t-tests

t-tests

1. One sample t-test

   • When and why?
     • compares the Mean of a single sample against the known population Mean.
   • How is it calculated?
     • Standard error for one-sample t-tests is estimated by

2. Matched samples t-test (paired samples)

   • When and why?
     • When: Compares the Means of the same sample, at different Time Points. It compares the sample's Means over time.
     • Why: If you want to measure the effectiveness of anti-depressant, you want to measure the same group of people (the exact same sample) at two different time points to measure the efficacy of the drug.
   • How?
   • Effect Size/Cohen's d for matched samples
     • The Mean of time 1 minus the Mean of time 2, divided by the s of time 1.
     • 0.20 is a small effect, 0.50 is medium and 0.80 or above is large.

3. Independent samples t-test

   • When and why?
     • When we are wanting to compare the Means of two different samples, and ascertain whether there is a correlation between the samples??
     • Used for comparing the sample Means of two independent groups
       • Uses Continuous DV's
       • There's a different formula when the sample sizes are different.
   • How?
     • re the Means of each sample against each other.
   • Part 3 Recorded Lecture questions
     • Calcu

4. Learning Objectives

   • LO1: Understand the concept of error
     • Standard error: the extent to which the sample Means deviate from the "overall population Mean".
       • IQ has a population Mean of 100
         • The expected range of sample Means is from 93-107 let's say.
           • My sample has an IQ Mean of 134. The Ho is that all professors have a standard IQ of 100.
             • So what 'could be expected by chance' is the critical values range?? And we normally use 0.5 as the alpha level.
             • This is a "statistically significant difference" from the known population Mean of 100.
         • this scenario is a one sample t-test
       • The average difference we would expect to see just be chance.... ??
       • It is the population's sd divided by square root of the number of participants
         • The more participants, the lower the standard error number, as the sample is a truer representation of the whole population.
     • To calculate the "standard error", we use the "Central Limit Theorem". Thankfully we don't really need to do the calculations much I think.
       • population sd divided by the square root of your sample size
         • So, it takes into account your sample size, so if you have a large sample size, it will reduce the size of error, because the more people you have in a sample, the larger the percentage of the actual population, therefore maths has to f'fill in' less.
   • Select the appropriate t test for a particular study design
   • Calculate and interpret a one-sample t test

5. Overview of t-tests

   • Used for measurement data
     • Differences between sample means
   • the t statistic is the Obtained Mean difference (between the samples, or sample and population). divided by the "Standard error(not, "difference"???)" expected by chance. This is another calculation.