## Q1 – Week 3 – 19-20

Week of 9/16 – 9/20

9/16 – Monday – period 7 – Academic Study Hall –  1:  Review Form quiz

– period 8

1. Continue with Excel data table/graph building – Lab 2

LAB 2 – Data Google Sheet Link

Excel File that we completed last week.

9/16 – Monday Homework:

1: Please try to make a graph that has the 2 series of data that was collected.
Make sure you expand the graph to see the changes. Save the file.
2 :  Please Watch the lecture below with the worksheet that I handed out in class. This is the new video:

Chi-squared Lecture with Mendelian Genetics.:

2:  You will be completing the backside with me but the key is posted below if you are running into trouble on the first side.

Biology statistics 4a – Mendelian Chi squared analysis.pdf

Biology statistics 4a – Mendelian Chi squared analysis key p .pdf

3.  Read my notes on Chi – squared Below

#### AP Biology Statistics

Chi- Squared Basics – (Notes for those Learners that like to read).

Chi- Squared is our last statistical value that will help us quantify our outcomes when dealing with data from categories, like how many plants have a certain phenotype.  It is similar to SEM (Standard Error of the Mean) in that we generate a probability value that helps us measure whether our hypothesis is supported or not supported.
Probability values that are within 95% is generally the line in the sand between accepting or not accepting an outcome.  Remember that 95% interval in SEM is +/- 2 SEM reliability from the true mean of the population.  If two means overlap WITHIN their respective 95% intervals there is no real difference between these 2 means and the probability that there is a statistical difference has a very low probability (less than or equal to a 5% probability).

SEM is really a variance (spread of measure values) around the True Mean of the population.

Chi- Squared is really a variance value around the “NULL HYPOTHESIS” which is a NULL statement that say’s “There is no difference between the observed results and the expected results.”  The line in the sand here is:  How much difference is there from what we observe and what we expect?  To measure how much difference between the observed and expected values in a research investigation we must measure from a “NULL” or a starting point of ZERO Difference.  If we measure how tall I am aren’t we measuring how many inches or centimeters I am from zero or “NULL”?  The key in CHi-Squared is that we ALWAYS measure from an expectation that there will be no difference between the observed and expected values and THUS we always run a Chi- Squared from AGAINST a NULL HYPOTHESIS.

Now you can setup your NULL Hypothesis so that you are testing a certain outcome. For instance in the example in the lecture above we setup our Null Hypothesis (line in the sand) so that THERE WILL BE NO DIFFERENCE between the observed phenotypes and a 9:3:3:1 ration of phenotypes expected in Mendelian Genetics.  If our Chi-Squared value is small that means that their is not much variance between the observed and the expected values and OUR NULL HYPOTHESIS will be accepted, meaning any small differences are due to sampling errors or Chance Events. Sampling errors are errors in that a random sample was not generated and that that there may have been a bias.   Example:  Measuring the height from a basketball team will not reflect the mean of the true population.  Chance events are those events that occur in the experiment that caused outcomes to differ because of “flipping a coin” does not always give us the same number of heads as tails.  In order to achieve a 9 : 3 : 3: 1 outcome the probabilities of chromosomes segregating into gametes must be 50% (heads or tails).  But there is chance that the probabilities are not 50%, especially in small samples.  How many families do you know have more boys than girls yet there is 50 – 50 chance to a have a girl or boy? In the entire world the amount of males and females are about 50 – 50 but in single family there is usually a deviation from 50% chance of males and females.

If our Chi-Squared value is LARGE that means that their is so much variance between the observed and the expected values and OUR NULL HYPOTHESIS will be rejected, meaning the difference is so large that the THERE MUST BE AN ALTERNATIVE  REASON that is DRIVING THE difference (beyond sampling errors and Chance events)!  We often will provide an Alternative Hypothesis as the possible reason that the NULL is rejected.  In the case of the example in the worksheet that is used in the lecture above, the Alternative Hypothesis could be that the alleles do not follow the Law of Independent Assortment (due to crossover).

What determines if we accept or reject the Null Hypothesis?  The Chi-Squared critical values table! This is given to you in your AP Biology reference table. Once we determine the degrees of freedom ( subtract 1 from the number of categories used) we see if the Chi-Squared value IS LARGE ENOUGH to fit in box that has a p value of 0.05 (5%) or a p value of 0.01% (1 %).

If it is LARGE enough that “fit” into those boxes then THERE IS TOO SMALL OF A PROBABILITY TO SUPPORT THE NULL HYPOTHESIS and we REGECT the NULL, which means that there is something (alternative hypothesis) DRIVING or causing the change. Remember the significance of 5%?  If the change or variance from the NULL is OUTSIDE the 95% range then THERE MUST BE A SIGNIFICANT DIFFERENCE (REGECT the NULL).

*Remember that the Chi-Squared is ALWAYS A TEST on the NULL and the p values determined  from the Chi – Squared critical values table are ALWAYS probabilities FOR THE NULL HYPOTHESIS!

The table reveals how much support the there is for the NULL If the Chi-squared value is BIG ENOUGH to fit in the box for p value of 0.05 or 0.01 there is TOO little support for the NULL meaning there is TOO small of a probability that the NULL is supported.

If the Chi-squared value DOES NOT fits in the box for p value of 0.05 or 0.01 there is TOO MUCH support for the NULL meaning there is a LARGE ENOUGH of a probability that the NULL is supported and we accept the NULL.  IS the NULL within the 95% probability range (high probability that the NULL is TRUE) or is it outside 95% probability range (low probability that the NULL is TRUE).  Chi- Squared is always based on the Null and the line in sand is the 95% probability range.

So from the homework you can see that the Chi-squared value of 2.04 is not BIGGER or EQUAL to 7.82 for 3 degrees of freedom so the p value is TOO large (greater than 0.05 or 5 %). This means there is enough probability (with the 0.95 or 95% range) to accept the NULL to be true. WE setup the Null so that the expected values would equal the 9 : 3 : 3: 1 ratios expected if Mendelian Genetics is supported.  OUR statistical analysts of Chi-Squared supports the Null and thus supports the outcome of Mendelian Genetics.  The reason there is some differences from EXACTLY 9: 3 : 3 : 1 ration is due to only sampling errors and chance events. Here is a table that could help: High Chi – Squared Value  Low Chi – Squared Value
Large difference between observed and expected values  Small difference between observed and expected values
Large enough to fit in 0.05 or 0.01   box in the Critical value table.  Small enough to NOT fit in 0.05 or 0.01 box in the Critical value table.
p value =  or < 0.05 or 0.01 (NOT in the 95th %)  p value > 0.05 (IN THE 95th %)
REJECT THE NULL HYPOTHESIS  ACCEPT THE NULL HYPOTHESIS
 SOMETHING OTHER THAN Sampling errors and Chance Events are responsible for the small differences between the observed and the expected results.THAT SOMETHING is the Alternative Hypothesis!
Sampling errors and Chance Events are responsible for the small differences between the observed and the expected results BUT there is no “Real Difference” between observed and expected values.

9/17 – Tuesday – period  – 7/8

1. Review Basics of Chi – squared – used Critical Values (p – values determination)
2.  Measure plant heights – DAY 11
3. Continue with Excel data table/graph building – Lab 2

b: Please add the previous days data.  We will cut and paste this into our EXCEL files.
*Remember to tell class to copy forward to the Day 11.
A) Interpret Data – Math that means something!
B) SEM review –

C) Chi – Squared contrasted with SEM

This is a Copy of my Excel File that I did with you in class today:
Flourescent LED Lab Data 2019.xlsx

9/17 – Tuesday Homework:

1: Review your Ant Article that I finished grading with . the posted key in Power School.
I will review in class tomorrow and take questions

2:  Complete the Chi squared Practice Problem.pdf worksheet below (handed out in class) and review with the key.

3:  If you need help please view the lecture below that will explain step by step how to complete the worksheet.

Chi squared Practice Problem.pdf

Chi- squared practice problem key p .pdf
End of Tuesday..

9/18 – Wednesday – period 7 – Academic Study Hall –

– period 8

1. Review of Chi- Squared HW.

a) Class demonstration of statistic based on whether my students cheat?!

2019 2020 Classroom Ch- squared demo.pdf

Todays classwork: This data is based on your last graded form.

Thanks for editing my work. I rejret that I do make some mistakes….

2019 2020 Classroom Ch- squared demo KEY p.pdf

9/18 – Wednesday – Homework:

1. Please complete the Chi-Squared Form below:

#### Chi-Squared Form 1 – 19-20

End of Wednesday..

9/19 – Thursday period 7,8 Lab Day!

1. Review of the Chi-Squared Form – Homework REview

2. Chi – Squared Activity:

Classwork Activity:
Biology statistics 4 – M&M Chi squared analysis 1718.pdf
9/19 – Thursday – Homework:

1: Complete the M & M Chi-Squared  Activity and hand in.
(you should have completed this in class but if you did not it is due Friday in                                                                                         the purple crate of fun.)

Open House:

9/20 – Friday –  period 7 – Academic Study Hall –

period 8:

1. Review Ant Article:

2. Lab 2 continues with Lab data and direction of the study.

This is a Copy of my Excel File that I did with you in class Tuesday:
Flourescent LED Lab Data 2019.xlsx
9/20 Friday – Weekend Homework:

1:  Stickleback Video and Form questions
2:  Lab 2 – start your Formal write – up

1: Sticklebacks:
A:  Please watch the short movie on the Stickleback fish:
B: Complete the form which is based on the Stickleback video above:

Lab 2: Begin formal write- up:

LAB WRITE- UP REQUIREMENTS:

Weekend HW:  : LAB 2

HERE IS A LINK to an example of a lab writeup from a student from last years class:

Please add a Title page, Background, Hypothesis, Materials, Procedure, Data sections to your Lab to the shared doc for Lab 2 that I sent you a link for on Friday.
In the lab Report Rubric LINK I outline how to do all of the above.
I want you now to complete your Data section by presenting your Calculated Data in an organized professional Data Table and Corresponding Graphs that are visual representations of your calculated data.
DATA TABLE:
OK So I want you to create a Nifty Data Table that represents your calculated data from YOUR RAW data.
I do not need to se every piece of data that you are using in your table.  You should be presenting the overall calculated values FROM your raw data (from marbles).  For instance If you have a tested a group and a control you should at least have an average, standard deviation, SEM and SEM +2/- 2 values for each group.
THESE ARE THE VALUES YOU ARE GOING TO USE FOR YOUR GRAPH!  You are required to use EXCEL to make this data Table.  I am posting how to create a basic table from Excel below.
*After you have completed this table in Excel, Please cut and paste this Table into the shared Google doc for the lab.  There are any ways to accomplish this and please try to find which way works best for you and your group.

GRAPHS:
Please create an appropriate graph from data table that illustrates the significance or insignificance of your data calculated the best in Excel  Based on your study a line graph may be better than a bar graph, especially if you are measuring rate (how fast).  These graph must have error bars unless you are doing a Chi- squared statistic.

Graphs must be labeled in each axis, have a title, and clearly illustrate outcomes, significant or not.  The graph should be a clear representation of your outcomes.  Presentation is key!!!!

Annotation in the Google Doc:
You need to make an annotation under each image that you bring into your google doc. For instance, you might write Table 1 under the Data Table or give it a formal name. This is so that when you write the Conclusion you can refer to the table appropriately.  “In table 1, or in figure 1 we see that ….”
This is due at 4:30 am Monday!!!

Tutorial video on creating Graphs (from your data table) in Excel:
I am making a line graph in this tutorial but you can just select a bar graph instead in the initial stage of the video and all of the other things I demonstrate would be the same in the video below.