A sleep researcher wanted to determine which of four different “treatments” for delayed onset insomnia (i.e., problems falling asleep) worked best.  The treatments were cognitive imagery (think peaceful, relaxing thoughts and scenes), drug (a mild, low dose sedative), sensory deprivation (using a blindfold and earplugs), or paradoxical intention (trying NOT to fall asleep).  The DV is the mean number of minutes taken to enter Stage 1 sleep.  There were 20 subjects in each condition. The following means were obtained:  Imagery Drug Sensory Deprivation. Paradoxical Intention 54.8 52.3 66.5 69.4 SSW =  4699          SSB= 2,832      Use alpha .01 to draw your conclusions and explain to a lay audience what you found.

Definition Definition Measure of central tendency that is the average of a given data set. The mean value is evaluated as the quotient of the sum of all observations by the sample size. The mean, in contrast to a median, is affected by extreme values. Very large or very small values can distract the mean from the center of the data. Arithmetic mean: The most common type of mean is the arithmetic mean. It is evaluated using the formula: μ = 1 N ∑ i = 1 N x i Other types of means are the geometric mean, logarithmic mean, and harmonic mean. Geometric mean: The nth root of the product of n observations from a data set is defined as the geometric mean of the set: G = x 1 x 2 ... x n n Logarithmic mean: The difference of the natural logarithms of the two numbers, divided by the difference between the numbers is the logarithmic mean of the two numbers. The logarithmic mean is used particularly in heat transfer and mass transfer. ln x 2 − ln x 1 x 2 − x 1 Harmonic mean: The inverse of the arithmetic mean of the inverses of all the numbers in a data set is the harmonic mean of the data. 1 1 x 1 + 1 x 2 + ...