Graphing Resources |
Using Error Bars in your Graph The knowledge that any individual measurement you make in a lab will lack perfect precision often leads a rearcher to choo to take multiple measurements at some independent variable level. Though no one of the measurements are likely to be more preci than any other, this group of values, it is hoped, will cluster about the true value you are trying to measure. This distribution of data values is often reprented by showing a single data point, reprenting the mean value of the data, and error bars癌症晚期能活多久 to reprent the overall distribution of the data. 跳棋棋盘图片Let's take, for example, the impact energy absorbed by a metal at various temperatures. In this ca, the temperature of the metal is the independent variable being manipulated by the rearcher and the amount of energy absorbed is the dependent variable being recorded. Becau there is not perfect precision in recording this absorbed energy, five different metal bars are tested at each temperature level. The resulting data (and graph) might look like this: For clarity, the data for each level of the independent variable (temperature) has been plotted on the scatter plot in a different color and symbol. Notice the range of energy values recorded at each of the temperatures. At -195 degrees, the energy values (shown in blue diamonds) all hover around 0 joules. On the other hand, at both 0 and 20 degrees, the values range quite a bit. In fact, there are a number of measurements at 0 degrees (shown in purple squares) that are very clo to measurements taken at 20 degrees (shown in light blue triangles). The ranges in values reprent the uncertainty in our measurement. Can we say there is any difference in energy level at 0 and 20 degrees? One way to do this is to u the descriptive statistic, mean. The mean, or average, of a group of values describes a middle point, or central tendency, about which data points vary. Without going into detail, the mean is a way of summarizing a group of data and stating a best guess at what the true value of the dependent variable value is for that independent variable level. In this example, it would be a best guess at what the true energy level was for a given temperature. The above scatter plot can be transformed into a line graph showing the mean energy values: Note that instead of creating a graph using all of the raw data, now only the mean value is plotted for impact energy. The mean was calculated for each temperature by using the AVERAGE function in Excel. You u this function by typing 形容变化快的成语=AVERAGE in the formula bar and then putting the range of cells containing the data you want the mean of within parenthes after the function name, like this: 喜剧小品In this ca, the values in cells B82 through B86 are averaged (the mean calculated) and the result placed in cell B87. Once you have calculated the mean for the -195 values, then copy this formula into the cells C87, etc. If you look back at the line graph above, we can now say that the mean impact energy at 20 degrees is indeed higher than the mean impact energy at 0 degrees. However, though you can say that the means of the data you collected at 20 and 0 degrees are different, you can't say for certain the true energy values are different. Can we ever know the true energy values? No, but you can include additional information to indicate how cloly the means are likely to reflect the true values. You can do this with error bars微博怎么搜索用户. There are two common ways you can statistically describe uncertainty in your measurements. One is with the standard deviation of a single measurement (often just called the standard deviation) and the other is with the standard deviation of the mean, often called the standard error. Since what we are reprenting the means in our graph, the standard error is the appropriate measurement to u to calculate the error bars. While we were able to u a function to directly calculate the mean, the standard error calculation is a little more round about. First you have to calculate the standard deviation with the STDEV function. It is ud much the same way AVERAGE was: The standard error is calculated by dividing the standard deviation by the square root of number of measurements that make up the mean (often reprented by N). In this ca, 5 measurements were made (N = 5) so the standard deviation is divided by the square root of 5. By dividing the standard deviation by the square root of N, the standard error grows smaller as the number of measurements (N) grows larger. This reflects the greater confidence you have in your mean value as you make more measurements. You can make u of the of the square root function, SQRT, in calculating this value: Using words you can state that, bad on five measurements, the impact energy at -195 deg C is 1.4 +/- 0.2 joules. The +/- value is the standard error and express how confident you are that the mean value (1.4) reprents the true value of the impact energy. Graphically you can reprent this in error bars. With the standard error calculated for each temperature, error bars can now be created for each mean. First click the line in the graph so it is highlighted. Now lect Format>Selected 桂平西山茶Select the Y Error Bars tab and then choo to Display Both (top and bottom error bars). Now click on the Custom button as the method for entering the Error amount. You will want to u the standard error to reprent both the + and the - values for the error bars, B89 through E89 in this ca. Note: it is critical to highlight the standardard deviation values for all of the temperatures. This way the unique standard error value is associated with each mean. The easiest way to do this is to click on the up arrow button as shown in the figure above. The dialog box will now shrink and allow you to highlight cells reprenting the standard error values: When you are done, click on the down arrow button and repeat for the other value cell. When you are done, click OK. Your graph should now look like this: The error bars shown in the line graph above reprent a description of how confident you are that the mean reprents the true impact energy value. The more the orginal data values range above and below the mean, the wider the error bars and less confident you are in a particular value. Compare the error bars to the distribution of data points in the original scatter plot above.Tight distribution of points around 100 degrees - small error bars; loo distribution of points around 0 degrees - large error bars. More precily, the part of the error bar above each point reprents plus one standard error and the part of the bar below reprents minus one standard error. With the error bars prent, what can you say about the difference in mean impact values for each temperature? If the upper error bar for one temperature overlaps the range of impact values within the error bar of another temperature, there is a much lower likelihood that the two impact values differ significantly. Therefore, we can say with some confidence that the impact energy at 0, 20, and 100 degrees is significantly greater than at -195 degrees. We can also say the same of the impact energy at 100 degrees from 0 degrees. However, we are much less confident that there is a significant difference between 20 and 0 degrees or between 20 and 100 degrees. How can we improve our confidence? One way would be to take more measurements and shrink the standard error. However, remember that the standard error will decrea by the square root of N, therefore it may take quite a few measurements to decrea the standard error. It is also possible that your equipment is simply not nsitive enough to record the differences or, in fact, there is no real significant difference in some of the impact values. If you are also going to reprent the data shown in this graph in a table or in the body of your lab report, you may want to refer to the resources on significant digits and designing tables. | 母亲节是什么时候|
本文发布于:2023-05-21 12:24:40，感谢您对本站的认可！
本文链接：https://www.wtabcd.cn/fanwen/fan/89/921874.html
版权声明：本站内容均来自互联网，仅供演示用，请勿用于商业和其他非法用途。如果侵犯了您的权益请与我们联系，我们将在24小时内删除。
| 留言与评论（共有 0 条评论） |
