# Does power of a test depend on number of cases or number of observations?

Cases and observations.

It is my understanding that sample size is determined by the number of individuals taking part in an experiment (from my undergrad Psychology stats course). For each individual a mean is calculated from the result of each trial. These means are entered as data in SPSS. The mantra of the stats course was “one line per each individual” in SPSS. For my current research I am consulting a professional statistician who says that power is determined by the total number of trials (observations) rather than by the number of individuals (cases). E.g. if there are 10 individuals in a study, and 80 trials per individual, there will be 800 observations, enough to conduct a multiple regression with several predictors. I am confused, since examples in books (stats for Psychology) equate sample size to number of individuals and state that the power of a test increases if more individuals are added to a sample. So, does power depend on cases or on observations? And another question (for those familiar with SPSS). Is it possible to enter the raw data (i.e. the results of every trial) instead of entering the means in SPSS? What happens with the “one line per individual” condition? Thanks!

• "One line per individual" is sort-of-correct in an introductory course. More precisely, it should be "one line per observation, and don't forget to model dependencies between observations, such as multiple observations coming from the same individual." Note how this is a bit longer than the original suggestion... SPSS is certainly able to work with so-called repeated measurements. I suggest reading up on this topic (there are roughly a bazillion introductory hits on Google) and posting any specific remaining questions on StackExchange with the SPSS tag. – S. Kolassa - Reinstate Monica Mar 17 '14 at 12:07
• @Stephan Kolassa Thanks! I searched web and books, but the "repeated measures" they refer to is the "within subject design". I am referring to a number of repeated trials within the same block, e.g measuring reaction time to a target, the individual would perform 10 identical trials. So is power dependent on number of individuals or on total number of observations (individuals X trials)? Our training involved calculating the mean of these trials and entering this value in the stats package. Therefore, the stats analysis was blind to the number of observations. This approach seems incorrect... – Gwen Mar 17 '14 at 20:25
• Yes, your design is exactly repeated measures: 10 repetitions per individual. Subjects are the blocks here. (More complex hierarchical models can also model additional correlations between observations, e.g., different locations.) And while averaging trials is defensible, I would definitely use all the data and run a repeated measures model. Power depends both on the number of subjects and the number of trials per subject, increasing either will increase your power. Whether one or the other is more important will depend on the intra- vs. inter-subject variability. – S. Kolassa - Reinstate Monica Mar 18 '14 at 7:56