Difference between revisions of "20.109(S24):M1D8"

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==Introduction==
 
==Introduction==
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Today is the final laboratory session for Module 1! You have completed all of the bench work for your research; however, there is still data analysis to complete for your experiments.  In addition to plotting the data, you will complete statistical analysis to determine the significance of your results.
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The goal for today is to give you time and space to get started on the Mod 1 major writing assignment, the Data summary. Be sure to take advantage of the 'work day' to discuss the assignment with your laboratory partner and to ask the Instructors any questions you may have about the material covered, data analyzed, or assignment details.
  
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Statistics are mathematical tools used to analyze, interpret, and organize data.  The specific tools that you will use are confidence intervals (CI) and the Student's ''t''-test.  To begin, review the following definitions:
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==Protocols==
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*Mean (or average) is defined as:
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===Part 1: Image EMSA experiment===
  
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<center>
 
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<math> \overline{\chi } =  \frac{\sum_{i}^{n}\chi _{i}}{n}</math>, ''where'' <math>\chi _{i}</math> = ''individual value and n  = number of samples''
 
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</center>
 
  
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===Part 2: Outline Data summary and divide workload accordingly===
  
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*With infinite data, the mean (<math> \overline{\chi }</math>) approaches the true mean (&mu;).
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In science publications it is uncommon to find single-author papers.  Most science is done in collaboration with peers and colleagues, and this is true for your Data summary assignment. You will work with your partner to prepare a draft and revision that describes the work you completed in Module 1.  To ensure the work is distributed evenly you will first assess what needs to be done to complete the assignment and then decide who will be responsible for which parts.
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*Standard deviation measures the variation in the data and is defined as:
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'''Assess what needs to be done'''
  
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<center>
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Prepare an outline for your Data summary that highlights the components that should be included (i.e. "Background & Motivation" and "Results, Figure 1").  For each component, list what has been done (for example, "prompts regarding information for Background & Motivation section from due M1D2 homework") and what  needs to be completed (for example, "use due M1D2 answers to write bullets for Background & Motivation section").
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<math> s = \sqrt{\frac{\sum_{i}^{n }(\chi _{_{i}}-\overline{\chi })}{n - 1}}</math>, ''where n - 1 = degrees of freedom''
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</center>
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'''Distribute what needs to be done between partners'''
  
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*With infinite data, the standard deviation (''s'') approaches the true standard deviation (&sigma;).
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With your partner, decide who will tackle which components of the assignment.  Discuss what work needs to be completed such that you are both in agreement on what is expected. Then discuss who will be responsible for that work.  Review the submitted homework assignments and comments as this may help determine which partner should complete which components (hint: which homework is most easily revised based on the comments?).
  
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An assumption is made when using standard deviation to report the variation in a data set.  It is assumed that sufficient data have been collected to generate a normal curve.
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Note that the assignment is graded as a whole and both partners will receive a score based on the whole and not their individual contributions.  In this, it is important that both partners are involved in all components...either as the primary writer or as a reviewer.  Next, coordinate times that you can meet to discuss the progress of the work and / or to review the work.  It is also helpful to set deadlines for when certain work should be done so both partners are able to stay on track and are accountable to each other.
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<font color =  #4a9152 >'''In your laboratory notebook,'''</font color> complete the following:
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*Based on your discussion with your laboratory partner, record the following:
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**What has been done?
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**What needs to be done?
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**Who will complete which components?
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**When will you meet to discuss progress and review the completed components?
  
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So, what does this all mean in regard to the data you will report?  As an example, if the calculated <math> \overline{\chi }</math> of a data set equals 80 au there is a 95% chance the &mu; is between 50 au and 110 au, where au = arbitrary units.  And how does this relate to ''s''?  If you know the &mu;, the &sigma; represents a 68% confidence interval. 
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===Part 3: Prepare Data summary===
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When interpreting data, the error bars are representative of the noise in the data or how different the data points are for each of the replicates. Replicates come in two types: technical and biological.  Technical replicates indicate that the same sample was tested multiple times and is measure of experimenter error (for example, pipetting errors between aliquots).  Biological replicates indicate that different preparations of the same sample were tested and is a measure of the difference in a response to a variable (for example, response to a treatment between separate cultures of the same cell line).  Though both types have value in data analysis, the interpretation of the error represented in each case is different.  Because of this it is important to indicate if the replicates used in the data analysis are technical or biological.  For your data, what type of replicates did you analyze for the &gamma;H2AX experiment?  For the CometChip experiment?
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Lastly, you will use Student's ''t''-test to report if your data are statistically different between treatments. 
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*Student's ''t''-test is defined as:
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<center>
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<math>t = \frac{\left | \overline{\chi_{_{1}}} - \overline{\chi_{_{2}}} \right |}{s_{pooled}}\sqrt{\frac{n_{1} n_{2}}{n_{1}+n_{2}}}</math>, ''where'' <math>s_{pooled} = \sqrt{\frac{s_{1}^{2} (n_{1} -1) + {s_{2}^{2} (n_{2} - 1)}{}}{n_{1} + n_{2} - 2}}</math>
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</center>
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The value you calculate with the Student's ''t''-test equation is referred to as ''t''<sub>calculated</sub>.  This ''t''<sub>calculated</sub> value is compared to the ''t''<sub>tabulated</sub> value in the the ''t'' table, according to the appropriate ''n'' - 1 using the p-value for the two-tailed distribution (which assumes that you do not know how the data will shift).  If the ''t''<sub>calculated</sub> value is greater than the ''t''<sub>tabulated</sub>, then the data sets are significantly different at the specific p-value.  So, what does this all mean in regard to the data you will report?  As an example, if the ''t''<sub>calculated</sub> for a data set with ''n'' - 1 = 10 is 3 (given that the ''t''<sub>tabulated</sub> is 2.228), then the data sets are different with a ''p''-value &le; 0.05.  Which means that there is less that a 5% chance that the data sets are the same.
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==Protocols==
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===Part 1: Image EMSA experiment===
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===Part 2: Practice statistical analysis===
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'''This exercise is optional.  If you are confident in your ability to apply the statistics tests discussed in the prelab lecture, feel free to continue to Part 3.  If you would like to practice the tests that were discussed, complete the exercise included here.''' 
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Review data from an experiment where cells were exposed to increasing amounts of radiation (linked [[Media: CometAssay_M1D6stats_F14.xlsx |here]]). Your goal is to determine if a statistically significant amount of DNA damage was induced. For the purpose of this exercise, the values in the spreadsheet are in arbitrary units of 'DNA damage', where the higher numbers indicate more damage. 
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When interpreting the statistics, consider how you may use the information to convince someone that the DNA damage was significant. You may find the spreadsheet originally created by Prof. Bevin Engelward and modified for the 20.109 laboratory, helpful for this exercise (linked [[Media: S09_20109_M2D5-Stats-4.xls‎ |here]]).
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<font color =  #4a9152 >'''In your laboratory notebook,'''</font color> complete the following:
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*Attach the completed spreadsheet.
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**Include a bar graph of the data with standard deviations.
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**Indicate if there is a statistically significant difference (''i.e.'' provide a ''p''-value) between the conditions tested.
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===Part 3: Complete data analysis===
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Use the remaining class time to prepare your Data summary!!.
  
 
==Reagent list==
 
==Reagent list==

Revision as of 20:56, 1 March 2024

20.109(S24): Laboratory Fundamentals of Biological Engineering

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Spring 2024 schedule        FYI        Assignments        Homework        Class data        Communication        Accessibility

       M1: Drug discovery        M2: Protein engineering        M3: Project design       


Introduction

The goal for today is to give you time and space to get started on the Mod 1 major writing assignment, the Data summary. Be sure to take advantage of the 'work day' to discuss the assignment with your laboratory partner and to ask the Instructors any questions you may have about the material covered, data analyzed, or assignment details.

Protocols

Part 1: Image EMSA experiment

Part 2: Outline Data summary and divide workload accordingly

In science publications it is uncommon to find single-author papers. Most science is done in collaboration with peers and colleagues, and this is true for your Data summary assignment. You will work with your partner to prepare a draft and revision that describes the work you completed in Module 1. To ensure the work is distributed evenly you will first assess what needs to be done to complete the assignment and then decide who will be responsible for which parts.

Assess what needs to be done

Prepare an outline for your Data summary that highlights the components that should be included (i.e. "Background & Motivation" and "Results, Figure 1"). For each component, list what has been done (for example, "prompts regarding information for Background & Motivation section from due M1D2 homework") and what needs to be completed (for example, "use due M1D2 answers to write bullets for Background & Motivation section").

Distribute what needs to be done between partners

With your partner, decide who will tackle which components of the assignment. Discuss what work needs to be completed such that you are both in agreement on what is expected. Then discuss who will be responsible for that work. Review the submitted homework assignments and comments as this may help determine which partner should complete which components (hint: which homework is most easily revised based on the comments?).

Note that the assignment is graded as a whole and both partners will receive a score based on the whole and not their individual contributions. In this, it is important that both partners are involved in all components...either as the primary writer or as a reviewer. Next, coordinate times that you can meet to discuss the progress of the work and / or to review the work. It is also helpful to set deadlines for when certain work should be done so both partners are able to stay on track and are accountable to each other.

In your laboratory notebook, complete the following:

  • Based on your discussion with your laboratory partner, record the following:
    • What has been done?
    • What needs to be done?
    • Who will complete which components?
    • When will you meet to discuss progress and review the completed components?

Part 3: Prepare Data summary

Use the remaining class time to prepare your Data summary!!.

Reagent list

Navigation links

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Previous day: Complete EMSA experiment
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