n(n2-1)
= 1 - 6 X 3.5 = 1 - 21
11(112-1) 1320
rs = 1 - 0.016
rs = 0.98
The critical value at 5% significance for 11 pairs of measurements is 0.62. As you can see, the Spearman Rank value achieved is 0.98, which exceeds the critical value. Therefore, you can reject the null hypothesis because the value achieved exceeds the critical value at 5% significance for the number of data sets. The results therefore show a strong positive correlation.
The experiment yielded data which show a positive correlation, proved by the spearman rank statistical test. The experiment proves that as you increase bile salt concentration, the volume of anthocyanin released by the beetroot cells will also increase due to the increase of leaking of the tonoplast of the cell membrane. The results shown on the tables confirm that an increase of bile salt concentration has increased the absorbance of light from the colorimeter. The table, ignoring anomalous results, shows a trend of the absorbance of the solution to increase as bile salt concentration increases. The difference of mean absorbance (arbitrary units) between bile salt concentrations of 0.0g/100g and 1.0g/100g is 0.40. This is a significant change which cannot possibly be put down to coincidence. Each of the 3 data sets, ignoring anomalous results, shows the increase in average absorbance as the bile salt concentration increases. The differences of absorbance between bile salt concentrations of 0.0g/100g and 1.0g/100g vary between the three data sets, but all show a positive increase in absorbance as bile salt concentration is increased. The graphs show graphical representation of the results obtained. The positive correlation of the graphs show the general trend that absorbance increases as bile salt concentration increases. The absorbance has increased due to the increased release of anthocyanin from the vacuole and cell by diffusion down the concentration gradient.
There is a scientific explanation of why this occurs. Anthocyanin is located in the vacuole of the beetroot cell as shown in the diagram below.
Anthocyanin is a very large molecule with a relatively large molecular structure as shown below (extracted from http://www.froguts.com/question439.htm).
As the diagram above shows, because it is such a large molecule, it cannot pass through the tonoplast or the cell membrane by simple diffusion, because the tonoplast and cell membrane are not permeable enough because the spaces between the phospholipids bilayer of the tonoplast and cell membrane are too small.
If there is a way to overcome to tonoplast and the cell membrane, the anthocyanin will use simple diffusion to pass out of the cell. This is because there is always a lower concentration of anthocyanin outside the tonoplast and cell membrane, than there is within the cell membrane. The anthocyanin would therefore move down the concentration gradient as much as possible, so there is equilibrium of concentration inside, and out of the vacuole and cell. However, because anthocyanin is such a large molecule, it cannot easily pass through the tonoplast. The phospholipid bi-layer does not have large enough spaces to let the anthocyanin diffuse through the membrane, and so the anthocyanin must find another way to diffuse out the membrane.
The bile salt consists of a hydrophilic head and a hydrophobic tail. When bile salts are allowed to interact with cell membranes, the hydrophobic tails of the individual bile salt molecules attach to the hydrophobic part of the proteins inside the phospholipid bi-layer. The hydrophobic section of the protein therefore becomes hydrophilic due to being covered in hydrophilic bile salt heads. Therefore, the protein will be removed from the cell membrane. This occurs many times around the cell membrane, and there are effectively many large punctures in the cell membrane and tonoplast, and so the anthocyanin leaks out of the cell due to simple diffusion due to large enough punctures.
Bile salts have a similar effect on the phospholipids in the membrane. Because the phospholipids consist of a hydrophobic tail and a hydrophilic head, the bile salts join with the individual phospholipids and effectively emulsify the phospholipids by turning them into liquid due to the large membrane turning into individual phospholipids. This will increase the release of anthocyanin from the tonoplast and cell membrane because there will a more permeable membrane because the bile salts will cause the emulsification of the phospholipids. The anthocyanin will therefore be able to diffuse out of the cell due to lower concentration of anthocyanin outside the cell, than inside the cell (down the concentration gradient) because there will be large spaces in the cell membrane due to the emulsification of some of the phospholipids in the membrane phospholipids bilayer.
Increasing the bile salt concentration increases the number of bile salt molecules. A higher bile salt concentration will therefore have more bile salt molecules to make more punctures in the cell membrane, and so more anthocyanin will leak.