Brain and Behavior Student Manual 2022

GENETICALLY MANIPULATING BEHAVIOR OF C. elegans

LABORATORY 9
GENETICALLY MANIPULATING BEHAVIOR OF C. elegans

SUMMARY
In this final experiment, you will explore how model organisms are used to study complex
diseases, like addiction, where susceptibility is both genetic and environmental. By comparing
the acute alcohol tolerance of wild-type and npr-1 deficient C. elegans you will observe how
genetic changes translate into behavioral differences.*
OBJECTIVES

 Understand the methodologies used in behavioral genetics
 Use a 2x2 experimental design to understand the influence of a gene on the behavioral

response to an environmental manipulation
 Quantify the effect of alcohol on C. elegans

*Adapted from The Effect of Alcohol on Caenorhabditis. elegans. Edvo-Kit #851. EDVOTEK, Inc. ©2018.
Available at www.edvotek.com

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INTRODUCTION

Using C. elegans to understand behavior and diseases

We know the entire C. elegans genome, the developmental cellular ancestry, which is the
sequence of cell divisions that occur in development of the 558-cell embryo into an adult C.
elegans, we also know the connectome (the ~7000 connections amongst all the 302 neurons of
the hermaphrodite and 383 neurons of the male C. elegans), knowledge that won the discoverers
multiple Nobel prizes. This is the animal we know the most about so scientists use the C. elegans
genome and neural system to study how genetics influences particular behaviors and mental
health conditions of humans.

One approach is to modify or silence a gene of interest to discover the biological function of that
gene. Such studies compare a mutant worm and a control worm without the mutation. These
nematodes are referred to as “wild-types”. In this experiment, you will compare the behavior of
wild-type nematodes to nematodes with non-functioning npr-1 genes; npr-1 stands for
neuropeptide receptor 1.

The npr-1 gene encodes a G-protein
coupled receptor (GPCR) protein.
GPCRs are a huge and diverse group of
cell membrane receptor proteins that
detect molecules outside of a cell and
signal that detection has occurred on
the inside of the cell (see Figure). In this
way, G proteins act as molecular
switches within a cell. When an
extracellular ligand binds to the GPCR it
causes a conformation change inside
the cell that can increase or decrease
the production of hundreds of internal messenger molecules. GPCR proteins have played a huge
part in the development of new medical treatments – close to one half of currently available
drugs are thought to target them.

The npr-1 protein is a receptor for neuropeptides, protein-like molecules produced by other cells,
and is found in several types of C. elegans neurons. Nematodes with high npr-1 gene expression
show solitary feeding habits, heat tolerance, and a low sensitivity to oxygen levels. In contrast,
nematodes with low npr-1 gene expression show social feeding, thermal avoidance, and move
towards certain oxygen levels (aerotaxis).

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Based on these observations the field has hypothesized that the NPR-1 protein (the product of
the npr-1 gene) slows or inhibits certain sensory pathways. A link has also been observed
between alcohol tolerance and npr-1 activity which has piqued interest for understanding drug
tolerance in people.

Although the npr-1 gene is not found in humans, it is homologous to the NPY (neuropeptide Y)
receptor family that has been linked to pain sensation, circadian rhythms, food consumption,
anxiety, and drug tolerance. Genes are homologous is they descend from a common ancestral
gene and often (but not necessarily) have very similar DNA sequences that generate similar
protein structures.

You will use a 2x2 experimental design to characterize the effects of a genetic manipulation
(npr-1 mutation) on the response to an environmental (alcohol exposure) manipulation. There
are 2 genetic conditions (npr-1 mutant, wild-type control) and 2 environmental conditions
(alcohol, control) and so 2x2 = 4 measurements are needed to determine the consequences of
the gene x environment interaction.

Environmental Condition

Control Alcohol

Genetic Wild-type
Condition Npr-1 mutant

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GENETICALLY MANIPULATING BEHAVIOR OF C. elegans

Brain & Behavior: CORE-UA 306

LABORATORY COVER SHEET
Name: _____________________________ Lab Partner’s Name: _________________________
Date of Lab: ___________________________ Date Due: _______________________________
Lab Instructor: _____________________________ Lab Section Number: __________________

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GENETICALLY MANIPULATING BEHAVIOR OF C. elegans

PROCEDURES and EXERCISES

In the previous lab session, you had an opportunity to observe how C. elegans move and navigate
through a liquid environment. You saw them display a rhythmic flexing motions centered on their
midpoint, and we can now define a single thrash as a complete movement through the midpoint
and back [Figure 1].

Figure 1. Movements of C. elegans swimming in a microdroplet,
imaged with a CCD camera and captured to computer with a PCI-1407 Image Acquisition card.

[Image source: http://www.wormbook.org/chapters/www_behavior/behavior.html]

This week, your goal is to count the number of thrashing movements of both mutant strand and
wild-type C.elegans in 30 seconds over a 20-minute period. At the end of the test period,
results of class data will be compiled and analyzed for comparison.
A. Your group will be given five experimental conditions:

1. Wild-type in Alcohol
2. Wild-type in Control solution
3. npr-1 mutants in Alcohol
4. npr-1 mutants in Control solution
5. Unknown in Alcohol

B. Each lab group will be prepared with the following materials:
 Compound Microscope
 2.5% Alcohol solution (snap-top tube, “Alcohol Solution”)
 Sterile Water (snap-top tube, “Control Solution”)
 Sharpie marker
 Large transfer pipets
 Small pipets
 Empty snap-top tubes
 Counting chamber
 Timer

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C. For each count period, try to focus on observing the behavior of a single worm.
This may require sliding the counting chamber on the microscope stage. The long times between
counts make it hard to follow a single individual worm throughout the entire experiment.
Therefore, to minimize variability between counts, select similarly aged and sized worms.
See Figure 2 for a reminder of the C. elegans life cycle and differences in size.
[HINT: focus on larger worms (right column) because the nervous system of C. elegans is not fully
developed until after the L4 stage.]

Figure 2. Images of C. elegans at various life cycle stages.
Image source: Wood, W.B. in The Nematode Caenorhabditis elegans
(ed. Wood, E.B.) 1-16 (Cold Spring Harbor Laboratory Press, Cold Spring Harbor, NY).

D. Answer questions and record data for analysis.
 Each group will answer questions before, during, and after exposure to the assigned test
solutions and observation periods.
 Note observations during the experiment
 Complete DATA tables

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QUESTION 1:
What are some effects of alcohol that you expect to be able to observe in both strains?

QUESTION 2:
Predict how each worm type might react to alcohol initially.
A. Wild-type. B. Mutant strain
A. Wild-type:
B. Mutant strain:

QUESTION 3:
Predict how each worm type might react to alcohol after prolonged exposure to alcohol.
A. Wild-type. B. Mutant strain.
A. Wild-type:
B. Mutant strain:

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1. Labeling:
With the Sharpie marker, write the abbreviation* of the worm type on:

- 1 snap-top tube
- 1 small pipet
*ABBREVIATIONS:
WTC = wild-type control, WTA = wild-type alcohol
MSC = mutant strain control, MSA = mutant strain alcohol
X = unknown
Counting Chamber
Ensure you skip one chamber in between each test mixture (i.e. WTC in chamber
number 1 and WTA in chamber number 3, etc.) to prevent any cross contamination.

2. Test Mixture:
A. Your instructor will distribute C. elegans of the assigned worm type, in a 50 L suspension, to
each group. Make sure your labeled snap-top tubes are open and ready.
B. To the same tube, add 450 L of the test solution to the snap-top tube.
- Close the top and tap the bottom of the tube on the benchtop at least 3-4 times to make sure
worms are evenly suspended.

3. Test Chamber:
Use your small pipet to transfer 1 drop (~10 L) of your test mixture to the opening of the
corresponding pre-labeled counting chamber.
NOTE: If correctly placed the solutions will rapidly move into the chamber by capillary action.
If the solution does not move into the chamber, check that the chamber is orientated so that the
triangular openings are facing upwards.

4. Observations:
Quickly place the chamber under a microscope and identify an adult C. elegans for observation.
Count the number of thrashes that occur in 30 seconds*.

5. Record Data:
Record your count in Tables 1 and 2.
*Repeat a 30-second observation at 0 minutes, 5 minutes, 10 minutes, 15 minutes, and 20
minutes for each condition, recording your data (i.e., thrash count) for each time interval as well.
Setting a timer will help keep you on task as you discuss your observations as a group and answer
the questions that follow.

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OBSERVATIONS

QUESTION 4:
Use this space to take notes of your observations throughout the experiment.
Use the next page to include sketches of your observations.
Remember to apply proper labeling technique:
- Time Interval (in minutes): 0, 5, 10, 15, 20
- Total Magnification: 10X, 40X,
- C. elegans-type: WT or npr-1, sex, life cycle stage
- Thrash per minute rate (Control/Alcohol): Thrash Count at 30s X 2 (Control/Alcohol)

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OBSERVATIONS

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DATA SHEET

I. Record the number of times you observe thrashing movements in your worm(s). Enter the
number of thrashes observed at each time interval in TABLE 1 – GROUP DATA.

TIME Action Thrash Thrash Thrash Thrash Thrash
Count Count Count Count
(minutes) Count WTC MSA MSC
X
WTA

0 1st 30 seconds -

count

5 2nd 30 seconds -

count

10 3rd 30 seconds -

count

15 4th 30 seconds -

count

20 5th 30 seconds -

count

TABLE 1 – GROUP DATA.

II. In TABLE 2 - CLASS DATA, Record the thrash counts for all groups to make comparisons and
solve the Unknown.

A. Calculate “% Difference in Mobility”:
- Subtract thrash counts in alcohol from thrash counts in control
- Divide the difference by thrash counts in control
- Multiply by 100 to get a percentage

(Thrash count in Control – Thrash count in Alcohol) x 100

Thrash count in Control

B. Compare class data to the UNKNOWN (UNK) group’s data to determine if their worms
are from the wild type or the mutant strain.

TABLE 2 – CLASS DATA.

THRASH COUNT UNKNOWN:
WT or npr-1?

TIME WT in WT in % Difference npr-1 in npr-1 in % Difference UNK in
(minutes) Control Alcohol in Mobility Control Alcohol in Mobility Alcohol

0
5
10
15
20

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RESULTS

QUESTION 5:
Graph the change in mobility over time in wild-type and mutant strains.
Include proper graph components: title, axes, legend, units

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QUESTION 6:
A. Discuss how your qualitative observations (what you saw under the microscope) and your
quantitative data (% difference in mobility) compare to the predictions you made before the
experiment.
B. Determine what could be changed in the experiment if the experiment were repeated.
C. Write a hypothesis that would reflect this change.

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OUTLOOK

QUESTION 7:
Vulnerability to alcoholism and addiction is a complex trait – multiple environmental and
inherited factors determine the likelihood that someone will become an alcoholic or addict.
Research and then describe a gene or environmental factor that may play a role in this disease.

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CLEAN UP PROCEDURES

 With clean gloves, wipe down the lab bench with 10% bleach solution. Discard all gloves and
paper towel in the RMW box (Regulated Medical Waste: lidded brown box with a red bag
inside, located near the sinks).

 Discard petri plates, pipets, loops, tubes, in the benchtop biohazard bags. If it becomes full
and there are no refills at your station, ask your instructor for extra.
o Twisty-tie the benchtop biohazard bag and discard in the RMW box

 Please leave your lab station as clean and orderly as when you arrived.
 Before leaving the lab, double-check your area for your personal belongings.

THE LAB STAFF IS NOT RESPONSIBLE FOR ANY LOST OR STOLEN ITEMS.
Failure to properly clean up will result in a 5-point deduction from your laboratory assignment.

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…

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FrequencySTATISTICAL APPENDIX

Over the course of this semester you have heard about manipulations that cause some kind of
change in the brain or in behavior, for example, ‘choline enhances memory’, or ‘sexual behavior
changes with brain levels of serotonin’. How do we know whether any specific change we observe
in the laboratory is real as opposed to random variation? That is, how reliable is the change, how
great is the change, and is the change due to the manipulation we made or some other factor?
To answer these questions, it is necessary to use methods of statistics. Statistical methods which
allow us to describe our data in concise mathematical terms are referred to as descriptive
statistics. Similarly, we use well-established norms for determining the significance of a finding
in the statistical method referred to as inferential statistics. The purpose of this Appendix is to
introduce you to the concepts behind these statistical methods.

Data Sets and Distributions

Each experimental investigation involves the collection of measurements that are usually
numerical. Each of those measurements is a datum (one data point). All the measurements
constitute a data set. Since these data range over a set of values, an alternative description is to
call it a distribution. One example with which you are familiar is the distribution of scores on a
test. The data set in this case can be represented in the form of a histogram, where we display
the frequency for each score in the distribution. Sometimes, if you have too many scores, they
can be grouped into specified ranges. This gives us a grouped histogram. An example of a test
score histogram is shown in Figure 1.

14

12

10

8

6

4

2

0
0-9 10-19 20-29 30-39 40-49 50-59 60-69 70-79 80-89 90-100
Scores

Figure 1: A histogram showing the frequency distribution of test scores.

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Measures of Central Tendency

We can compare the data sets if we use descriptive statistics. You will note from looking at the
data set in Figure 1 that the values show variation but also that some values occur more
frequently than others. The central tendency of a data set is a single number that characterizes
the data by providing information about its “middle” value. However, there are three commonly
used measures of central tendency: mean, median, and mode.

Consider the following data set that has been arranged in ascending order:

48 48 64 64 74 74 81.5 81.5 81.5 84 84 84 84 85 85 86.5 86.5 86.5

The mode of this distribution is the score that occurs most frequently (84).
The median is the mid-point of the distribution; that is, the score that divides the distribution
into equal halves. In the above example, there are 18 scores; therefore, the mid-point occurs
between the 9th and 10th score (82.75).
The mean is an arithmetic average symbolized by the expression x̄ (pronounced ‘x-bar’) when
referring to a sample of a population, or by the Greek letter μ (pronounced ‘mew’) when
referring to an entire population. Thus, the following equation can be utilized to calculate mean

for either condition:

Sample Mean (x̄ ) = ∑ or Population Mean ( ) = ∑


… where ∑ (pronounced ‘Sigma ’) is the sum (∑) of the scores ( ) and

(or ) is the total number of scores.

For this sample distribution, ∑ / = 76.8. If the distribution was perfectly symmetric, so that

the data were distributed similarly on either side of the average, the mean and median would be

equal. In this example, they are not equal, therefore the distribution is not perfectly balanced

and is referred to as skewed.

Variability of Data

The variability describes the amount of variation among the values in the data set. If the scores
are tightly clustered around the mean, then variability is low; if they are widely scattered, the
variability is high. One quick way to describe variability is to calculate the range of the data
(highest score - lowest score). In the example given above, the range is 38.5. If the data were
instead 9 scores of 74 and 9 scores of 78, the range would be 4.

The range does not give us all the information we need, however; a more complete description
of the variability is to calculate the variance, or a related measure called standard deviation.
These measures are based on the difference between each score in the data set and the mean
value, and therefore describe the dispersion of the data around the mean.

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We take the difference between each measurement and the mean, square each difference (so
the result is positive), add them up, and divide by –1 to get the variance; the standard deviation
is simply the square root of the variance. Since this procedure calculates the variance and
standard deviation of a sample, the formula for standard deviation is written as:

= �Σ( −− 1 )2

… where is used to express standard deviation of a sample, or

σ = �Σ( −− 1 )2

… where σ (also pronounced ‘sigma’, but with a different meaning)
is used to express standard deviation of a population

The mean and the standard deviation have the same units, and a set of measurements is often
summarized as ± s. For the data set given above, the standard deviation is about 12.
If we consider the second case, where the data were 9 scores of 74 and 9 scores of 78, the mean
would still be similar (76) but the standard deviation would be much smaller (2). In some cases,
when the number of data points is large, the experimental distribution approximates a
theoretical curve called a normal distribution, often referred to as a bell curve because of its
characteristic bell-shaped graph (Figures 2, 3, and 4).

For a normal distribution, 67% of the data points are contained within a range of one standard
deviation above and below the mean ( ± s), and 93% of the data points are contained within
two standard deviations either side of the mean ( ± 2s).

The figure below shows the comparison of two theoretical distributions with the same number
of measurements (n) and the same mean ( ), but with different values of standard deviation (s).
In one case the standard deviation is small, so the distribution appears as a tall and narrow peak.
This reflects the fact that almost all the data values are very close to the mean and there is little
variability in the sample. In the other case, however, the distribution is short and spread out since
only a small number of the data points are close to the mean, which produces a large standard
deviation. Since each distribution has the same value of n, the area under the curve is equal in
both cases despite the difference in shape. The total area is equal and adds up to 1 (or 100%),
but the distribution of the area under
the curve is different – and this is not
because of n.

Figure 2: A comparison of two distributions
with the same mean but different values of
the standard deviation.

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Comparing Data Sets

We are often interested in comparing two data sets and assessing whether there is a difference.
Suppose we wanted to ask the following question: Are men taller than women? To investigate
this question experimentally, we would need to collect data on the heights of a population of
men and a population of women. Once the data have been obtained, they can be represented as
two distributions that each have a mean and standard deviation. Figure 3 shows a graph of the
distributions of men and women in a hypothetical example:

Figure 3: Distributions of standing height for men and women in a population.

What conclusions can we draw from these two data sets to answer our question? According to
the figure, the mean height for men is larger than the mean height for women. This would lead
us to answer the question in the affirmative. However, you will notice that the distributions
overlap in the region of intermediate height. Consequently, there are some tall women whose
height is greater than that of some short men. If this is true, can we accurately say that “men are
taller than women”? Therefore, we need to refine our question.
We certainly cannot say that “all men are taller than all women” because the distributions
overlap, and some women are taller than some men. Furthermore, there is almost always a
difference in measurements just due to chance. So, is the difference that we see in mean height
between men and women due to gender? Or is it just due to chance variability? This is the
question statistics seeks to answer: is the difference that we see in our data due to chance or to
a real phenomenon? If our results indicate that the difference is not due to chance, we say that
the difference in mean height between men and women is statistically significant.
The question of whether there is a significant difference between two data sets arises repeatedly
in scientific investigation. In the response time lab, for example, we asked the question: “Is there
a difference between response times for sight, sound, and touch?”
When collecting the data for each stimulus, there will be a certain amount of variation in the
times that you measure. This variation can be characterized by the standard deviation for each
data set. Therefore, it is necessary to compare the distribution of sight response times to the
distribution of touch response times (and similarly for the other pairwise comparisons).

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Suppose that we were measuring response times for sound (1) versus touch (2). Two possible
scenarios for the outcome are listed in Figure 4. In case A there is a difference between the
means, but the standard deviation of the distributions is large, resulting in substantial overlap. In
case B the difference between the means is the same but the standard deviations are much
smaller, resulting in no overlap between the distributions. It is therefore easier to ascertain a
difference between reaction times for sound and touch in case B compared to case A.

Figure 4: Two scenarios for comparing distributions of sound (1) and touch (2). In case A, each distribution
has a large standard deviation that results in considerable overlap. In case B, the standard deviations are
much smaller, and the two distributions are readily distinguishable.

The t-test

To determine whether two distributions have a statistically significant difference we employ a
statistical test known as a t-test. In short, the t-test tells us the degree of likelihood that the
difference we observe between two types of response times is a real phenomenon and is not
caused purely by chance. In order to be more precise, we use a reference point, or a statement
about the true state of affairs, called the null hypothesis, which states that there is no statistically
significant difference between the two means. We then perform the t-test to determine exactly
how likely (probability) our difference is, if the null hypothesis is true.

Consider two distributions with means μ1 and μ2 and standard deviations s1, s2. For simplicity,

the two distributions contain the same number of data points, N. The equation to calculate the

value of t is given by: 1 − 2
� 1 2 + 2 2
=

Simply calculating the value of t, however, is insufficient to make a conclusion about statistical
significance. One other factor that must be considered is the degrees of freedom (df ) of the test,
which is calculated using the formula: df = (N1 – 1) + (N2 – 1)

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In this formula, N1 is the number of data points in one distribution (e.g., sound response times)
and N2 is the number of data points in the other distribution (e.g., sight response times).
The number of degrees of freedom is therefore directly connected to the size of the sample.
The calculated value of t must exceed a critical value for the number of degrees of freedom for
your sample in order to be considered significant.
We determine statistical significance if our p-value (which is the probability of our result under
the null hypothesis distribution) is less than a certain probability (designated by the Greek
symbol α, pronounced ‘alpha’), which is usually specified to be 0.01 (1%) or 0.05 (5%).
For example, if the difference in reaction times for sight and touch are statistically significant to
a level of 0.01, there is a 1% probability that the result occurred by chance, if our null hypothesis
is true. We, therefore, reject our null hypothesis and conclude that our results were not likely to
have happened by chance. We can say that is is unlikely that the difference in reaction times
between sight and touch is due to chance variability and that there is an actual difference
between the groups. The t-Table lists the critical values of t for different values of p (top row)
and number of degrees of freedom (far left column). Alpha is our cutoff probability for statistical
significance.

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t-Table*

A cum. prob t .50 t .75 t .80 t .85 t .90 t .95 t .975 t .99 t .995 t .999 t .9995

B one-tail 0.50 0.25 0.20 0.15 0.10 0.05 0.025 0.01 0.005 0.001 0.0005

C two-tails 1.00 0.50 0.40 0.30 0.20 0.10 0.05 0.02 0.01 0.002 0.001

df

1 0.000 1.000 1.376 1.963 3.078 6.314 12.71 31.82 63.66 318.31 636.62

2 0.000 0.816 1.061 1.386 1.886 2.920 4.303 6.965 9.925 22.327 31.599

3 0.000 0.765 0.978 1.250 1.638 2.353 3.182 4.541 5.841 10.215 12.924

4 0.000 0.741 0.941 1.190 1.533 2.132 2.776 3.747 4.604 7.173 8.610

5 0.000 0.727 0.920 1.156 1.476 2.015 2.571 3.365 4.032 5.893 6.869

6 0.000 0.718 0.906 1.134 1.440 1.943 2.447 3.143 3.707 5.208 5.959

7 0.000 0.711 0.896 1.119 1.415 1.895 2.365 2.998 3.499 4.785 5.408

8 0.000 0.706 0.889 1.108 1.397 1.860 2.306 2.896 3.355 4.501 5.041

9 0.000 0.703 0.883 1.100 1.383 1.833 2.262 2.821 3.250 4.297 4.781

10 0.000 0.700 0.879 1.093 1.372 1.812 2.228 2.764 3.169 4.144 4.587

11 0.000 0.697 0.876 1.088 1.363 1.796 2.201 2.718 3.106 4.025 4.437

12 0.000 0.695 0.873 1.083 1.356 1.782 2.179 2.681 3.055 3.930 4.318

13 0.000 0.694 0.870 1.079 1.350 1.771 2.160 2.650 3.012 3.852 4.221

14 0.000 0.692 0.868 1.076 1.345 1.761 2.145 2.624 2.977 3.787 4.140

15 0.000 0.691 0.866 1.074 1.341 1.753 2.131 2.602 2.947 3.733 4.073

16 0.000 0.690 0.865 1.071 1.337 1.746 2.120 2.583 2.921 3.686 4.015

17 0.000 0.689 0.863 1.069 1.333 1.740 2.110 2.567 2.898 3.646 3.965

18 0.000 0.688 0.862 1.067 1.330 1.734 2.101 2.552 2.878 3.610 3.922

19 0.000 0.688 0.861 1.066 1.328 1.729 2.093 2.539 2.861 3.579 3.883

20 0.000 0.687 0.860 1.064 1.325 1.725 2.086 2.528 2.845 3.552 3.850

21 0.000 0.686 0.859 1.063 1.323 1.721 2.080 2.518 2.831 3.527 3.819

22 0.000 0.686 0.858 1.061 1.321 1.717 2.074 2.508 2.819 3.505 3.792

23 0.000 0.685 0.858 1.060 1.319 1.714 2.069 2.500 2.807 3.485 3.768

24 0.000 0.685 0.857 1.059 1.318 1.711 2.064 2.492 2.797 3.467 3.745

25 0.000 0.684 0.856 1.058 1.316 1.708 2.060 2.485 2.787 3.450 3.725

26 0.000 0.684 0.856 1.058 1.315 1.706 2.056 2.479 2.779 3.435 3.707

27 0.000 0.684 0.855 1.057 1.314 1.703 2.052 2.473 2.771 3.421 3.690

28 0.000 0.683 0.855 1.056 1.313 1.701 2.048 2.467 2.763 3.408 3.674

29 0.000 0.683 0.854 1.055 1.311 1.699 2.045 2.462 2.756 3.396 3.659

30 0.000 0.683 0.854 1.055 1.310 1.697 2.042 2.457 2.750 3.385 3.646

40 0.000 0.681 0.851 1.050 1.303 1.684 2.021 2.423 2.704 3.307 3.551

60 0.000 0.679 0.848 1.045 1.296 1.671 2.000 2.390 2.660 3.232 3.460

80 0.000 0.678 0.846 1.043 1.292 1.664 1.990 2.374 2.639 3.195 3.416

100 0.000 0.677 0.845 1.042 1.290 1.660 1.984 2.364 2.626 3.174 3.390

1000 0.000 0.675 0.842 1.037 1.282 1.646 1.962 2.330 2.581 3.098 3.300

D z 0.000 0.674 0.842 1.036 1.282 1.645 1.960 2.326 2.576 3.090 3.291

0% 50% 60% 70% 80% 90% 95% 98% 99% 99.8% 99.9%
E Confidence Level

*Table available at http://www.sjsu.edu/faculty/gerstman/StatPrimer/t-table.pdf

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t-Table KEY:

A – cum. prob = cumulative probability – the probability that the value of a random variable falls
within a specified range or that a random variable is less than or equal to a specified value.

B – One-tail and Two-tails: If you are using a significance level of .05 …
… a One-tailed test allots all of your alpha to testing the statistical significance in the one direction
of interest. This means that .05 is in one tail of the distribution of your test statistic.
… a Two-tailed test allots half of your alpha to testing the statistical significance in one direction
and half of your alpha to testing statistical significance in the other direction. This means that
.025 is in each tail of the distribution of your test statistic.

One-tailed test

This left area shaded This right area shaded
is .05 of the total area is .05 of the total area
under the curve under the curve

Two-tailed test This right area shaded
is .025 of the total
This left area shaded area under the curve
is .025 of the total
area under the curve

C – df: degrees of freedom = sample size minus 1 (i.e. n-1)
D – Z-score: referes to how many standard deviations from the mean a specific result is.
E – Confidence Level: the probability that the value of a parameter falls within a specified range
of values.

[Images: https://stats.idre.ucla.edu/other/mult-pkg/faq/general/faq-what-are-the-differences-between-one-tailed-and-two-tailed-tests/]

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Using the t-Table.

The use of the table is best illustrated by a specific example. Suppose that we have performed an
experiment to compare reaction times between sound and touch, collecting 6 data points for
each stimulus. The number of degrees of freedom would be calculated as:

df = (6 – 1) + (6 – 1) = 10
Select the row in the table for which df = 10. The next column gives the t-value for a significance
level of p = 0.2000, which in this case is t = 1.372. For this value of t, we are 80% certain that the
difference observed between two distributions is significant and did not occur by chance.
As you proceed along the row (with df = 10), you will see higher values of t corresponding to
smaller values of probability and higher confidence. When t = 1.812, p = 0.1000 and we are now
90% certain that the difference is significant. In order to be 99% certain (p = 0.0100), we must
calculate a t-value of 3.169.
Suppose that we use the numerical values of the means and standard deviations in the
experiment to calculate a value of t = 2.546. Using the table, we can conclude that the difference
between reaction time for sound and touch is statistically significant for a probability level of
0.05; this is because the calculated value of t exceeds the critical value (t = 2.228) for df = 10 and
p = 0.05. However, we also see that the difference does not reach significance at the next higher
level of confidence, p = 0.02. Therefore we conclude that the probability that our results occurred
by chance (if the null hypothesis is true) is between 2 and 5 percent, and our difference is
significant at the level of p = 0.05.

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