Oakes Irrigation Research
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Carrington Research Extension Center * North Dakota State University
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STATISTICS, 1999
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 are given for each variety or treatment. The values may appear different whether the statistics say they are or not. I have used two ways to help the reader know if the values are significantly different. The first is called the LSD (least significant difference). It is placed at the bottom of a column of values and indicates how big a difference there needs to be between values in that column before the difference is "real". For example, in Table 11 there is a column labeled "processing". At the bottom of the column the LSD is listed as "1.2". In this column Navajo has a value of 5.0 and Primecut 59 has a value of 5.8. Because the difference between these two values is less than the LSD (5.8 - 5.0 < 1.2), they are not significantly different. Bolero has a value of 6.8. That value is significantly different from the value for Navajo because the difference in values is greater than the LSD (6.8 - 5.0 > 1.2). If there are no significant differences between any values in a column, I put an "NS" at the bottom of that column of values, as in the "cello" column of Table 11. Another way to show whether values are different 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 "overall score" in Table 7, Bobcat has the value 6.7 followed by the letters "a-d" (a-d means all the letters between a and d, inclusive (a,b,c,d)). Balbro has the value of 6.2 followed by the letters "de". Since at least one of the letters following the value for Bobcat also appears after the value for Balbro, the values are not significantly different. Strukton has an "overall score" value of 5.8 followed by the letter "e". Since the letter following the value for Strukton does not appear after the value for Bobcat, these values are significantly different.
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. The lower the value, the greater the probability that there is a real difference between 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 11 the probability value of 0.057 at the bottom of the "cello" column indicates that the differences in values in that column are non-significant (note the "NS" for the LSD value). In the "processing" column of Table 11 the probability value is 0.0003, indicating the differences between values in that column are very significant.