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Analyzing Experimental Data

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Analyzing Experimental Data H OW CAN WE U NDERSTAND OUR WATER R ESOURCES? Analyzing Experimental Data he information in this chapter is a following format. The layout for the data table short summary of some topics that is based on the variables for the experiment. Tare covered in depth in the book The first column lists the different values or Students and Research written by Cothron, levels of the independent variable, and the Giese, and Rezba. See the end of this chapter remaining columns list the corresponding for full information on obtaining this book. observed values of the dependent variable. The book is an invaluable resource for any Values for each repeated trial are listed in middle or high school science teacher. separate columns, and then in the last column the average value. The average value will usual- SETTING UP SIMPLE DATA TABLES ly be a mean value, but there are some situa- AND GRAPHS tions where a median value or even mode value would be more appropriate. The labels for the Students should be encouraged to set up independent and dependent variable columns data tables and graphs on a computer should both include the measuring unit if whenever possible. This can be done by applicable, and the table as a whole should be first entering data into a spreadsheet given a title. The example below is a data table program such as Microsoft Excel. for a simple experiment to measure the effect of Making simple data tables... the length of a pendulum string on the number of pendulum swings per minute. A simple data table can be set up in the THE EFFECT OF LENGTH OF PENDULUM STRING ON THE NUMBER OF SWING CYCLES PER MINUTE Length of Number of Swing Cycles per Minute Pendulum String (cm) Trial 1 Trial 2 Trial 3 Average 30 50 70 90 A NALYZING E XPERIMENTAL D ATA 6/13 H OW CAN WE U NDERSTAND OUR WATER R ESOURCES? Displaying data with graphs... in presenting results is in graphical form, and the highest level is when the results can Displaying data from an experiment with be summarized in the form of a mathematical a graph makes it easier to see trends and equation. patterns in the data. The graph presents the data in a visual format that often brings out Depending on the exact nature of an experi- the significance of the data much more clearly ment, students may need to display their data than a data table. There is a hierarchy of ways using different types of graphs. As usual, the to present results from an experiment that best way to make the appropriate decision allows increasing levels of understanding of the about the experiment is to base the decision on meaning of the results. The lowest level is a the nature of the independent and dependent simple qualitative description of the results variables for the experiment in question. The using words. Quantitative data, with measure- table below summarizes the different graphs ments of numerical data, allows for greater that can be drawn in different situations. understanding. The third level of complexity DECIDING ON A GRAPH FOR DIFFERENT EXPERIMENTS Independent Variable Dependent Variable Type of Graph Standard Scale with Equal Intervals Quantitative Bar Graph or Line Graph Examples: Temperature, Qualitative Frequency Distribution Height, Weight, Volume Graph Discrete Categories Quantitative Bar Graph Examples: Day of the Week, Gender, Qualitative Frequency Distribution Color, Brand of Detergent Graph One advantage of drawing a line graph over a A frequency distribution graph is a type of bar bar graph is that extra information can then graph. In a frequency distribution graph, there be obtained from the graph. The line can be will be several bars for each value of the used to infer values of the dependent variable independent variable. The bars represent the corresponding to given values of the independ- number of counts for each possible category ent variable that were not measured in the of the dependent variable. For example, an experiment. A line graph is not appropriate experiment could be carried out to record the when the independent variable is represented leaf quality of plants grown with different by discrete categories. In these cases, intervals amounts of a fertilizer. If the leaf quality is between categories have no significance and a recorded using a rating scale of 1-4, the bar graph is a more appropriate choice. frequency distribution graph would have bars A NALYZING E XPERIMENTAL D ATA 6/14 H OW CAN WE U NDERSTAND OUR WATER R ESOURCES? showing the number of plants with each leaf These sentences can be written directly on quality rating, and sets of bars would be drawn the piece of graph paper. for each different level of fertilizer. There are some important things to require of SUMMARIZING EXPERIMENTAL DATA: students when they draw graphs. First of all DESCRIPTIVE STATISTICS the values for the independent variable should Making summary data tables... be plotted on the horizontal x-axis and the A simple data table shows all of the measure- values for the dependent variable on the ments collected in an experiment. It can be vertical y-axis. Setting up numerical scales will better to simplify the display of data by usually be the hardest part of the graph for reducing the amount of information with the student to accomplish, and you may need a summary data table, especially if the to help students with this. Certainly, you will experiment is a big or long one. A summary need to check them carefully as they work on data table reduces the information by summa- this. If students are drawing a graph with two rizing the raw data using measures of central numerical scales, they should usually begin the tendency and variation. A measure of central scales of both axes from zero. The reason for tendency is a typical or average value for a set this is that the (0,0) data point often has real of data. This can be a mean, median, or mode significance and should be the starting point value. A measure of variation is a measure of for a line-of-best-fit. For example, if students how consistent the data are. Simple measures were carrying out a simple experiment to see of variation include range and frequency how the height a ball is dropped from affects distribution. Standard deviation can also be the height it bounces to, they would know for used as a measure of variation in a sample, certain that if the ball was dropped from zero if this is desired when working with older height then it would also have zero bounce. students. The line graph should begin from this point. Students should be required to label their Whichever descriptive statistics students are graphs clearly. This means labeling both the using, they should see how to calculate the axes, including the measuring units when statistics by hand first and then by using a appropriate, and also writing a title for the graphing calculator or possibly a computer. whole graph. There is a standard format that can be used for summary data tables. The following table When students are carrying out simple experi- is an example of a summary data table for an ments and not necessarily writing a long experiment measuring the effect of different conclusion, it is useful to ask them to finish concentrations of a chemical on the height their graph by writing one or two sentences to of plants. Ten plants were observed for each summarize their conclusions from the graph. concentration of the chemical. A NALYZING E XPERIMENTAL D ATA 6/15 H OW CAN WE U NDERSTAND OUR WATER R ESOURCES? THE EFFECT OF DIFFERENT CONCENTRATIONS OF CHEMICAL X ON THE HEIGHT OF TOMATO PLANTS IN CENTIMETERS Descriptive Concentration of Chemical X (%) Information 0 10 20 30 Mean Height (cm) 15.3 18.1 10.5 6.0 Range 7664 Maximum 19 20 14 8 Minimum 12 14 8 4 Number of Plants 10 10 10 10 Choosing appropriate measures of central tendency and variation... The most appropriate measure of central tendency and of variation depends on the experiment carried out and the type of data collected. APPROPRIATE MEASURES OF CENTRAL TENDENCY AND VARIATION Independent Variable Dependent Variable Measure of Central Measure of Tendency Variation Standard Scale with Equal Quantitative Mean Range or Intervals (Sometimes Median) Standard Examples: Deviation Temperature, Height, Qualitative (Ordinal) Median Frequency Weight, Volume Example: Rating Distribution Scale from 1 – 5 Qualitative (Nominal) Mode Frequency Examples: Gender, Color Distribution Discrete Categories Quantitative Mean Range or Examples: Day of the (Sometimes Median) Standard Week, Gender, Color, Deviation Brand of Detergent Qualitative (Ordinal) Median Frequency Example: Rating Distribution Scale from 1-5 Qualitative (Nominal) Mode Frequency Examples: Gender, Color Distribution A NALYZING E XPERIMENTAL D ATA 6/16 H OW CAN WE U NDERSTAND OUR WATER R ESOURCES? The following table is an example of a summary data table for a qualitative experiment recording the effect of different concentrations of chemical on leaf quality of plants. The leaf quality was recorded using an ordinal rating scale judging leaf quality from Quality 4 to Quality 1. Since the data are ordinal, the measure of central tendency is the median and the measure of variation is frequency distribution. These measures are displayed in the summary data table. THE EFFECT OF VARIOUS CONCENTRATIONS OF CHEMICAL X ON LEAF QUALITY Descriptive Concentration of Chemical X (%) Information 0102030 Median 4421 Frequency Distribution Quality 4 10 6 0 0 Quality 3 0330 Quality 2 0173 Quality 1 0007 Number 10 10 10 10 Displaying data trends..
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