data skills- Testing means

How to test of the significance of a hypothesis

1. State the null and alternative hypothesis

2. calculate the value of the test statistic

3. find the p-value of the data

4. state a conclusion using either the p-value or the test statistic

null and alternative hypothesis

Null: also known as H0 is a statement of no effect, implying that there is no relationship between the means of the variables

• often that the mean or difference between means = 0

Alternative: also known as H alpha, is the statement of an effect or that there is a relationship between two variables

• either mean or difference is not 0 or is in fact a particular variable

what is a test statistic

A standardised measure of how different data is, with values closer to zero indicating that the null hypothesis can be retained

• TS = sample mean - hypothesised value/standard error of estimate

• can also be a measure of difference between means

what is the p-value

The probability that when H0 is assumed to be true, you get results that are not consistent with H0

• the smaller the p-valeu the weak the evidnce against the null hypothesis

what are the ranges for the p-value

• 0.05 to 0.1 = weak evidence

• 0.01 to 0.05 = string evidence

• less than 0.01 = very string evidence

how to determine significance of results

involves determining whether the strength of the evidnce is enough to reject the null hypothesis

• done by comparing the significance level, often 5% or 0.05, to the p-value

• if p-value is lower than the significance level, reject the null hypothesis

• if p-value is grater than the null hypothesis then we retain the null hypothesis ( aka fail to reject)

what is a two sample t-test

A test that determines if there is a significant difference between the population means of tw idenpendent groups from different populations

• can either be two groups experiencing two treatments, or two differently characterised groups experiencing the sample treatment

what are the assumptions for a two sample t-test

• Simple random sampling was used

• the samples are independent of one another in terms of random sampling and allocation

• Both populations are normally distributed (or can comply with the Central Limit Theorem) - can be checked using a q-qplot

• each group comes from distinct population (either 1 sample split into and treatment and a control or 2 samples from two populations)

what are the hypotheses for a two-sample t-test

in a two-sample t-test this involves comparing the means of each sample

• can either be that the first mean minus the secound does(H0) or doesn’t(H alpha) equal 0

• of can be that the mean are the same(H0) or not he same(H alpha)

how is a test statistic calculated in a two sample t-test

uses a t-distribution with whatever is small between n1 - 1 or n2 - 1

• involves us subtracting the point estmate of each sample and dividing it by the square root of ecah sample SD/ sample size added together

how is a p-value calculated in a two sample t-test

calculated by R using a t-distribution with a degree of freedom of whatever is smaller between n1-1 pr n2-1

how are confidence intervals calculated in a t-test

Calculated using a t-distribution, not a normal distribution, meaning the critical value is now t*

• is calculating the general range of differences between the means of each sample

• the margin of error is also calculated with the t*

what are the 2 ways to calculate two sample t-test using RStudio

• The first way uses the calculations above and assumes that the variance between the populations is different

• the second way is used when the variances are the same and uses different formulas

How to interpret the results confidence of a t-test

if the intervals of confidence include zero or the null value, then we can retain the null hypothesis, as there is a possibility that the population mean is 0/the null value

what is a matched pair test

Involves comparing the difference between either a before-and-after test where one group receives both conditions, or comparing the results of two individuals who are linked together across groups and assigned to different treatments

• we are looking specifically at the difference between groups

• in before and afters subjects are used as their own control group

what are the assumption need for a match pair test

• You have a simple random sample

• the 2 samples are dependent and are naturally or selectively linked in some way

• each subject only does to one group ( no true before and after)

• the sampling distribution of the sample means is or close to being normally distributed

What are the hypotheses used for a matched pair test

since we are look at the difference between two treatment/induviduals the hypothesis are

• null: the mean different between the samples is 0

• alternate: the mean difference between the sample is not 0

how is a matched pair t-test done in r-studio

Need to create a new data set with the differences between the samples, and they do a t-test using that data set

• Technically gives you the results you would get if doing a one-sample test

how do the formula for a matched pair test differ to a two-sample

• The test statistic is the mean difference between the samples / the SD of the differences / the square root of the combined sample size

• The p-value is calculated using a t-distribution with a df of n-1

• confidence intervals also using t* and are used to calculate an interval that contains the true population mean of differences

What is a one-sample t-test

Determines the difference between the population mean and a certain null value

• Used when the population standard deviation is unknown

• caluclations done the same as matched pair but we are calulationg the diference between the sample and the null value

what are the assumptions for a one-sample t-test

• The sampling method is simple and random

• the samples are independent

• the sampling distribution is normal or complies with the central limit theorem

what are the hypothesis for a one sample t-test

null: the mean of the population = the null value

alternative: the mean of the population doesn’t = the null value

how can the presence of an outlier affect the results of a one-sample t-test

It can invalidate the results of the test

• If it is a real measurement, then a non-parametric hypothesis test can be used

• if it is an error then it can be removed along with proper justification