¶ … phosphorus levels in 2004 and in 2007.
/ The sample that is collected consists of 20 different pondwater samples for each of the two years.
/ The parameter being measured is the phosphorus levels in the pondwater samples measured in ug/L.
/ The null hypothesis in this example is that there was no change in phosphorus levels between 2004 and 2007, i.e., nothing happened.
/ The alternate hypothesis is that there was an increase in phosphorus levels as a result of the contamination.
/ In terms of this example, for the dataset to fail to have a normal distribution would mean that the 2007 phosphorus levels would not fall on the part of the distribution curve that is established by the 2004 levels that indicate probability of no increase. If mathematically the probability of the 2007 levels of being significantly different from the 2004 levels -- indicating an increase in phosphorus levels -- we would reject the null hypothesis.
/ The alpha value is the conservative standard that indicates a level of change that is scientifically or statistically significant. In this case, a conservative standard for alpha-value would probably be .05, which is the customary number (indicating a 5% probability that the null hypothesis is incorrect).
8 / The p-value is the likelihood of the observed statistics having occurred due to chance. A comparison of the p-value with the alpha-value tells us whether the recorded statistics are significantly different from the null hypothesis, and therefore consistent with proof of the alternate hypothesis. If the p-value is less than or equal to the alpha-value, this is considered significant. Assuming we have set the alpha-value at .05, a p-value...
e of .03 is less than the alpha-value, and we reject the null hypothesis and accept the alternate hypothesis as proven.
9/
2004 2007
MEAN PHOSPHORUS LEVEL (ug/L): 238.95-311.40
STANDARD DEVIATION PHOSPHORUS LEVEL: 14.33-26.57
10/
MEAN PHOSPHORUS LEVELS MEASURED IN ug/L
1 = 2004, 2 = 2007
1 / The variables here are two measurements, dry season depth and wet season depth, for each of 3 ponds (DM, OE, and H).
2 / The sample is 10 random depth measurements for each time period for each of 3 ponds.
3 / The parameter being measured is the average water level for each pond in the year, and the average water level for each pond during wet season.
4 / The null hypothesis is that there is no significant difference in average water level for the three ponds.
5 / The alternate hypothesis is that there will be a significant difference in average water level, indicating one pond could accommodate more water.
6 / If the dataset does not have a normal distribution, that means we must accept the likelihood that a greater fluctuation in average water levels is something other than chance (i.e., that there is a measurable difference).
7 / We would set the alpha-level here at .05 since that is the standard.
8 / Again if the p-value is .03, that indicates that there is a statistically significant result and the null hypothesis should be rejected.
9/
OE H DM
MEAN WATER DEPTH, ANNUAL (cm) 23.65-141.76-107.26
STANDARD DEV., ANNUAL (cm) 3.94-25.35-23.62
MEAN WATER DEPTH, WET SEAS (cm) 25.15-148.11-115.25
STANDARD…
