What is Standard Deviation and Standard Error

Kristina Alas Author

04/25/2022 Added

100 Plays

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A brief description for what Standard Deviation and Standard Error are and what they mean in the context of research and how it is used.

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[00:00:07.790]Previously, we looked at this data,
[00:00:10.000]which is of the decomposition of biomulch in the soil
[00:00:13.410]for the 2013 cucumber field trial.
[00:00:16.890]And we have our two biofabric treatments,
[00:00:20.020]BK-1-270 and BK-2-360,
[00:00:24.660]and then we took the average
[00:00:26.860]of biomulch remaining in the soil
[00:00:28.900]at zero, six, and 12 months for both of the treatments.
[00:00:32.950]And with that, we decided to create a bar graph
[00:00:36.100]so we can easily see what is happening
[00:00:38.940]or how much biomulch is remaining in the soil over the year,
[00:00:43.640]so over the zero, six, and 12 months timeline.
[00:00:48.790]So this is our graph
[00:00:49.880]of the average biomulch remaining in the soil
[00:00:52.370]for our two biofabric treatments,
[00:00:55.030]and it seems like BK-2-360 is increasing over time
[00:01:00.110]and BK-1-270 is increasing just slightly
[00:01:04.530]between six and 12 months.
[00:01:06.730]However, this is impossible.
[00:01:09.030]So what we want to calculate is the standard error
[00:01:12.820]and this will help us read this graph accurately.
[00:01:16.300]The standard error will tell us how reliable our mean is,
[00:01:20.500]our mean, or our average, is.
[00:01:24.330]To calculate standard error,
[00:01:26.160]we must first calculate the standard deviation
[00:01:28.860]because the standard error is derived
[00:01:30.820]from standard deviation.
[00:01:32.890]So the standard deviation measures the variability
[00:01:35.720]among the data set.
[00:01:37.220]It tells how spread out the data is from the mean.
[00:01:40.800]The more spread out the data distribution is
[00:01:43.160]the higher the standard deviation.
[00:01:45.740]And here are the steps to calculate standard deviation.
[00:01:48.860]However, we'll never ask you to calculate it by hand.
[00:01:53.200]Instead, we'll use Excel
[00:01:55.180]to calculate the standard deviation for us,
[00:01:58.440]and we'll never ask you to do that
[00:02:00.750]because it is a very complex process and it's slow
[00:02:03.940]and the chances of making a mistake are pretty high.
[00:02:09.275]So I have the standard deviation calculated here,
[00:02:12.480]and I created videos for you to watch, a small screencast,
[00:02:17.270]that will show you how to calculate standard deviation
[00:02:20.660]and the standard error in Excel.
[00:02:23.360]And as you can see,
[00:02:26.920]immediately after incorporation for BK-1-270,
[00:02:30.620]it has a high standard deviation,
[00:02:32.920]and you can see that the data points
[00:02:35.740]range really high compared to the average.
[00:02:38.590]So we got from 228 to one.
[00:02:42.160]And for six months after incorporation,
[00:02:45.500]we have a smaller standard deviation of 14,
[00:02:49.110]and those data points are really close to the average.
[00:02:56.030]So now that standard deviation has been calculated,
[00:02:58.800]we can calculate our standard error,
[00:03:01.060]and again, our standard error is derived
[00:03:04.240]from our standard deviation.
[00:03:06.470]The standard error is the standard deviation
[00:03:09.360]divided by the square root of our sample size.
[00:03:12.730]So for example, we have 101.65 for a standard deviation
[00:03:18.107]and we divide that by the square root of four
[00:03:20.700]'cause we have four replications.
[00:03:23.890]And so, what does the standard error tell us?
[00:03:26.440]Well, it tells us how reliable our mean is.
[00:03:33.250]So looking at this biofabric treatment,
[00:03:35.640]we'll notice that when the standard error is small,
[00:03:40.250]it'll be more representative of the true mean.
[00:03:43.510]And when we have a larger standard error,
[00:03:46.420]it means there may be some notable irregularities.
[00:03:50.380]And so one thing we'll notice also
[00:03:52.290]is that the standard error is always smaller
[00:03:55.440]than our standard deviation.
[00:03:59.710]So on this graph,
[00:04:00.790]I have my two biofabric treatments
[00:04:03.190]and I have the average and standard error
[00:04:05.480]for zero, six, and 12 months.
[00:04:07.750]So now that I have my standard error calculated,
[00:04:10.570]I can go back into my graph that I made
[00:04:14.130]of the average biomulch remaining in the soil
[00:04:16.620]and add standard error bars.
[00:04:21.750]To refresh your memory,
[00:04:22.900]here is what the graph looked like
[00:04:25.260]of just the average biomulch remaining in the soil,
[00:04:30.000]and here is the graph of the averages
[00:04:31.820]including the standard error bars.
[00:04:34.060]So if we only looked at the graph
[00:04:35.650]with average biomulch remaining in the soil,
[00:04:37.850]it tells a different story
[00:04:39.720]than if we were to interpret the data
[00:04:41.790]with these standard error bars.
[00:04:43.830]So the bigger overlap in the bars,
[00:04:47.420]that means that the difference
[00:04:49.010]is not statistically significant.
[00:04:51.720]So if we have a smaller overlap,
[00:04:54.180]that means there's probably a significant difference.
[00:04:57.540]And if we didn't see any overlap in these error bars,
[00:05:00.440]that means the difference is significance.
[00:05:02.980]So we do see overlap in here,
[00:05:04.980]so that is just telling us
[00:05:06.650]that our mean may not be as reliable as we think it is.
[00:05:12.380]And so we created a bar graph with standard error bars
[00:05:15.940]for the data that Dr. Wortman collected.
[00:05:19.520]He used a line graph with the standard error bar.
[00:05:22.910]And so there's several ways
[00:05:24.170]that you can incorporate standard error bars
[00:05:26.630]into your graphs.

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What is Standard Deviation and Standard Error

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