Wk 9: Comparing Two Groups Flashcards
If we increase the size of our sample, we would expect that the sample standard deviation will be the ______ (same/different). Why?
same
because the population is fixed.
If we increase the size of our sample, we would expect that the standard deviation of the sample mean will be _______ (larger/smaller). Why?
smaller
As we get more people in the sample, they will be closer together - smaller standard deviation
x4 sample size, then standard deviation will 1/2
If we increase the size of our sample, we would expect that the standard deviation of the sample mean will be ______. As we get more people in the sample, they will be closer together - smaller standard deviation x4 sample size, then standard deviation will be _________.
smaller; 1/2
What are 2 things that normal distributions describe?
- Describes the distribution of observations
- Describes the distribution of statistics, such as the sample mean and sample proportion
- Sample proportion is a type of sample mean
In any normal distribution, _____% of data fall within _____ standard deviations of the mean.
95; 2
Why do we have standard error?
In practice, we usually do not know the population standard deviation, so we have to estimate it using the sample standard de viation.
What is standard error?
The estimated standard deviation of a statistic
Why do we use Student’s T Distribution?
- Using the sample standard deviation instead of the population standard deviation adds more uncertainty to our estimation.
- We use Student’s T distribution instead of a normal distribution as it accounts for the extra variability introduced.
- We use Student’s T distribution based on the degrees of freedom of our estimate.
If mean difference is outside the 95% confidence interval, then it ______ (supports/rejects) the “effect” hypothesis.
supports
What are the circles, vertical lines, half length of vertical line, grey and red on this graph? What changes the length of the vertical lines?
- Circles are sample mean
- Margin of error is the vertical lines
- Half the length of vertical line is standard error of mean x 1.96
- Grey = the population mean is within confidence interval (94% are in, which is close to 95% confidence)
- Red = the population mean is not within confidence interval
- Extra variability changes the length of vertical lines
What is Significance? What supports the “effect” hypothesis and what supports the null hypothesis?
Significance is the P value
- If P value is outside the 95% confidence interval, then it supports the “effect” hypothesis.
- If P value is within the 95% confidence interval, then it supports the null hypothesis.
What is the P value?
If a decision is required then a threshold for evidence needs to be set.
What is the natural suspicion level?
The natural suspicion level is α = 0.05.
If we find a P value <0.05, we would ______ (support/reject ) H0 null hypothesis and say that the results were significant at the 5% level.
reject
What is the P value a transformation of?
Data > Mean > T value > P value
- Random the whole way through, so P-value is a random variable like the sample mean.
Similarly, a confidence interval procedure generates _____ intervals.
random
If the null hypothesis is true, the shape of the P-value distribution will be ________.
uniform (flat)
Usually it is worthwhile to do the experiment if the probability of P <0.05 is ≥_____ % - this means you have _____ % chance that the “effect” hypothesis is true.
80; 80
What are type 1 errors?
Rejecting a true null hypothesis.
- The probability of making a Type 1 error is the significance level α that we choose for making decisions
What are type 2 errors?
Retaining a false null hypothesis.
- The probability of making a Type 1 error is β
What is power?
The power of an experiment is the probability of detecting an effect when there is indeed an effect.
More power is _____ (better/worst)
better
What are 4 ways that power can be improved?
- Increasing the effect size
- Decreasing the variability: Stricter protocol, more accurate measurement etc. to account for other things that affect variability.
- Increasing the sample size
- Increasing the significance threshold α
What is the Effect of signal to noise?
μ/σ
Where:
- μ = effect size (signal)
- σ = variability (noise)
- μ/σ = 1 means signal equals to noise
- μ/σ = 0.5 means signal is half as much as noise
What does more power mean for effect size and variability?
Higher effect size, lower variability = more power
What does this show?
- μ/σ=1
- Larger sample size = more power
What does this show?
- μ/σ = 0.5
- Larger sample size = more power, but the power increases slower this time because the noise is double as much as the signal.
What are 3 things when choosing sample size?
- Typically we want to design our study to have a power of ≥80%.
- This involves estimating the effect size and variability, and then choosing a sample size accordingly.
What are independent samples T-test?
We take the difference between the two sample means and compare it to the standard error of the difference.
What is the t statistic in independent samples T Test?
the number of standard errors that the difference between our groups is away from a hypothesised difference of 0.
What are the 4 assumptions that the independent samples T test is based on?
- The two groups are independent
- The populations have normal variability
- The variances are equal (optional)
- Outliers can dilute the results by in inflating the standard error.
What are equal variances?
the same amount of variability (spread) between two groups.
If we can assume equal variances then we use a _______. Why?
pooled t test
- Slightly more powerful and also generalises easily to comparing more than two groups.
If we can’t assume equal variances then we use a _______.
Welch t test
What is the Levene’s Test?
It has the null hypothesis that the populations have equal variances.
If Levene’s test outcome is signifcant (P _____ (>/<) 0.05 ), then it suggests there is ____ (equal/different) variances > use _____ t test.
>; different; Welch
If Levene’s test outcome is not significant (P _____ (>/<) 0.05 ), then it suggests there is ____ (equal/different) variances > use the _____ t test.
<; equal; pooled t test
How should you analysis this data for P value?
- First, look at Levene’s Test P value (0.239).
- If P >0.05, then use the first row of data.
- If P<0.05, then use the second row of data.
- Second, look at T test P value and see whether it falls between the mean differences and standard error difference.
- If it falls within, then it supports the “effect” hypothesis.
- If it does not fall within, then it supports the null hypothesis.
