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The SD quantifies how much the values vary from one another: scatter or spread The SD does not change predictably as you acquire more data. Mean is a good fit of the data Large S.D.: data distant from the mean: mean is not an accurate representationĢ9 SD and SEM (SEM = SD/√N) What are they about?
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= √(SS/N-1) = √(s2) = s The standard deviation is a measure of how well the mean represents the dataĢ8 Standard deviation Small S.D: data close to the mean: Problem with variance: measure in squared units For more convenience, the square root of the variance is taken to obtain a measure in the same unit as the original measure: the standard deviation S.D. Solution: to divide the SS by the number of observations (N) As we are interested in measuring the error in the sample to estimate the one in the population we divide the SS by N-1 instead of N and we get the variance (S2) = SS/N-1 To avoid the problem of the direction of the error: we square them Instead of sum of errors: sum of squared errors (SS): SS gives a good measure of the accuracy of the model But: dependent upon the amount of data: the more data, the higher the SS.
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It can be considered as a model because it summaries the data Example: a group of 5 persons: number of friends of each members of the group: 1, 2, 3, 3 and 4 Mean: ( )/5 = 2.6 friends per person Clearly an hypothetical value How can we know that it is an accurate model? Difference between the real data and the model createdĢ5 The mean (2) Calculate the magnitude of the differences between each data and the mean: Total error = sum of difference = 0 No errors ! Positive and negative: they cancel each other out. Describe them: Mean, variance, standard deviation, standard error and confidence intervalĢ4 The mean Definition: average of all values in a column
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How to determine it? Substantive knowledge, previous research, pilot study ... 2 The Standard Deviation (SD) Variability of the data In ‘power context’: effect size: combination of both: e.g.: Cohen’s d = (Mean 1 – Mean 2)/Pooled SDĨ 3 The significance level usually 5% (p0.99).Ģ3 Quantitative data They take numerical values (units of measurement)ĭiscrete: obtained by counting Example: number of students in a class values vary by finite specific steps or continuous: obtained by measuring Example: height of students in a class any values They can be described by a series of parameters: Mean, variance, standard deviation, standard error and confidence interval Discrete numb pups in a litter continous hight, weitght, different scale Data can be messy so then you go back to qualitative data. minimum meaningful effect of biological relevance the larger the effect size, the smaller the experiment will need to be to detect it. This is to be determined scientifically, not statistically. The power analysis depends on the relationship between 6 variables: the difference of biological interest the standard deviation the significance level the desired power of the experiment the sample size the alternative hypothesis (ie one or two-sided test) Effect sizeħ 1 The difference of biological interest Translate the hypothesis into statistical questions: What type of data? What statistical test ? What sample size? Very important: Difference between technical and biological replicates. Hypothesis Experimental design Choice of a Statistical test Power analysis: Sample size Experiment(s) Data exploration Statistical analysis of the resultsĥ Experimental design n=3 n=1 Think stats!! Main output of a power analysis: Estimation of an appropriate sample size Too big: waste of resources, Too small: may miss the effect (p>0.05)+ waste of resources, Grants: justification of sample size, Publications: reviewers ask for power calculation evidence, Home office: the 3 R: Replacement, Reduction and Refinement. Translation: statistical power is the likelihood that a test will detect an effect when there is an effect to be detected. Presentation on theme: "Introduction to Statistics with GraphPad Prism 7"- Presentation transcript:ġ Introduction to Statistics with GraphPad Prism 7Ģ Outline of the course Power analysis with G*Powerīasic structure of a GraphPad Prism project Analysis of qualitative data Chi-square test Analysis of quantitative data t-test, ANOVA, correlation and curve fittingģ Power analysis Definition of power: probability that a statistical test will reject a false null hypothesis (H0) when the alternative hypothesis (H1) is true.