In Lab 7 you will be doing linear regressions with data you collect. If you’ve never done a linear regression with a graphing calculator, use the data in Figure 7.8 of your lab manual to practice doing linear regressions by following the instructions on pages 158-160.
Reminder about next week’s Lab 6
Remember, for Lab 6 you need to write your flow charts and calculate the pH of the buffer you will make before you come to lab. If you lost your half-sheet of paper with this information for your section, here is the text on these half-sheets.
Measuring the pH of a buffer Addendum for Lab 6
As per the information at the beginning of Lab 6, here are the concentrations of acetic acid and sodium acetate you will use, and what you need to calculate the pH of this buffer (and record in your lab notes) before you come to Lab 6.
Sections 001, 002, 003, 004
0.2 M acetic acid
0.5 M sodium acetate
Sections 005, 006, 007, 008
0.5 M acetic acid
0.1 M sodium acetate
See your lab manual, and Lab 6 Prep Lecture for examples of how to do these calculations, and be sure to calculate the pH of the buffer for your lab section.
Reminder about next week’s Lab 5
Remember, for Lab 5 you need to write your flow charts and calculate the pH of the two weak acids and one weak base before you come to lab. If you lost your half-sheet of paper with the weak acids and base for your section, here is the text on these half-sheets.
Addendum for Lab 5
As per the information at the beginning of Lab 5, here are the weak acids and base you need for calculating (and recording in your lab notes) their pH for their given concentration before you come to Lab 5.
Sections 001, 002, 003, 004
0.005 M citric acid (pK_{a} of 3.14)
0.0025 M lactic acid (pK_{a} of 3.08)
0.0005 M ammonia (pK_{a} of 9.25)
Sections 005, 006, 007, 008
0.01 M citric acid (pK_{a} of 3.14)
0.015 M lactic acid (pK_{a} of 3.08)
0.0025 M ammonia (pK_{a} of 9.25
See your lab manual for examples of how to do these calculations.
Class Announcement about LON-CAPA downtime 9/24/16 4-8 PM
Class Announcement: LON-CAPA at Purdue will be unavailable on Saturday 24 September 2016 between 4 PM and 8 PM ET for scheduled maintenance.
Reminder about next week’s Lab 4
Remember, for Lab 4 you need to use the “Handout for Lab 4 Exercises” you received for your lab section number during this week’s Lab 3 to write your flow charts/diagrams with all their calculations on your Lab 4 notes pages for all the exercises on both sides of the handout. You need to have all these flow charts/diagrams with their calculations done before you come to your lab section next week.
Lab 3 mitosis & meiosis simulations; t-tests and chi-squared tests
Mitosis and meiosis simulations
You left lab 2 with a plastic bag with pipe cleaners and beads so you could practice simulating mitosis and meiosis before you come to lab 3. Remember, you need to bring your pipe cleaners and beads in their bag back with you to lab 3. For your information, we recycle these pipe cleaners and beads for use next semester.
Above is a diagram of mitosis (click on image to see it bigger). At the top is the key to identifying the maternal and paternal chromosomes of this somatic cell undergoing mitosis. At the left is the cell in interphase. As you know, during interphase the DNA of the chromosomes replicate. So when the cell enters prophase each chromosome has a two part structure consisting of sister chromatids joined by a centromere. At metaphase, the chromosomes randomly align at the metaphase plate perpendicular to the spindle. Also at metaphase the centromeres duplicate. At anaphase, the sister chromatids are pulled to opposite poles of the cell by the spindle fibers. The separated sets of chromosomes become enclosed in a nuclear membrane at telophase. Cytokinesis will complete the mitotic division. The two cells that are the result of this mitotic division are genetically identical to the original cell at the left.
Incidentally, your bag of pipe cleaners and beads has two different colored pipe cleaners to represent maternal and paternal chromosomes (and their sister chromatids), and it has extra beads so you can simulate the centromeres duplicating in both mitosis and meiosis.
Below is a stop motion animation of the mitosis simulation like you will do in lab 3.
(Direct link to YouTube video.)
The diagram above shows 1 of 2 alignments of homologous chromosomes at metaphase 1 of meiosis (click on image to see it bigger). Again, at the top is the color code for the maternal and paternal chromosomes of this germ cell undergoing meiosis. Please note that in this diagram of meiosis, there is no crossing over of sister chromatids. At the left is a germ cell in interphase, where it replicates its DNA, such that when this germ cell enters prophase 1, each chromosome has a two part structure consisting of sister chromatids joined by a centromere. At metaphase 1 of meiosis, homologous chromosomes pair and align at the metaphase plate in an alignment that determines the maternal and paternal chromosome complement of the resulting gametes. Following metaphase 1, is anaphase 1, and the maternal chromosomes go to one pole of the dividing germ cell, and the paternal chromosomes go to the other pole. Following telophase 1, the two meiotic products progress through prophase 2, metaphase 2, and anaphase 2. It is important to point out that there is no DNA replication between telophase 1, and prophase 2 of meiosis.
Carefully compare the alignment of maternal and paternal homologous chromosomes at metaphase 1, and the maternal and paternal chromosome complement of the resulting gametes. We call these resulting gametes, parental gametes. Below is a stop motion animation showing you how to simulate meiosis for “alignment 1″ and paternal gametes.
(Direct link to YouTube video.)
The diagram above illustrates alignment 2 of homologous chromosomes at metaphase 1 of meiosis, and recombinant gametes (click on image to see it bigger). At the left is the germ cell in interphase where it replicates its DNA, such that when this germ cell enters prophase 1, each chromosome has a two part structure consisting of sister chromatids joined by a centromere. Again, at metaphase 1 of meiosis, the homologous chromosomes pair, and align at the metaphase plate in an alignment that, again, determines the maternal and paternal chromosome complement of the resulting gametes. Be sure to note that this alignment 2 is different from the alignment 1.
Again, there is a correlation between the alignment of maternal and paternal homologous chromosomes at metaphase 1, and the maternal and paternal chromosome complement of the resulting gametes; we call these resulting gametes, recombinant gametes. Below is a stop motion animation showing you how to simulate meiosis for “alignment 2″ and recombinant gametes.
(Direct link to YouTube video.)
So why are these two different alignments at metaphase I of meiosis so important? The genetic makeup of the gametes formed depends in a large part on the alignment of maternal and paternal chromosomes at metaphase I of meiosis, and it’s random as to how the chromosomes align at metaphase I of meiosis. Furthermore, when two gametes come together at fertilization, the genetic makeup of an offspring is set, and the coming together of gametes is a random event as well.
Try to do t-tests with data collected in Lab 2 before come to Lab 3
Since you have your data from Lab 2, you can write out your flow chart for the t-tests in your Lab 3 notes before you come to Lab 3, then do (or attempt to do) your t-tests in your Lab 3 notes (after your t-test flow charts). Doing so saves you time during Lab 3, and gives you the opportunity to correct any mistakes you may have made, plus get out early or on time.
Preview of chi-squared tests you do in Lab 3
In Lab 3 you will count the phenotypes of the progeny from different parental corn monohybrid or dihybrid crosses. Once you have these counts, then you do χ^{2} tests to determine the genotypes of the parents of each cross.
You received a handout for Lab 3 during Lab 2 with all the genotypes and phenotypes of monohybrid and dihybrid corn crosses you will see in Lab 3. You count the frequency of phenotypes of offspring of these crosses. For example, there will be flats of corn seedlings from a monohybrid cross with a seedling height gene (the wild-type tall allele T, and the recessive dwarf t allele; T/T or T/t = tall height, and t/t = dwarf or stunted height). Here’s a labeled photo illustrating these two seedling phenotypes.
To illustrate how you do χ^{2} tests, let’s say for a monohybrid cross with the seedling height gene described above you count 46 wild-type tall seedlings, and 56 dwarf seedlings. The first thing you want to do is set up an observed and expected phenotype table like the one below.
wild-type tall | dwarf | Total | |
Observed phenotype | 46 | 56 | 102 |
Expected phenotype |
As you can see, the “expected” cells in the table above are empty right now. This is because we have to first decide what genetic cross are we going to do a χ^{2} test. First, you want to note that there are offspring with two different phenotypes from this monohybrid cross, tall and dwarf. Now what are the genotypes of parents that would give tall and dwarf offspring, and what would be the phenotypic frequency of offspring? One of two crosses would be T/t × T/t ⇒ 3 tall : 1 dwarf, and the other would be T/t × t/t ⇒ 1 tall : 1 dwarf. (Note, while there are other parental crosses for this allele, these two are the only ones to give tall and dwarf offspring.) We need to do a χ^{2} test for each of these two possible parental crosses to be sure of our results. So, we test whether our offspring counts come from a parental cross of T/t × T/t. The first thing we need to do is to complete the table above with our expected frequency for a total of 104 offspring for this cross of T/t × T/t ⇒ 3 tall : 1 dwarf offspring, as shown below.
wild-type tall | dwarf | Total | |
Observed phenotype | 46 | 56 | 102 |
Expected phenotype | 76.5 (i.e., 76 or 77) | 25.5 (i.e., 26 or 25) | 102 |
Now we state our H_{0} and H_{a} hypotheses. H_{0} is that our observed frequency does not differ from the expected frequency for a parental cross of T/t × T/t. H_{a} is that our observed frequency differs from the expected frequency for a parental cross of T/t × T/t. Next we use the equation for calculating χ^{2}.
As stated in Lab 3 of your manual, we’ll be using an α = 0.05, and as described in Lab 3, the df = 1 for this χ^{2} test. So we use the Critical Values of the χ^{2} Distribution at the back of your manual, and we find that χ^{2}_{calculated} ≥ χ^{2}_{critical}. Thus we reject our H_{0} that our observed frequency does not differ from the expected frequency, i.e., it’s unlikely that the parental cross was T/t × T/t.
Next we test whether our offspring counts come from a parental cross of T/t × t/t ⇒ 1 tall : 1 dwarf, going through the same steps as above.
wild-type tall | dwarf | Total | |
Observed phenotype | 46 | 56 | 102 |
Expected phenotype | 51 | 51 | 102 |
Our H_{0} and H_{a} hypotheses for this χ^{2} test are: H_{0} is that our observed frequency does not differ from the expected frequency for a parental cross of T/t × t/t. H_{a} is that our observed frequency differs from the expected frequency for a parental cross of T/t × t/t. Here is the equation for calculating this χ^{2}.
Here we find that χ^{2}_{calculated} < χ^{2}_{critical}. Thus we accept our H_{0} that our observed frequency does not differ from the expected frequency, i.e., there’s a 95% probability that the parental cross was T/t × t/t.
Here are some labeled photos to show you the phenotypes of corn kernels and other corn seedlings from monohybrid and dihybrid crosses you will see in Lab 3. Plus there are counts you can use to practice doing more χ^{2} tests.
Sample corn kernel/seed counts
Monohybrid cross counts (observed numbers)
purple = 300 kernels
white = 98 kernels
Dihybrid cross counts (observed numbers)
purple flint = 123 kernels
purple sweet = 41 kernels
white flint = 30 kernels
white sweet = 12
Sample corn seedling counts
Another monohybrid cross counts (observed numbers)
tall = 82 seedlings
dwarf = 28 seedlings
Dihybrid cross counts (observed numbers)
tall green = 61 seedlings
dwarf green = 19 seedlings
tall albino = 16 seedlings
dwarf albino = 6 seedlings
Our Signal Alerts
As of this Monday morning, when you log into our Blackboard class site you will see a traffic signal icon showing a green, yellow, or red light, and a text description below indicating how you are doing in BIOL 13500, plus a link to your Bb grade book. In your Bb grade book you now see your “MyTotal” + “MyPercent” through Lab 1. Next Monday your “MyTotal” + “MyPercent” will be updated through Lab 2, and you will also see your “LastPercent” (to compare your current “MyPercent” with your preceding week’s percent, i.e., Lab 1′s “MyPercent”). From now on, your total, percent, and signal alert will be updated after the class completes each lab remaining in this class. The purpose of our signal alert system is to let you know how you are doing throughout the semester so you can earn the grade you want. Incidentally, I will send out a class tweet and FB post letting you know when I’ve updated our class Bb grade book.
Finally, don’t get discouraged if your “MyPercent” is not what you want to be earning during the first part of the semester. Just get more help, or start preparing for your next lab earlier.
How to Read the Vernier Scale
In Lab 2 you use a Vernier caliper to measure the length of objects. Most of you have never used a Vernier caliper, so this blog post has more images illustrating how to read the Vernier scale than what’s shown in your lab manual.
Below are photos of Vernier calipers (like you’ll use in Lab 2) being used to measure the length and/or width of different objects. Additionally, each photo includes a metric ruler so you can get an approximate linear measurement of what you are measuring with a Vernier caliper, i.e., so you use the correct “movable” OUTSIDE or INSIDE scale. Note, all the measurements illustrated below are external measurements (like you will do in lab), and they all use the movable OUTSIDE scale. We will tell you in lab about when you would use the INSIDE scale to make internal measurements.
What we cover in Lab 2 that some students find difficult
How to calibrate an electronic balance
Below is a short video illustrating how to calibrate an electronic balance. Note, the video starts after we’ve already pressed the “Zero” button on the electronic balance. There is no audio with this video.
(Direct link to YouTube video.)
Dimensional (data) analysis
Data analysis also includes what is commonly called dimensional analysis. You may not realize it, but you do dimensional analysis almost everyday, and you are probably pretty good at doing dimensional analysis. For example, you do dimensional analysis when you drive into a gas station with $10 in your pocket and the sign outside the station says that they are selling gas for $3.29 a gallon. Your dimensional analysis is what gives you a good idea of how much gas you can put in your car. You will do a lot of dimensional analysis in our lab, and there will be other examples of dimensional analysis throughout this class. And you will find that you do dimensional analysis in all your science classes, not just your biology classes. Additionally, another way of describing dimensional analysis is that you are estimating what your solution to a calculation will be before you even start doing any calculations.
Statistics
The formal method of data analysis is to use statistics. Statistics is the collection, analysis, interpretation, and presentation of large batches of empirical, or numerical data. You need to know that empirical data is based on observation, and numerical data is based on measurements, counts, etc.. Furthermore, you may not be aware that there are two major subdivisions of statistics. They are descriptive statistics, and inferential statistics. Lab 2 focuses on descriptive statistics and lab 3 focuses on inferential statistics.
Populations and samples
Students often do not realize that doing statistics using an entire population is different from doing statistics with a sample from a population. Remember, a population is the entire group from which we collect data and draw conclusions. Since populations may be very large and inconvenient to work with, we almost always perform statistical tests with a sample from a population. To make inferences about the whole population that are based on a sample, our sample needs to represent that population. For a sample to represent its population, it needs to be made up of randomly and independently chosen sample individuals. Remember, randomness means that we choose individuals for our sample at random, and independence means that choosing any one individual from our population, does not in any way change the probability of choosing another individual from our population.
Descriptive statistics calculations and significant figures
While students rarely have problems doing the statistics calculations dealing with central tendency, like, calculating the mean, median, or mode, or with calculations dealing with the variability or dispersion of a sample, like the variance, standard deviation, sometime students have difficulty on how to report significant figures when doing statistics calculations. Because descriptive statistics are summaries of data that are typically measurements, the number of significant figures we report, reflects the statistic done. For example, when we find the mean of a sample, we are summarizing the central value of all the measurements of a sample; therefore, we typically report the mean value to a level of accuracy one significant figure greater than the least significant measurement in our sample. When we deal with the standard deviation, or the standard error of a sample, we report one more significant figure than we used for the mean, which means, two more significant figures than the least accurately recorded measurement of our sample.
Please realize that how many significant figures to report when doing statistics are more rules of thumb, rather than strict scientific facts. There’s another approach for deciding how many significant figures described in your manual and it depends on sample size being used. Again, this other approach is more a rule of thumb than a strict scientific fact.
TI-83 calculator and descriptive statistics calculations
As a reminder, be sure you understand the descriptive statistics you will do with the data you collect in Lab 2, and that you can use your TI-83 as instructed in order to do these descriptive statistics. Also, don’t forget to bring your TI-83 (or greater) calculator to every lab.
Normal distribution of a sample and a population
Your lab manual shows a histogram to illustrate the normal distribution of the frequency of heights of a sample of 148 males, and it has the stereotypical normal distribution of a population. The distribution of the sample of the frequency of heights of males is not a perfect bell-shaped curve like the stereotypical normal distribution of a population, but it’s a pretty good approximation. In the stereotypical normal distribution of a population has approximately 68 percent of the population lying plus or minus one standard deviation about the mean of the population, and approximately 95 percent of the population lies plus or minus two standard deviations about the mean. These percentages are important when we get to inferential statistics in lab 3.
Parametric and non-parametric statistics
OK, now what distinguishes parametric statistics from non-parametric statistics? We call the statistics which depend on data sampled from a population with an underlying normal distribution parametric statistics. And we call the statistics dealing with distribution-free data, non-parametric statistics, which typically means we are dealing with a sample of discrete variables. A couple of examples of what would be discrete variables could be something like eye-color in the fruit fly, Drosophila melanogaster being either red or white, or corn seedling height being short dwarf or normal tall.
Unit conversions with squared or cubed units
I can see that some of you are having problems with LON-CAPA Lab01Prep problems dealing with unit conversions. It’s easy for you to convert something like pm to nm as shown below.
Where you have problems is when you need to convert squared or cubed units, like pm^{3} to nm^{3}. (Recall, 1 pm^{3} = 1 pm × 1 pm × 1 pm)