Wk 9: Comparing Two Groups Flashcards

1
Q

If we increase the size of our sample, we would expect that the sample standard deviation will be the ______ (same/different). Why?

A

same

because the population is fixed.

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2
Q

If we increase the size of our sample, we would expect that the standard deviation of the sample mean will be _______ (larger/smaller). Why?

A

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

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3
Q

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 _________.

A

smaller; 1/2

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4
Q

What are 2 things that normal distributions describe?

A
  1. Describes the distribution of observations
  2. Describes the distribution of statistics, such as the sample mean and sample proportion
    • Sample proportion is a type of sample mean
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5
Q

In any normal distribution, _____% of data fall within _____ standard deviations of the mean.

A

95; 2

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6
Q

Why do we have standard error?

A

In practice, we usually do not know the population standard deviation, so we have to estimate it using the sample standard de viation.

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7
Q

What is standard error?

A

The estimated standard deviation of a statistic

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8
Q

Why do we use Student’s T Distribution?

A
  • 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.
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9
Q

If mean difference is outside the 95% confidence interval, then it ______ (supports/rejects) the “effect” hypothesis.

A

supports

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10
Q

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?

A
  • 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
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11
Q

What is Significance? What supports the “effect” hypothesis and what supports the null hypothesis?

A

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.
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12
Q

What is the P value?

A

If a decision is required then a threshold for evidence needs to be set.

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13
Q

What is the natural suspicion level?

A

The natural suspicion level is α = 0.05.

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14
Q

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.

A

reject

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15
Q

What is the P value a transformation of?

A

Data > Mean > T value > P value

  • Random the whole way through, so P-value is a random variable like the sample mean.
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16
Q

Similarly, a confidence interval procedure generates _____ intervals.

17
Q

If the null hypothesis is true, the shape of the P-value distribution will be ________.

A

uniform (flat)

18
Q

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.

19
Q

What are type 1 errors?

A

Rejecting a true null hypothesis.

  • The probability of making a Type 1 error is the significance level α that we choose for making decisions
20
Q

What are type 2 errors?

A

Retaining a false null hypothesis.

  • The probability of making a Type 1 error is β
21
Q

What is power?

A

The power of an experiment is the probability of detecting an effect when there is indeed an effect.

22
Q

More power is _____ (better/worst)

23
Q

What are 4 ways that power can be improved?

A
  1. Increasing the effect size
  2. Decreasing the variability: Stricter protocol, more accurate measurement etc. to account for other things that affect variability.
  3. Increasing the sample size
  4. Increasing the significance threshold α
24
Q

What is the Effect of signal to noise?

A

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
25
Q

What does more power mean for effect size and variability?

A

Higher effect size, lower variability = more power

26
Q

What does this show?

A
  1. μ/σ=1
  2. Larger sample size = more power
27
Q

What does this show?

A
  1. μ/σ = 0.5
  2. Larger sample size = more power, but the power increases slower this time because the noise is double as much as the signal.
28
Q

What are 3 things when choosing sample size?

A
  1. Typically we want to design our study to have a power of ≥80%.
  2. This involves estimating the effect size and variability, and then choosing a sample size accordingly.
29
Q

What are independent samples T-test?

A

We take the difference between the two sample means and compare it to the standard error of the difference.

30
Q

What is the t statistic in independent samples T Test?

A

the number of standard errors that the difference between our groups is away from a hypothesised difference of 0.

31
Q

What are the 4 assumptions that the independent samples T test is based on?

A
  1. The two groups are independent
  2. The populations have normal variability
  3. The variances are equal (optional)
  4. Outliers can dilute the results by in inflating the standard error.
32
Q

What are equal variances?

A

the same amount of variability (spread) between two groups.

33
Q

If we can assume equal variances then we use a _______. Why?

A

pooled t test

  • Slightly more powerful and also generalises easily to comparing more than two groups.
34
Q

If we can’t assume equal variances then we use a _______.

A

Welch t test

35
Q

What is the Levene’s Test?

A

It has the null hypothesis that the populations have equal variances.

36
Q

If Levene’s test outcome is signifcant (P _____ (>/<) 0.05 ), then it suggests there is ____ (equal/different) variances > use _____ t test.

A

>; different; Welch

37
Q

If Levene’s test outcome is not significant (P _____ (>/<) 0.05 ), then it suggests there is ____ (equal/different) variances > use the _____ t test.

A

<; equal; pooled t test

38
Q

How should you analysis this data for P value?

A
  1. 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.
  2. 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.