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| 1 | +Power simulations for count data in one factorial designs |
| 2 | +=================== |
| 3 | + |
| 4 | +This app runs power calculations for one factorial designs. |
| 5 | +One the left you can specify the expected `Effects` to simulate, |
| 6 | +settings for the `Simulation` design and the `Inference` procedure. |
| 7 | + |
| 8 | +To run the app with default options, simply hit the `Run simulation` Button and explore the results for a global test and a test for LOEC. |
| 9 | +After making changes on the left, you have to hit the `Run simulation` Button again. |
| 10 | + |
| 11 | + |
| 12 | + |
| 13 | + |
| 14 | +### Data |
| 15 | +Count data are simulated from a negative binomial distribution ($NB(\mu, \kappa)$) with mean = $\mu$ and variance = $\mu + \mu^2 / \kappa$. |
| 16 | + |
| 17 | +$\kappa$ is a dispersion parameter: |
| 18 | + |
| 19 | +* if $\kappa \rightarrow 0$ overdispersion increases |
| 20 | +* if $\kappa \rightarrow \infty$ data become Poisson distributed (no overdispersion) |
| 21 | + |
| 22 | +The summary in the `Simulation-Design` tab gives mean and variances per treatment as well as graphical representation of the simulated data (assuming a sample size of 1000). |
| 23 | + |
| 24 | +### Design |
| 25 | +Data are simulated for a one factorial design with 4 treatments and a step effect between treatments 2 and 3: |
| 26 | + |
| 27 | +Abundance in in treatments 1 + 2 are draw from $NB(\mu_c, \kappa)$, whereas the mean abundance in treatments 3 + 4 are reduced by factor $r$: $NB(r \times \mu_c, \kappa)$. |
| 28 | +Therefore, the LOEC is at treatment 3 and NOEC at treatment 2. |
| 29 | + |
| 30 | +Note, that $\kappa$ is equal between all treatments. |
| 31 | + |
| 32 | +$\mu_c$, $\kappa$ and $r$ can be controlled by the sliders (on the left, `Effects`). |
| 33 | +The `Simulation-Design` tab on the right gives a graphical representation of the design. |
| 34 | +For demonstration purposes, 1000 data points per replicate are drawn from the specified design. |
| 35 | + |
| 36 | + |
| 37 | +### Models |
| 38 | + |
| 39 | +Two type of models are currently implemented: |
| 40 | + |
| 41 | +1. Linear model on transformed data |
| 42 | +2. Quasi-Poisson model |
| 43 | + |
| 44 | +Both are computationally feasible and give correct Type I errors. |
| 45 | + |
| 46 | + |
| 47 | +### Inference |
| 48 | +The global treatment effect is assessed using an F-test. |
| 49 | +LOEC is determined via Dunnett contrasts. |
| 50 | +The type of hypothesis (one-sided / two-sided) can be specified (on the left, `Inference`). |
| 51 | + |
| 52 | + |
| 53 | +### Simulations |
| 54 | +Power is calculated using simulations. |
| 55 | +The number of simulated datasets can be specified (currently max. 250 to take care of the server). |
| 56 | +Moreover, up to 5 sample sizes (displayed on the x-axis) can be entered. (on the left, `Simulations`) |
| 57 | + |
| 58 | +Press the `Run simulation` button to start the simulations. |
| 59 | + |
| 60 | + |
| 61 | +## Output |
| 62 | +Results for the global test and LOEC determination are given graphical and in tabular form on the right. |
| 63 | +Both can be downloaded using the respective buttons. |
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