Laboratory Notebook and Reports

Laboratory Notebook

Your laboratory data must be recorded directly into a bound, quadrille laboratory notebook that has duplicate ("carbon-copy") pages. Reserve the first few pages for a table of contents, which should be kept up-to-date. Entries should be legible and clear and made when an operation is performed or when the data is generated. These entries should be made in your lab notebook and not on a loose piece of paper to be copied later. All entries must be in black or blue ink in the English language. Each page should have the day’s date at the top. If entries are made at a later date, a new page should be used. Always include units of measurement when recording data. Do not include any data that is not relevant to the lab, including pictures, drawings, or editorials. You should not use your lab notebook to take notes. Errors should be crossed out with a single line, not made illegible, just in case the "errors" later turn out to be important, and the correction should be written near (above, below, or to the side if possible) the original entry. The original information should still be able to be read. In industrial laboratories, it is required that these corrections have a written explanation of why the correction was needed (typically as a footnote). It is at the discretion of your TA whether this will be required. Most data should be handwritten, but it is permissible to tape a page into your notebook if the 4 corners are marked so that it will be obvious if the page is removed. You should also initial and date across one side of the page so that the partial initials and date are visible on both the taped page and the notebook page.

All information regarding an experiment should be recorded in your notebook. Prior to the lab, you should carefully read through the lab manual and prepare your notebook with the following parts.

1. Title of experiment
2. Purpose of the experiment - What is your goal for the lab?
3. Outline of the procedure - A paragraph or two summarizing the important parts from the lab manual. This should not be word for word, but rather just enough information for you to use as a reference as you perform the lab.
4. Data and observations section - It is advisable to make data tables in your lab notebook prior to coming to the lab, as they will make entering data at the time you take it simpler.

Your TA will check your notebook prior to entry into the lab. Any student who has not completed this notebook preparation is unprepared to safely perform the assigned experiment and will have to leave the laboratory until they have finished preparing.

At the end of the laboratory period, your TA must initial each page of your notebook that was used during the lab to confirm that the work was completed by you during the lab.

 

Lab Reports

Your lab report should include the following parts:

1. Title of the experiment - This should capture the essence of the work being reported. Be specific. An article's title is important for indexing and retrieval purposes and should include important keywords about the experiment performed. The first author (you) has an asterisk next to your name; Partners should be listed as co-authors. The name of the institution and the date go below.
2. Purpose of the experiment - What is your goal for the lab?
3. Outline of the procedure - A paragraph or two summarizing the important parts from the lab manual. This should not be word for word but rather enough information that someone else could replicate your results. This includes the actual measurements performed in the lab (if the manual says to weigh 0.1 g and you weighed 0.1103 g, you should report here that you measured 0.1103 g).
4. Data and observations section - It is advisable to make data tables in your lab notebook before coming to the lab, as they will make it simpler when you enter the data you collect.
5. Calculations section.
6. Discussion - Analyze your data in the context of the purpose of the lab. Quantify how well your computed/measured values compare to literature (this includes statistical analysis such as percent error and standard deviation). Include discussions on possible sources of error in the execution of the experiment and how they might have affected the outcome. How might they be avoided in the future? This section should include answers to the lab manual questions - Show your work and provide answers.
7. Figures - These can be included in the discussion or added at the end as an appendix and referenced in the report. If you include a figure, it should be referenced in the text.
8. Conclusions - State the main findings of the experiment, and relate them to the purpose in the introduction. Concisely summarize your work.

Your TA may have specific instructions for the reports of each individual lab, but the format above should generally be followed. Turn in your report and the carbon copies of your lab notebook to your TA one week following the scheduled completion of that experiment.

You will perform your experiments with lab partners, and it is encouraged that you should discuss your data, analysis, and interpretation with your partner, with other students in the class, or with your TA. However, all work performed and reported should be your own. Plagiarism of any kind will not be tolerated and will be reported to Student Judicial Affairs.

 

Statistical Treatment of Data

Introduction

In physical and analytical chemistry, you are often left with large sets of data you will need to transform into useful information. This will require some manipulation of data and some calculations. Understanding your data begins with understanding that a histogram of an infinitely large number of good measurements typically follows a Gaussian (Normal) distribution. The equation for this distribution is given by:

\[ f(x_i) = \frac{1}{\sqrt{x\pi\sigma}}e^{-\frac{({x_i-\bar{x}})^2}{2\sigma^2}} \]

where \( \sigma \) is the standard deviation and \( \bar x \) is the average of your data, both defined below. Important features from this distribution are that the function is centered at the true average of the measurements, and the width of the distribution is related to the standard deviation, or the clustering of the data.

The reason this matter is a finite set of data will also follow this distribution, but there is uncertainty in where exactly the true average lies, and what the true deviation from it is, without doing an infinite number of measurements. When you report data, you will want to report it in these terms, taking the uncertainty in the true value into account. Below are some procedures for averaging data, finding the standard deviation, finding the relative deviation, finding the confidence interval, and analyzing poor data.

Averaging Data

The arithmetic mean, often called the average, is the sum of the measurements divided by the total number of measurements:

\[ \bar{x} = \frac{1}{n}\sum\limits_{i=1}^{n}x_i \]

where \( \bar{x} \) is the mean of the measurement of \( x \), \( x_i \) is the \( i \)th measurement of \( x \), and \( n \) is the total number of measurements being averaged. When you take repeat measurements of your data, you should calculate the average for your results for your report.

Standard Deviation

The standard deviation, \( \sigma \), measures how close values are clustered about the mean. The smaller your standard deviation, the higher the precision of your measurements.

The standard deviation for small samples is defined by:

\[ \sigma = \sqrt{\frac{1}{n-1}\sum\limits_{i=1}^{n}(\bar{x}-x_i)^2} \]

The square of the standard deviation is called the variance.

Relative Standard Deviation

You sometimes will want to convert the standard deviation into a relative standard deviation to compare how precise it is compared to other measurements of different magnitudes. This is calculated by:

\[ RSD = 100 \times \frac{\sigma}{\bar{x}} \]

Confidence Interval

With a finite number of data points, it is not possible to find the true mean or the true standard deviation, as a small sample size will not cover the entirety of the normal distribution of data. What we calculated in the earlier sections is the sample mean and the sample standard deviation. The confidence interval is an expression that states that the true mean is likely to lie within a certain distance from the measured and reported mean, \( \bar{x} \). The confidence interval is given by:

\[ \mu = \bar{x}\pm \frac{t\sigma}{\sqrt{n}} \]

where \( \mu \) is the interval, and \( t \) is the students \( t \), which can be looked up in the student's \( t \) table (available in many textbooks or online). The value of \( t \) for a 95% confidence interval can be found in Table \(\PageIndex{1}\):

Table \(\PageIndex{1}\): Student \( t \) table for a 95% confidence interval.

degrees of freedom \( (n-1) \)	95% Confidence Interval \( t \) Value
1	12.706
2	4.303
3	3.182
4	2.776
5	2.571
6	2.447
7	2.365
8	2.306
9	2.262
10	2.228
15	2.131
20	2.086
25	2.060
30	2.042
40	2.021
60	2.000
120	1.980
∞	1.960

Discarding Data

You should always be cautious of discarding data. Just because a data point is an outlier does not mean it is wrong; that may turn out to be your most accurate measurement. Two methods are generally accepted when deciding to reject data. The first is rejecting data that you know to be low quality due to the procedure of measuring it. You can do this by adding notes in your lab notebook, such as any issue in the lab, extra solvent added, a little bit of spilled powder, or instrument malfunctions, leading to problematic data collected. If you know you did something wrong, you can discard that data as bad data.

The other method for rejecting a single outlier (you can only perform this procedure once on a dataset) is called the q-test. For \( 3\leq n \leq 10 \), where n is the number of measurements of the same quantity, calculate:

\[ Q = \frac{\left| \text{suspect value} - \text{value closest to it}\right|}{\text{highest value}-\text{lowest value}} \]

Compare the value of \( Q \) with \( Q_c \) from Table \(\PageIndex{2}\). If \( Q > Q_c \), you can reject the suspect value.

Table \(\PageIndex{2}\): Critical \( Q \) values for rejection of a discordant value at a 90 % confidence level

\( n \)	\( Q \)
3	0.94
4	0.76
5	0.64
6	0.56
7	0.51
8	0.47
9	0.44
10	0.41

Significant Figures

When reporting data, you should only report the number of figures that are "significant." The number of digits used in a number denotes the highest precision that the number can be determined. For a balance that is accurate out to 0.0001, the precision of its measurements extends to the ten-thousandth place. There are many rules governing how significant figures can be found and propagated through a calculation, but for this class, we will use a simplified method in your reports.

To decide how many decimals to include in your reported measurements:

1. Calculate the standard deviation (or confidence interval for a finite number of data points).
2. Truncate the standard deviation (or CI) to either 1 or 2 significant figures. If truncating the sig figs to 1 significant figure would result in that digit only being a 1 or a 2, you will want to leave it at 2 significant figures.
3. Report your mean as the same number of decimal places as your standard deviation.

So, for example, if your mean is 10.12345 ppm, and your standard deviation is 0.032 ppm, you will report your measurement as 10.12 \( \pm \) 0.03 ppm (don’t forget units). Or, if your mean is 10.3452 \( {\mu}V \), and your CI is 0.0194 \( {\mu}V \), you will report your measurement as 10.345 \( \pm \) 0.019 \( {\mu}V \).