Bonferroni's method provides a pairwise comparison of the means. To determine which means are significantly different, we must compare all pairs. There are k = (a) (a-1)/2 possible pairs where a = the number of treatments.
Full Answer
How to determine if treatment means are different?
Feb 17, 2016 · Distribution of estimations of the mean in the treatment group for two sample sizes. The horizontal axis is RBC size in femtoliter (fL). Sample size=10,000 (red). Sample size=100 (blue). Mean of comparison group=89 fL (green). The sample size of 100 is insufficient to discriminate between the treatment group mean and the comparison mean.
How do you test for differences between means?
Use the two-sample t-test to determine whether the difference between means found in the sample is significantly different from the hypothesized difference between means. Analyze Sample Data Using sample data, find the standard error, degrees of freedom, test statistic, and the P-value associated with the test statistic.
What is the best way to test for significance between treatments?
For binary variables, the POB statistic can be computed from the absolute difference (AD) in treatment response as follows: POB = 0.5(AD+1). AD is computed by subtracting the percentage of patients who improved with placebo from the percentage who improved with treatment.
How do you compare multiple process means (treatments)?
difference between the means of the two samples. Paired t test: Sometimes called the t-test for correlated data, this is used to test for a difference between means where the two variables are paired, typically for a within-subjects design. An example would be a pretest post design where the mean difference in arm girth is compared
How do you know if treatments are significantly different?
How do you determine if there is a difference in means?
In order to test the hypothesis that your results could be significant, run a hypothesis test for differences between means. To compare two independent means, run a two-sample t test . This test assumes that the variances for both samples are equal.Dec 11, 2014
Which test can be used to compare two treatments?
When do we use t-test and z-test?
When do you use chi-square vs t-test?
When do you use a chi-square test example?
...
When to Use a Chi-Square Test (With Examples)
- Eye color (e.g. “blue”, “green”, “brown”)
- Gender (e.g. “male”, “female”)
- Marital status (e.g. “married”, “single”, “divorced”)
What does a chi-square test tell you?
What statistical test should be used to compare two groups?
Why is it not possible to examine all cases?
The examination of all cases is usually not done for the following reasons: it is difficult to identify all cases, it is resource intensive, and from a statistical point of view it provides little added certainty. Additionally, examination might involve destruction of the biological sample (e.g., estimating the weight of biologic organs on a scale is limited to pathologic specimens removed as warranted by surgery or at autopsy). For these reasons, the researcher is likely to use a sample in order to estimate values related to the greater population. In order to assure an accurate estimation, that sample must be representative of the population.
How does confidence interval change with sample size?
In chart 1, we can observe how the ‘confidence interval’ changes with sample size, becoming more precise with increasing sample size. When the sample size is 10,000 (row 3), the SD of the mean (SEM) is 100 times less (0.15 fL) than the SD of the sample (15 fL). By varying the sample size, the researcher can make the estimate of the mean as precise as desired.
What is inferential statistics?
When using inferential statistics, the researcher is attempting to predict an unknown value (e.g., the mean) that applies to all such patients. The true value for the entire group of all such patients is initially unknown and remains unknown. The nature of inferential statistics is the calculation of an estimate and qualification of the estimate in terms of its accuracy.
What is standard deviation?
Standard deviation is a measure of variability of the population.
What is the true mean of a population?
As with all normal distributions, the true mean of the population will be the mean of the estimates, will be the most frequent value (mode), and will lie at the center of the distribution (median). Consequently, 50% of the estimates will lie below the true mean and 50% will lie above the true mean.
Why is it important to have a representative sample?
Because the researcher attempts to make a generalization based on the sample at hand, it is extremely important that the sample be representative of the population of interest. If the sample is not representative, then the estimated value will likely be incorrect. Errors in statistical prediction that are related to the way the study is constructed or carried out are said to be the result of ‘bias’ or ‘systematic error’. Statistical use of the word ‘bias’ does not imply any intention or prejudice. Error resulting from bias is contrasted with error resulting from mathematically predictable variability.
Is the SD of the estimates of the mean normal?
The SD of the estimates of the mean is referred to as the SEM.
What is the purpose of the two-sample t-test?
Use the two-sample t-test to determine whether the difference between means found in the sample is significantly different from the hypothesized difference between means.
Why is sampling method appropriate?
Specifically, the approach is appropriate because the sampling method was simple random sampling, the samples were independent, the sample size was much smaller than the population size, and the samples were drawn from a normal population.
What is analysis plan?
The analysis plan describes how to use sample data to accept or reject the null hypothesis. It should specify the following elements.
What is the P value of a test statistic?
P-value. The P-value is the probability of observing a sample statistic as extreme as the test statistic. Since the test statistic is a t statistic, use the t Distribution Calculator to assess the probability associated with the t statistic, having the degrees of freedom computed above. (See sample problems at the end of this lesson for examples of how this is done.)
What is the first set of hypotheses?
The first set of hypotheses (Set 1) is an example of a two-tailed test, since an extreme value on either side of the sampling distribution would cause a researcher to reject the null hypothesis. The other two sets of hypotheses (Sets 2 and 3) are one-tailed tests, since an extreme value on only one side of the sampling distribution would cause a researcher to reject the null hypothesis.
What is the sampling method for each sample?
The sampling method for each sample is simple random sampling.
How many steps are there in a statistical analysis?
This approach consists of four steps: (1) state the hypotheses, (2) formulate an analysis plan, (3) analyze sample data, and (4) interpret results.
Why should treatment choices not be made based on comparisons of statistical significance?
When the results of clinical trials are statistically significant, treatment choices should not be made based on comparisons of statistical significance, because the magnitude of statistical significance is heavily influenced by the number of patients studied. Therefore, a small trial of a highly effective therapy could have a statistically significant result that is smaller than a result from a large trial of a modestly effective treatment.
How should health care professionals choose among the many therapies claimed to be efficacious for treating specific disorders?
Ideally, health care professionals would compare different treatments by referring to randomized, double-blind, head-to-head trials that compared the treatment options. Although individual medications are typically well researched when these placebo-controlled studies are performed, studies that directly compare treatments are rare. In the absence of direct head-to-head trials, other evidence comes from indirect comparisons of two or more therapies by examining individual studies involving each treatment.
How to calculate POB statistic?
For binary variables, the POB statistic can be computed from the absolute difference (AD) in treatment response as follows: POB = 0.5(AD+1).
What is the SMD measure of effect?
The standardized mean difference (SMD) measure of effect is used when studies report efficacy in terms of a continuous measurement, such as a score on a pain-intensity rating scale. The SMD is also known as Cohen’s d.5
How to calculate absolute measure?
For continuous variables, one simple approach to computing an absolute measure is the weighted mean difference, which is created by pooling results of trials that have used the same outcome measure in a manner that weights the results of each trial by the size of the trial. The weighted mean difference is readily interpretable, because it is on the same scale of measurement as the clinical outcome measure. The problem with using this method is that different trials typically use different outcome measures even when they are focused on the same concept.
How many meta-analyses did Song et al.2examine?
Song et al.2examined 44 published meta-analyses that used a measure of effect magnitude to compare treatments indirectly. In most cases, results obtained by indirect comparisons did not differ from results obtained by direct comparisons. However, for three of the 44 comparisons, there were significant differences between the direct and the indirect estimates.
What is an absolute measure?
Absolutemeasures express the magnitude of effect without making such comparative statements. Instead, they define a continuous scale of measurement and then place the observed difference on that scale. For example, a simple absolute measure is the difference in improvement rates between two groups.
What to do instead of a student's T test?
Instead of a student's T test, try a paired T-test.''
What is the assumption of repeated measures ANOVA?
So, these two options are too much simple. The Repeated Measures ANOVA has an assumption called "Sphericity", which is rarely met. I suggest you an alternative approach. Use Nested ANOVA, with factors nested in this way: Treatment < Tank < Time.
What is a mixed model ANOVA?
1.Mixed model ANOVA used to assess whether there were significant differences between and within treatments over time.
Is Matheus's ANOVA repeated?
As I understand, the analysis suggested by Matheus is a repeated measures ANOVA on the data in 'long' format. The analysis I proposed is the same, but on the data in 'wide ' format. With only 3 repeated measures, the 'sphericity' issue is not really a huge problem. With most common statistical software packages (SAS, SPSS, R, STRATA) one can model the covariance structure.
How to get confidence interval for difference in means?
After doing random permutations and getting a null distribution, it is possible to get a confidence interval for the distribution of difference in means. This is simply the 2.5th 2.5 t h and 97.5th 97.5 t h percentiles of the null distribution, and directly related to the P-value calculation above.
What is the ratio of true negatives to the sum of true negatives and false positives?
The ratio of true positives to the sum of true positives and false negatives ( T P T P +F N T P T P + F N) is known as sensitivity. And, again, we usually want to decrease the FN and get higher sensitivity. Sensitivity is also known as the “power of a test” in the context of hypothesis testing. More powerful tests will be highly sensitive and will have fewer type II errors. For the t-test, the power is positively associated with sample size and the effect size. The larger the sample size, the smaller the standard error, and looking for the larger effect sizes will similarly increase the power.
What is the base function of p.adjust?
In R, the base function p.adjust () implements most of the p-value correction methods described above. For the q-value, we can use the qvalue package from Bioconductor. Below we demonstrate how to use them on a set of simulated p-values. The plot in Figure 3.10 shows that Bonferroni correction does a terrible job. FDR (BH) and q-value approach are better but, the q-value approach is more permissive than FDR (BH).
What is the difference between a hypothesis and an alternative hypothesis?
Decide on a hypothesis to test, often called the “null hypothesis” ( H 0 H 0 ). In our case, the hypothesis is that there is no difference between sets of samples. An “alternative hypothesis” ( H 1 H 1) is that there is a difference between the samples.
Is hypothesis testing error free?
We should think of hypothesis testing as a non-error-free method of making decisions. There will be times when we declare something significant and accept H 1 H 1 but we will be wrong. These decisions are also called “false positives” or “false discoveries”, and are also known as “type I errors”. Similarly, we can fail to reject a hypothesis when we actually should. These cases are known as “false negatives”, also known as “type II errors”.
Can a t-test tolerate deviations from normality?
A final word on t-tests: they generally assume a population where samples coming from them have a normal distribution, however it is been shown t-test can tolerate deviations from normality, especially, when two distributions are moderately skewed in the same direction. This is due to the central limit theorem, which says that the means of samples will be distributed normally no matter the population distribution if sample sizes are large.
Does R use t test?
Luckily, R does all those calculations for us. Below we will show the use of t.test () function in R. We will use it on the samples we simulated above.
How to determine which treatment means differ?
If we want to determine which treatment means differ, we compute a confidence interval for the difference between each pair of means.
What does it mean when the confidence interval for the difference between a pair of treatments includes 0?
If a confidence interval for the difference between a pair of treatments means includes 0, then there is no difference in the pair of treatment means.
