Oakes Irrigation Research
Site
Carrington Research Extension Center * North Dakota State University
P.O. Box 531, Oakes, ND 58474-0531, Voice: (701) 742-2189, FAX: (701)
742-2700, email: rgreenla@ndsuext.nodak.edu
STATISTICS
Statistics are tools used to decide if differences seen between treatments are really different. For example: Joe drank a cup of water from a paper cup and John drank a cup of water from a styrofoam cup. Then they had a pushup contest. Joe did 30 pushups and John did 10 pushups. Can we conclude from this that drinking water from a paper cup helps one do pushups? No! The difference in the number of pushups depended on the strength of each person, not on the cup he drank water from. On the other hand, if Joe drove 30 nails into a log using a hammer and John drove zero nails into a log using a banana, we would conclude that the difference in the number of nails hammered into the log was due to the instrument used. In my studies, each treatment or variety is assigned at random to three or four plots. All plots cause some differences in yields, plant height, etc. The statistics help decide how much of the differences between yields, etc. is due to the plots and how much the treatments or varieties caused. If the treatments or varieties affected the outcome enough then the differences between yields, etc. are said to be significant, otherwise, the differences (or apparent differences) between yields, etc. are said to be non-significant. Or, put another way, statistics help determine if the treatments caused enough difference that if the experiments were repeated, under similar conditions and with new plot assignments (or on a farmer's field), the results would be the same.
In the tables of this report, values, such as yield, height, density, etc., are given for each variety or treatment. The values may appear different whether the statistics say they are or not. We used two methods to show whether values are really (statistically) different. One method is with letters placed after the values. Those values in the same column that have the same letter (not group of letters) following them are not significantly different. Looking at the column for “yield” in Table 5 , Cambria has the value “25.5" followed by the letters "b-e" (b-e means all the letters between b and e, inclusive (b,c,d,e)). Bronco has the value of “28.3" followed by the letters "ab". Since at least one of the letters following the value for Bronco also appears after the value for Cambria, the values are not significantly different. Almanac has an “yield” value of “32.5" followed by the letter "a". Since the letter following the value for Almanac does not also follow the value for Cambria, these values are significantly different. Using this method, if there are no letters following the values in a column, then there are no significant differences between any of the values in that column or, in other words, all the values in that column are equal.
The other method used to show whether two values in a column are significantly different is to use the Least Significant Difference (LSD). The LSD is placed at the bottom of a column of numbers. If the difference between any two values in that column is equal to or greater than the LSD, then the two values are significantly different. For example, in the “yield” column in Table 21 the value for Optiko is 23.3 and the value for Bilko is 20.2. Because the difference between these two values is greater than the LSD given at the bottom of that column (3.0), these two values are significantly different. But the value for Nikko is not significantly different from the value for Optiko because the difference is less than the LSD (23.6 - 23.3 < 3.0). To help avoid confusion, we will not use both methods in the same table.
The C.V. (coefficient of variation) at the bottom of some tables indicates how variable the data were. The higher the C.V. the more variable the data. Probability values at the bottom of a table indicate the probability of no significant differences between any values in that column (or all values in that column are equal). The lower the value, the greater the probability that there is a real difference between at least two of the values in that column. If probability values are greater than 0.05, any differences between values in that column are generally considered non-significant. For example: In Table 5 the probability value of “0.24" at the bottom of the “Early stand” column indicates that the differences in values in that column are not significant (note that there are no letters following the values in that column). In the “yield” column of Table 5 the probability value is “<.0001", indicating an excellent probability that the differences between at least some of the values in that column are significant.