ab 1: Introduc on to Science
only be one independent variable in each experiment. This is because if a change occurs, scien sts need to be able to pinpoint the cause of the change. Independent variables are always placed on the x‐ axis of a chart or graph.
Dependent variables are variables that scien sts observe in rela onship to the independent variable. Common examples of this are rate of reac on, color change, etc. Any changes observed in the depend‐ ent variable are caused by the changes in the independent variable. In other words, they depend on the independent variable. There can be more than one dependent variable in an experiment. Depend‐ ent variables are placed on the y‐axis of a chart or graph.
A control is a sample of data collected in an experiment that is not exposed to the independent varia‐ ble. The control sample reflects the factors that could influence the results of the experiment, but do not reflect the planned changes that might result from manipula ng the independent variable. Con‐ trols must be iden fied to eliminate compounding changes that could influence results. O en, the hardest part of designing an experiment is determining how to isolate the independent variable and control all other possible variables. Scien sts must be careful not to eliminate or create a factor that could skew the results. For this reason, taking notes to account for uniden fied variables is important. This might include factors such as temperature, humidity, me of day, or other environmental condi‐ ons that may impact results.
There are two types of controls, posi ve and nega ve. Nega ve controls are data samples in which you expect no change to occur. They help scien sts determine that the experimental results are due to the independent variable, rather than an uniden fied or unaccounted variable. For example, suppose you need to culture bacteria and want to include a nega ve control. You could create this by streaking a sterile loop across an agar plate. Sterile loops should not create any microbial growth; therefore, you expect no change to occur on the agar plate. If no growth occurs, you can assume the equipment used was sterile. However, if microbial growth does occur, you must assume that the equipment was con‐ taminated prior to the experiment and must redo the experiment with new materials.
Alterna vely, posi ve controls are data samples in which you do expect a change. Let’s return to the growth example, but now you need to create a posi ve control. To do this, you now use a loop to streak a plate with a sample that you know grows well on agar (such as E. coli). If the bacteria grow, you can assume that the bacteria sample and agar are both suitable for the experiment. However, if the bacteria do not grow, you must assume that the agar or bacteria has been compromised and you must re‐do the experiment with new materials.
Lab 1: Introduc on to Science
The scien fic method also requires data collec on. This may reflect what occurred before, during, or a er an experiment. Collected results help reveal experimental results. Results should include all rele‐ vant observa ons, both quan ta ve and qualita ve.
A er results are collected, they can be analyzed. Data analysis o en involves a variety of calcula ons, conversions, graphs, tables etc. The most common task a scien st faces is unit conversion. Units of me are a common increment that must be converted. For example, suppose half of your data is meas‐
ured in seconds, but the other half is measured in minutes. It will be difficult to understand the rela‐ onship between the data if the units are not equivalent.
When calcula ng a unit conversion, significant digits must be accounted for. Significant digits are the digits in a number or answer that describe how precise the value actually is. Consider the following rules:
Addi on and subtrac on problems should result in an answer that has the same number of significant decimal places as the least precise number in the calcula on. Mul plica on and division problems should keep the same total number of significant digits as the least precise number in the calcula on. For example:
Addi on Problem: 12.689 + 5.2 = 17.889 → round to 18
Mul plica on Problem: 28.8 x 54.76 = 1577.088 → round to 1580 (3 sig. digits)
Any non‐zero number (1‐9) is always significant 45 has two significant digits
3.99 has three significant digits 248678 has six significant digits
Any me a zero appears between significant num‐ bers, the zero is significant
4005 has four significant digits 0.34000000009 has eleven significant digits
Zeros that are ending numbers a er a decimal point or zeros that are a er significant numbers
before a decimal point are significant
45.00 has four significant digits 15000.00 has seven significant digits
Zeros that are used as placeholders are NOT sig‐ nificant digits
62000000 has only two significant digits .0000000897 has only three significant digits
A zero at the end of a number with no decimal can be a significant digit
50 cm exactly has two significant digits (not rounded)
Lab 1: Introduc on to Science
Scien fic nota on is another common method used to transform a number. Scien fic data is o en very large (e.g., the speed of light) or very small (e.g., the diameter of a cell). Scien fic nota on provides an abbreviated expression of a number, so that scien sts don’t get caught up coun ng a long series of zeroes.
There are three parts to scien fic nota on: the base, the coefficient and the exponent. Base 10 is al‐ most always used and makes the nota on easy to translate. The coefficient is always a number be‐ tween 1 and 10, and uses the significant digits of the original number. The exponent tells us whether the number is greater or less than 1, and can be used to “count” the number of digits the decimal must be moved to translate the number to regular nota on. A nega ve exponent tells you to move the deci‐ mal to the le , while a posi ve one tells you to move it to the right.
For example, the number 5,600,000 can be wri en as 5.6 x 106. If you mul ply 5.6 by 10 six mes, you will arrive at 5,600,000. Note the exponent, six, is posi ve because the number is larger than one. Al‐ terna ve, the number 0.00045 must be wri en using a nega ve exponent. To write this number in sci‐ en fic nota on, determine the coefficient. Remember that the coefficient must be between 1 and 10. The significant digits are 4 and 5. Therefore, 4.5 is the coefficient. To determine the exponent, count how many places you must move the decimal over to create the original number. Moving to the le , we have 0.45, 0.045, 0.0045, and finally 0.00045. Since we move the decimal 4 places to the le , our exponent is ‐4. Wri en in scien fic nota on, we have 4.5 x 10‐4
Although these calcula ons may feel laborious, a well‐calculated presenta on can transform data into a format that scien sts can more easily understand and learn from. Some of the most common meth‐ ods of data presenta on are:
Table: A well‐organized summary of data collected. Tables should display any informa on relevant to the hypothesis. Always include a clearly stated tle, labeled columns and rows, and measurement units.
Variable Height Wk. 1 (mm) Height Wk. 2 (mm) Height Wk. 3 (mm) Height Wk. 4 (mm)
Control (without nutrients) 3.4 3.6 3.7
Independent (with nutrients)
3.5 3.7 4.1 4.6
Table Example: Plant Growth With and Without Added Nutrients
Lab 1: Introduc on to Science
Graph: A visual representa on of the rela onship between the independent and dependent variable. They are typically created by using data from a table. Graphs are useful in iden fying trends and illus‐ tra ng findings. When construc ng a graph, it is important to use appropriate, consistent numerical intervals. Titles and axes labels should also reflect the data table informa on. There are several differ‐ ent types of graphs, and each type serves a different purpose. Examples include line graphs or bar graphs. Line graphs show the rela onship between variables using plo ed points that are connected with a line. There must be a direct rela onship and dependence between each point connected. More than one set of data can be presented on a line graph. By comparison, bar graphs: compare results that are independent from each other, as opposed to a con nuous series.
Figure 4: Top speed for Cars A, B, C, and D
Figure 3: Plant growth, with and without nutrients, over me
Lab 1: Introduc on to Science
A er compiling the data, scien sts analyze the data to determine if the experiment supports or re‐ futes the hypothesis. If the hypothesis is supported, you may want to consider addi onal variables that should be examined. If your data does not provide clear results, you may want to consider run‐ ning addi onal trials or revising the procedure to create a more precise outcome.
One way to analyze data is to calculate percent error. Many experiments perform trials which calcu‐ late known value. When this happens, you can compare experimental results to known values and cal‐ culate percent error. Low percent error indicates that results are accurate, and high percent error indi‐ cates that results are inaccurate. The formula for percent error is:
Note that the brackets in the numerator indicate “absolute value”. This means that the number in the equa on is always posi ve.
Suppose your experiment involves gravity. Your experimental results indicate that the speed of gravity is 10.1 m/s2, but the known value for gravity is 9.8 m/s2. We can calculate the percent error through the following steps:
The scien fic method gives us a great founda on to conduct scien fic reasoning. The more data and observa ons we are able to make, the more we are able to accurately reason through the natural phe‐ nomena which occur in our daily lives. Scien fic reasoning does not always include a structured lab report, but it always helps society to think through difficult concepts and determine solu ons. For ex‐ ample, scien fic reasoning can be used to create a response to the changing global climate, develop medical solu ons to health concerns, or even learn about subatomic par cles and tendencies.
Although the scien fic method and scien fic reasoning can guide society through cri cal or abstract thinking, the scien fic industry typically promotes lab reports as a universal method of data analysis and presenta on. In general terms, a lab report is a scien fic paper describing the premise of an ex‐ periment, the procedures taken, and the results of the study. They provide a wri en record of what
Percent Error = |(Experimental—Actual)| x 100% Actual
Percent Error = |(10.1 m/s2 ‐ 9.8 m/s2)| x 100% (9.8 m/s2)
Percent Error = |0.3 | x 100% (Note the units cancel each other out) (9.8 )
Percent Error = 0.0306 x 100% = 3.1% (Remember the significant digits)