Lecture 4 - Hypothesis Testing (One sample t-Test) Flashcards
What are the most common types of statistical inference?
- Significance tests
- Confidence intervals
The _____ the sample size = the smaller the variance
larger
The smaller the variance, the more ______ the sample is
accurate
T or F: If the original population is itself normally distributed then the sample means will be normally distributed for any size sample
True
What is the purpose of the Central Limit Theorem ?
- It provides some reassurance when we are not certain whether observations are normally distributed
- Means of reasonable sized samples will have a distribution that is approximately normal
- Inference procedures based on the sample mean can therefore often use the normal distribution
- Care must be taken not to input no reality to the original observations
What do we use to describe the variability of individual observations?
standard deviation
What do we use to describe the variability of a sampling distribution ?
standard deviation of the sampling distribution of means (the standard error of the mean)
sem
What is the formula for sem ?
sem = SD / square root (n)
For ____ distributions, the mu +/- SD contains 68.26% of the observations
normal
For _____ distributions, the mean +/- sem contains 68.26% of the observations
sampling
As the sample means are normally distributed, we can define a ______ ______ (limits); a range of values used to estimate the true value of the population parameter
confidence interval
For a 90% confidence interval, what is alpha ?
0.1
For a 99% confidence interval, what is alpha ?
0.01
For a 95% confidence interval, what is alpha ?
0.05
What happens when we decrease alpha ?
increase our confidence but reduce our precision (widen the CI)
How do you find 95% CI for for a sampling distribution?
x +/- 1.96(sem)
sem = SD/square root of n
What are our assumptions for confidence intervals?
1) Random sampling - If the sample is biased our conclusions are not valid
2) Independent observations - If this assumption is violated, confidence intervals cannot be obtained.
ex. we do a pop quiz, other kids do a pop quiz later = independent
ex. we do a pop quiz on Tues and then do the same pop quiz on Thurs = not independent
3) Sampling from a normal population - We know that if the population is not normal, CI can still be obtained. From central limit theorem we know that if we have a large enough sample size we compensate for non-normal population.
What is the formula for degrees of freedom?
df = n - 1
so 21 subjects would have a df of 20
Describe the steps in hypothesis testing
1) State the null hypothesis: Any differences in the data are due to chance
2) State the alternative hypothesis: Any differences in the data are real or significant
3) Set the decision level, alpha: Hypothesis testing involves establishing P(H0 true). If this is very small we may reject H0. By convention, small means P < alpha with alpha=0.05
4) Choose the test statistic
5) Calculate P(H0 true): That is, assume H0 is true and calculate the probability of the outcome of the investigation being due to chance alone (due to random effects); we use an appropriate sampling distribution for this calculation
6) Make a decision concerning H0: It follows that if we reject H0 we are in a position to accept Ha as the logical alternative
P(H0 is true) < 0.05; reject H0
P(H0 is true) > 0.05; retain H0
What way do you round degrees of freedom ?
Round down
One sample t test, you are comparing it to the ____
mean
Two sample t test, you are comparing them to ____ ____
each other
