Special Topics 504: Practical Methods in Analyzing Animal Science Experiments Arithmetic mean:x̄ = Σ x n Variance:s 2 = Σ (x – x̄) 2 n – 1 Standard Deviation:s = s 2 = Σ (x – x̄) 2 n – 1 Standard Error of the Mean:SEM = s n

Special Topics 504: Practical Methods in Analyzing Animal Science Experiments The Normal (Gaussian) Distribution The “Z score”Z = x – μ σ The standard score is where: x is a raw score to be standardized; μ is the mean of the population; σ is the standard deviation of the population.

Special Topics 504: Practical Methods in Analyzing Animal Science Experiments Parametric tests assume an underlying Normal distribution and because of the Central Limit Theorem means of samples follow this. The “test statistic” in all tests is calculated as: systemic variation / random variation or (measured difference between sample means) / (mean difference expected by chance) or (variability between treatments) / (variability within treatments)

Special Topics 504: Practical Methods in Analyzing Animal Science Experiments Thus, the common principle of measurements for an experiment are: 1.A sample (a set of scores) is measured for each population or treatment condition. 2.For each sample, the mean and an indictor of spread (variance or SD or sum of squares) is calculated. 3.The difference between the sample means is calculated. ( this is the numerator of the test statistic and indicates systematic (predictable) difference(s) between treatment conditions. 4.The variation within each sample indicates unsystematic (random, unpredictable) variation. This is the denominator of the test statistic.

Special Topics 504: Practical Methods in Analyzing Animal Science Experiments Design Types Simplified 1.Single sample designs: take data from a single sample to test a hypothesis about a single population. 2.Independent measures designs: take separate samples from each population or treatment. 3.Related-samples designs: a.Repeated measures designs: one sample, with each subject measured under all treatment conditions. b.Matched-subject designs: each subject in one sample is matched with a subject in each of the other samples.

Special Topics 504: Practical Methods in Analyzing Animal Science Experiments A simplified parametric test key 1.How many separate samples? a.1 sample – go to 2 b.2 samples – go to 4 c.> 2 samples – go to 5 2.How many measurements for each sample? a.1 measurement – go to 3 b.2 measurements – use a matched-pair t-test c.>2 measurements – use a repeated measures ANOVA 3.Is the population standard deviation known? a.Yes – use a “z score” b.No – use a single-sample t-test 4.Are the samples matched? (non-independent) a.Yes – use a matched-pair t-test b.No – use an independent measures t-test 5.Are the samples matched? (non-independent) a.Yes – use a repeated-measures ANOVA b.No – go to 6 6.How many independent variables? a.1 variable – use a single factor ANOVA b.2 variables – use a two-factor ANOVA…