Here is an example of error bars on a line graph Here is an example of error bars on a line graph. Again the overlap makes the two conditions similar.

Calculate the Standard Deviation for a Sample with this formula

Luckily Excel can do it. Click on the cell where you want the Std.dev value Go to formulas Use “more functions” Click on statistical Scroll down to STDEV.S Select the values for which you want a Std. Dev. Note: This is the standard deviation for a sample. Rarely will you have the entire population (there is a different formula for that).

To make a bar graph of your data for class 1 Highlight the 2X2 box that contains control 1. treatment 1 and contains the averages you calculated. Click on the insert tab at the top of excel Click on bar graph Click on all chart types Click on the vertical bar graph in the top right corner.

Stepanie Castle is an IB teacher Stepanie Castle is an IB teacher. Her site has a lot of good things in it including video instructions for making a graph with individual error bars. https://www.youtube.com/watch?v=G10_qGcuELA Follow her instructions to add your calculated standard deviation to the graph. Repeat but this time create a graph of all 8 results by highlighting the entire section OR create 3 separate graphs for the other 3 classes.

Things you should see You should probably have concluded in class 4 and probably class 1 there is no significant difference between the groups. You should probably have concluded that there is a significant difference in class 3 as well. You are likely most uncertain about class 2 where the means are different but there is overlap with Std. Dev.

For class 2, we will calculate a t-test A t-test is a statistical test to determine if two sets of data are different from each other. In this case we have unpaired data (since it is not the same person tested twice) We also will make the assumption that it is a two tailed test. We will also make the assumption the variance is not the same in each group (it is not the same, I tested it). We are looking for P values less that 0.05 (5%) to say that the numbers are different.

To calculate the T test:….

Or use excel Click on the box where you want the T-test stat to be. Under the formula tab click on more functions and then T.TEST For array 1 select the group A data and for array 2 select the second group B data. For tails: enter “2” For type: enter “3” (unpaired and unequal variance) Drag the formula to other squares to calculate the T-test P value for each of the classes. Check the P value vs the critical value P=0.05

This video may also help https://www.youtube.com/watch?v=JlfLnx8sh-o

Next Steps? At this point you can probably say that two classes had a significant difference but two did not. It is still unclear how useful this intervention is as it sometimes seems to work and sometimes does not seem to have much effect. As a next step you could group those 4 classes together. Click on tab 3 in excel and calculate the Average, Std Dev and a T-test for the complete data set. What is your conclusion now?