Science Buddies: "Ask an Expert"

Hi!

My science fair project board is due Nov. 4th and I am having difficulty figuring out how to apply my data in calculating the standard deviation.

My data consists of hue (degrees), saturation (%), and brightness (%) for four different colors of dye (red, purple, yellow, orange) on two types of fabrics (wool and silk). I also experimented with how metal salt mordants affect the dye colors so I have the same data set (hue, saturation, and brightness) for the same four dyes and same two fabrics using two different mordants (aluminum sulfate and ferrous sulfate). I did three trials for each.

Wool - No Mordant
Red - 3 trials, average
Purple - 3 trials, average
Yellow - 3 trials, average
Orange - 3 trials, average

Silk - No Mordant
Red - 3 trials, average
Purple - 3 trials, average
Yellow - 3 trials, average
Orange - 3 trials, average

Wool - Aluminum Sulfate
Red - 3 trials, average
Purple - 3 trials, average
Yellow - 3 trials, average
Orange - 3 trials, average

Silk - Aluminum Sulfate
Red - 3 trials, average
Purple - 3 trials, average
Yellow - 3 trials, average
Orange - 3 trials, average

Wool - Ferrous Sulfate
Red - 3 trials, average
Purple - 3 trials, average
Yellow - 3 trials, average
Orange - 3 trials, average

Silk - Ferrous Sulfate
Red - 3 trials, average
Purple - 3 trials, average
Yellow - 3 trials, average
Orange - 3 trials, average

THEN I exposed all my samples above to sunlight for a period of several weeks and measured the hue, saturation, and brightness for all trials listed above to determine colorfastness. So I have the same number of data sets listed above for the exposed samples.

In total, I have 48 averages (dye colors, exposed dye colors). QUESTION: HOW DO I ORGANIZE MY DATA AND CALCULATE THE STANDARD DEVIATION? WILL I HAVE MORE THAN ONE STANDARD DEVIATION?

My board is due Nov. 4, 2015.

Thank you!

Hello proscience15,

Congratulations on completing your experiment! Your experiment is very extensive and you’ve certainly collected an impressive amount of data.

Standard deviation is a statistic that indicates how much variation there is for a set of data. A couple of links with more information about standard deviation are:

http://www.mathsisfun.com/data/standard-deviation.html

https://www.khanacademy.org/math/probab ... -deviation

One common way of treating experimental results with multiple trials is to calculate the average and standard deviation for each set of trials. The standard deviations in this case indicate the amount of variation among measurement trials of the same experimental conditions.

In your experiment each of the test conditions for which you made three trial measurements represents a set. You could calculate an average and standard deviation for each of these sets. So you’d have a total of 48 average and standard deviation values.

Standard deviation is used to help decide if differences in data are due to chance or the effect of an independent variable in an experiment. A difference in your data between two experimental conditions (say red wool has a different value from red silk) that is larger than the standard deviations of the repeat trials was likely due to an effect of fabric (wool vs silk).

I hope this helps. Please post again if you have more questions.

A. Norman

Thank you very much for your reply!

I used Excel and made three separate graphs for hue, saturation, and brightness. I combined my initial trials along with the exposed to sunlight trials. My x-axis is the combination of each sample (wool,onion skin, no mordant), etc. for a total of 48 samples. My y-axis for graph 1 is hue, graph 2 saturation, and graph 3 brightness.

The hue standard deviation graph trend (added trend line to my graph) was pretty consistent for all the samples with spikes in the 250 degree range for red cabbage on silk.

The standard deviation graph for saturation was very jagged (a lot of zig-zagging), the trend line shows a decrease in saturation which I would expect from fading.

The standard deviation graph for brightness was also very jagged with a gradual decrease in the trend line, which I would expect since brightness is related to saturation.

Can a standard deviation graph be very jagged? It looks like an EKG. As you mentioned, could this be due to the variation in the fiber and the dye material not being consistent throughout the experiment? I think that the inconsistency of color is what makes this experiment interesting. It is a surprise because you never know what you might get. I guess the variations in color is what makes the natural dyes so beautiful.

If you could please comment if I set up my standard deviation properly, I would appreciate it. Also is the jagged line in the graph okay if I explain the reason for it in my discussion? Does this make my experiment invalid if my results are inconsistent?

Thanks!

Hi proscience15,

I’m assuming that you calculated standard deviation values for the three trials of each of your 48 samples. Next you used those standard deviation values to make the graphs you described in your post.

As you’ve pointed out, standard deviation values can vary and sometimes you can find trends in the variation. Please keep in mind that some of the variation in your standard deviation values may be due to variation in the average values. Do the graphs of your average values (for hue, saturation and brightness) show patterns similar to the corresponding standard deviation graphs? If so, some of the patterns in your standard deviations may be due to variation in the averages. You can calculate the “relative standard deviation” by dividing your standard deviation values by your average values. Trends in the relative standard deviation should be due to variability and not changes in the average values.

Yes, a standard deviation graph could be jagged. One explanation might be different amounts of fiber or dye variability for different experimental conditions as you suggest. Or as mentioned above, the average values changed across experimental conditions and the standard deviation values followed the averages. Try taking a look at the relative standard deviation before finalizing your conclusions about trends in your standard deviation data.

A jagged line in your graph is OK because the graph reflects what you observed in your experiment. And it would be great to provide a well-reasoned explanation for the jagged line. No, the kind of results you’ve described does not invalidate your experiment. Given the range of test conditions you examined it seems to me that some variation in replicate trial standard deviation would be expected.

I hope this helps. Please post again if you have more questions.

A. Norman

Hi A. Norman!

I went ahead and followed your suggestions by graphing the averages and the relative standard deviation for each of my 48 samples.

The average graphs and the standard deviation graphs for hue, saturation, and brightness follows the EXACT same pattern. I don't know if this is normal, or if I did something wrong when selecting my data for the graph in Excel.

I then created a graph for the relative standard deviation in Excel and got a different pattern for each graph (hue, saturation, and brightness). The relative standard deviation graph for brightness appears to be the inverse of the standard deviation graph. The graphs for the averages and the relative standard deviation are still very jagged.

Here is some information based on my graphs:

Standard Deviation
Hue High value: 36.61056 for wool, red cabbage, no mordant
Hue Low value: 0.57735 for wool, turmeric, no mordant
Saturation High value: 17.61628 for wool, onion skin, ferrous sulfate, exposed to UV
Saturation Low value: 1 for silk, red cabbage, no mordant, exposed to UV
Brightness High value: 18.24829 for silk,onion skin, aluminum sulfate
Brightness Low value: 0 for wool, turmeric, aluminum sulfate, exposed to UV

Relative Standard Deviation
Hue High value: 0.23809524 for silk, red cabbage, no mordant, exposed to UV
Hue Low value: 0.01124708 for wool, red cabbage, ferrous sulfate, exposed to UV
Saturation High value: 0.85739931 for silk, red cabbage, ferrous sulfate, exposed to UV
Saturation Low value: 0.0080937 for silk, turmeric, ferrous sulfate
Brightness High value: 0.35714286 for wool, onion skin, ferrous sulfate, exposed to UV
Brightness Low value: 0 for wool, turmeric, aluminum sulfate, exposed to UV

What do you think? If this data seems to be okay, which graphs should I put on my science fair board? I have very limited space on the board itself. Should I display my standard deviation graphs for hue, saturation, and brightness, or relative standard deviation graphs for hue, saturation, and brightness? Did I apply error bars to these graphs? I will have to start gluing information on my board tomorrow (Mon) since my board is due on Wed., Nov. 4.

Thank you very much for your help!

Hi proscience15,

From what you’ve described I think the “jagged graph” of your data is due to the effects of your experimental conditions. You tried 48 different combinations of dyes, fabrics, mordants and light exposures. The resulting average hue, saturation and brightness values must have varied quite a bit. The standard deviations for multiple trials of your experimental conditions follow the averages and thus show the same pattern in your graphs.

I think the relative standard deviation values are more important to consider because they represent variation within your replicate trials that didn’t come from changes in the average values. Do the relative standard deviation graphs show something of interest about your experiment? If so, you might want to include the graphs on your board.

You mentioned “error bars” in you post. As an alternative to the relative standard deviation graphs you might consider displaying the standard deviations as error bars around the average values in graphs (Excel has this capability). This is a common way of displaying data and it allows the viewer a quick way of understanding the amount of variability associated with the data.

I hope this helps. Please post again if you have more questions.

A. Norman

Hi!

I looked at the highest peaks (the points with the greatest relative standard deviation values) and found that in all cases, the deviations were due to outlier trial values for either hue, saturation, or brightness. Even though the highest peaks applied to different variations of fibers, dye material, mordants, and exposure to UV, the one thing they all had in common was one outlier trial value. My guess would be this may have been due to the fact that the red cabbage did not dye any of the wool fibers. Since there was no dye on the fiber to begin with, putting the fiber in the mordant bath only allowed the metal (iron) to attach to the fiber. Ferrous sulfate crystals are green, so that may be why the sample might have ended up with a greenish color throwing off the average and affecting the relative standard deviation. On the lighter dyes like mint, the aluminum sulfate could have had the same affect as the iron mordant. Aluminum sulfate usually brightens colors, but if the dye color was very light it may have become whiter and it would also skew the averages.

I suppose this would show that natural dyes can vary greatly depending on the plant material (every plant is different), how the fiber was treated before dyeing. Also, red cabbage dye baths usually require vinegar in order deprotonate so it can bond with the fiber or the mordant. I didn't add vinegar because I wanted to keep all conditions constant as much as possible. I guess I shouldn't have used the red cabbage in my experiment because I seems that it was responsible for the majority of the deviations in my experiment. According to my research, wool usually take dyes easily.

My conclusion looking at the relative standard deviation graphs is that red cabbage is a highly fugitive dye. Tumeric is also. And possibly mint, but I think the problem with mint is that it doesn't give a very strong color to begin with.

So my standard deviation was affected by my average values, which were affected by the dye materials, fibers, and the weak chemical bonds between the fiber and the dye material. The iron mordant fixed itself to the fiber okay. Overall though, the UV light from the sunlight eventually broke down the chemical bonds which ended up fading all my samples to some extent. The best mordant was ferrous sulfate for fixing the dye colors to the fibers.

Did you think I should use the relative standard deviation graphs based on my interpretation explained above? Or should I use the average value graph with error bars? If you think I should use the relative standard deviation graph, do I need to add error bars to the graph?

Thanks!

Hi proscience15,

I think you’ve written a well-reasoned explanation for your observations on standard deviations of your trial values. Also, nice work on picking through the details of your data and thinking through the meaning of it!

I think the information you derived from the relative standard deviation data adds interest to your project and including the graphs may emphasize your explanation. I’m assuming that you will include graphs of your average values on your display board. If so and if you have room, I think you should include the relative standard deviation graphs as well. If you have average and relative standard deviation graphs, I see no need for error bars on the average graphs.

If you have room for only one set of graphs on you board, I suggest using the averages with error bars. Regardless of which graphs you use, you might consider highlighting (different color or symbol) the data sets that contain the outliers you discussed in your explanation.

I hope this helps. Please post again if you have more questions.

A. Norman

Okay, I will try to eliminate something on my board so I can include both types of graphs.

My final questions:

I did not use UV spectroscopy, just a HTML color picker. Just to verify that I understand my research correctly, if my dye colors changed from red-orange to brown with onion skin when using ferrous sulfate as a mordant, can I assume that the ferrous sulfate caused a hypsochromic shift in the quercetin towards blue to make the dyed fiber brown? And if the ferrous sulfate caused the red cabbage dye to change from purple to greenish-blue, could I say that the ferrous sulfate caused a hypsochromic shift in the anthocyanine in the cabbage? Or is that only valid when using a spectroscope?

Does aluminum sulfate also cause bathochromic or hypsochromic shifts?
Could the bathochromic and hysochromic shifts go either way when using ferrous sulfate or aluminum sulfate depending on the color change?
Can I make a pretty solid educated guess by using a color wheel to determine which shift occurred?
Do hue scales only go in one direction, like from yellow to green to blue to purple to red to orange?

Thanks A. Norman! I really learned a lot from you.

Hi proscience15,

I think it’s OK to discuss your color changes in terms of hypsochromic or bathochromic shifts regardless of how you made your measurements.

You seem to be on the right track with your discussion of how your color changes came to be. But it’s not quite correct to say that the color shifts were in the quercetin or anthocyanin. Rather, the characteristic colors of quercetin and anthocyanin are due to interactions of these compounds with visible light. Iron can form complexes with either compound and these complexes will have interactions with visible light that are different from the non-complexed compounds. Changes in light interaction due to the iron complexes can result in blue (hypsochromic) or red (bathochromic) shifts in color.

Aluminum may also form complexes with quercetin and anthocyanin and I would expect different visible spectra for the complexes. So, yes it’s possible that aluminum sulfate might cause bathochromic or hypsochromic shifts.

Yes, I think you could use a color wheel (or a linear representation of the visible spectrum) to figure out which kind of shift you have. If your color changed toward the violet end of the spectrum you have a hypsochromic shift (toward a shorter wavelength). If the change was toward the red end of the spectrum you have a bathochromic shift (toward a longer wavelength).

I must say that I have no understanding of hue scales. I don’t know if there is a standard arrangement for hue scales. A few examples I saw online began with red at a value of zero. Numeric values increased as the colors transitioned toward violet so the number scale roughly parallelled light frequency (inverse of wavelength).

I hope this helps and good luck at your science fair. Please post again if you have more questions.

A. Norman

Hi A. Norman,

Thanks for replying so quickly. I now have my graphs (averages and relative standard deviation). Just to be sure, my graph for RSD should have the RSD on the y-axis and the units should be in %, correct? Also, when I calculated the RSD in Excel, I used the following formula: Standard Deviation * 100 divided by the mean to get RSD in percent. Is that correct?

This should be my last post for this project. Thank you very much for your help!

Hi proscience15,

Yes, the RSD should go on the y-axis of your graph in percentage units. And your formula for RSD is correct.

Good luck and please post again if you have more questions.

A. Norman