block 5-8

Question 1

fill in the blanks:

if sample is large enough, the distribution of sample means ____(will/ won’t) be normal, even though the distribution of data in pop _____ (is/ isn’t) normal

Answer 1

if sample is large enough, the distribution of sample means will be normal, even though the distribution of data in pop is NOT normal

Question 2

The mean of what, is the true population mean?

Answer 2

The mean of the sampling distribution of means is the true population mean

Question 3

fill in the blanks:

Since the sample distribution is normal: ___% of the sample mean falls within ____ times the standard error.

Answer 3

Since the sample distribution is normal: 95% of the sample mean falls within 1.96 times the standard error.

Question 4

What is the sampling distribution of a mean?

Answer 4

The sampling distribution of a mean = the distribution of sample means.

Question 5

What is confidence interval?

Answer 5

Interval around the estimated mean where we have a certain level of confidence that it contains the true mean.

Question 6

Does the confidence interval tell us the probability that an interval contains the true mean?

Answer 6

No, it does not tell us the probability that the confidence interval contains the true mean, because true mean is a fixed point and it either is or is not in the interval.

Question 7

Fill in the blank:

The confidence interval extends to _____ side of the mean by a multiple of _______.

Most commonly is calculated to be what ___

Answer 7

The confidence interval extends to either side of the mean by a multiple of the standard error.

Mostly commonly calculated as 95% CI, this extends 1.96 SE either side of the mean.

Question 8

Fill in the blank:

If we took thousands of samples, and for each sample calculated the mean and associated 95% confidence interval, we would expect ___% of these confidence intervals to include the population mean.

Answer 8

If we took thousands of samples, and for each sample calculated the mean and associated 95% confidence interval, we would expect 95% of these confidence intervals to include the population mean.

Question 9

What is the formula for calculating the confidence interval?

What information is necessary?

Answer 9

95% confidence interval = x ± 1.96 SE (x)
(the x’s have lines above them)

x = mean height
SE (x) = standard error

Question 10

What multiple is used when calculating a:
90% CI
95% CI
99% CI

Answer 10

90% CI – 1.56
95% CI – 1.96
99% CI – 2.56

Question 11

what is the z value, and what is its formula

Answer 11

z value = test statistic

formula
(estimated mean - hypothesized mean)/ SE

Question 12

(pg 29, BS05)

If the “Distribution of x if Null Hypothesis were true”, was plotted as a normal distribution, which part of the distribution curve corresponds with the p value?

Again, what is the z value?

Answer 12

Z value is the test statistic, to calculate the difference between the estimated mean and the hypothesized mean.

The P value is area under the curve that’s distal to the z values.

Question 13

What does a large p-value mean?

Answer 13

If the p-value is large, the chance of observing the value as extreme as the sampled one is high if the Null Hypothesis were true.

-or-
The larger the p-value, the less evidence against Null Hypothesis (no difference).

Question 14

A small p value means?

Answer 14

The chance of observing this value if the Null Hypothesis were true, is low. More evidence against Null. That the value is less likely due to sample variation and more likely to reflect a real difference.

Question 15

If the hypothesized mean is NOT included in the 95% CI, this is evidence FOR or AGAINST the null hypothesis?

Answer 15

If hypothesized mean is NOT included in the 95% CI, this is evidence against the Null Hypothesis, meaning there is likely a real difference.

Question 16

fill in the blanks

When the sample size is small, ______ is not a good approximation, rather ______ is used.

Answer 16

When the sample size is small, normal distribution is not a good approximation, rather t-distribution is used.

Question 17

What determines the shape of a t-distribution?

Answer 17

Degrees of freedom.

Question 18

What are degrees of freedom?

Answer 18

Degrees of freedom are a measure of how small the sample size is. It determines the shape of the t-distribution curve.

t distribution = sample size minus 1

Question 19

The smaller the degrees of freedom mean what?

Answer 19

Smaller degrees of freedom mean lower the probabilities around the mean and higher the probabilities at the tails. The curve is shorter and wider.

Question 20

How does increasing degrees of freedom affect the t-distribution curve in relation to the normal distribution curve?

Answer 20

Bigger degrees of freedom mean larger sample sizes, which means the t-distribution resembles the normal distribution curve more and more.

Question 21

What is the formula for the 95% CI of mean for small sample size?

Answer 21

estimated mean +/- multiplier x standard error of estimate

multiplier = value of t corresponding to a two sided p = 0.05

Question 22

In what situations are two tailed and one tailed used for p-values?

Answer 22

Most commonly, 2 tailed used because the alternative hypothesis simply states the estimated mean is not equal to the hypothesized mean.

H1: u ≠ u0

Less commonly, 1 tailed is used when alternative hypothesis is:

H1: u > u0. or u < u0

Question 23

Historically, what p value is deemed “enough” evidence

Answer 23

p < 0.05

Question 24

Fill in the blank:

When the result of a test has a P-value smaller than 0.05, the 95% confidence interval _____ (will/ won’t) include the hypothesized value.

Answer 24

When the result of a test has a P-value smaller than 0.05, the 95% confidence interval will not include the hypothesized value.

Question 25

What is paired data?

What is a common example of this for quantitative data?

Answer 25

Paired samples occur when each observation in the first sample is matched in the 2nd sample.

Example is doing repeated observations on the same person with quantitative data.

• When measuring a reaction to a TB test, two field workers will measure the skin reaction on the same person.
• Pulse was checked for each runner before and after the run.

Question 26

What is unpaired data?

What are examples

Answer 26

Unpaired data are when individual observations in one sample are completely independent of observations made in another sample.

Ex:

• A gp of patients were divided into 2 groups. Gp A received a new novel drug treatment, whereas Gp B received conventional treatment. Effect of the drug was measured and compared.
• Students were divided into 2 gps. Gp A received a new computer teaching method, and Gp B received a conventional teaching method. Test scores were compared.

Question 27

When analyzing paired data, what’s the first step?

Answer 27

Calculate the difference between the two individual observations in each pair.

Question 28

How can we assess whether there’s a difference between measurements from 2 samples? what can we calculate to answer the above question?

Answer 28

Can calculate:

• mean difference between the two samples
• confidence interval
• then run a test to see if it’s significantly different from zero

Question 29

What information is needed to calculate the CI and run a test to see if it’s significantly different than zero?

Answer 29

• mean difference
• standard deviation of differences
• standard error of mean difference
• SD needed to calculate SE

Question 30

What’s the formula for calculating the standard error (SE)?

Answer 30

standard deviation divided by square root of individual/ observations

Question 31

When calculating the 95% CI, what multiplier is used? How does this chance if the sample size is small?

Answer 31

If sample size is large, the multiplier is 1.96.

If sample size is small, need to use a multiplier found on a t-distribution table.

Question 32

What does the z value tell us?

Answer 32

Z value is the test statistic, to calculate the difference between the estimated mean and the hypothesized mean.

Calculating a z-value in the hypothesis test, tells us how many standard errors away the observed mean is from the centre of the distribution defined by the null hypothesis.

The number of SE between the observed difference in means and the centre of the distribution defined by the null hypothesis.

Question 33

State the difference when analyzing the mean of paired and unpaired data.

Answer 33

Unpaired:
the difference between two independent means

Paired:
the mean difference of two paired observations

Question 34

What’s the z value?

Answer 34

Z value is the test statistic, to calculate the difference between the estimated mean and the hypothesized mean.

Calculating a z-value in the hypothesis test, tells us how many standard errors away the observed mean is from the centre of the distribution defined by the null hypothesis.

The number of SE between the observed difference in means and the centre of the distribution defined by the null hypothesis.

Question 35

How do you find the “multiplier” when calculating the 95% CI for a small batch?

Answer 35

The formula for 95% CI is
estimated mean +/- multiplier x SE

In the 2 tailed p table, the DF (degrees of freedom) is n-1. And the p is set at 0.05.

Question 36

What is a difference when calculating CI and test hypothesis for small sample unpaired/ independent data?

Answer 36

The difference is in the calculation of SE.

Formula for degrees of freedom is:
n1 + n2 - 2

Question 37

What is the difference between SD (standard deviation) and SE (standard error)?

Answer 37

SD- tries to quantify the variation from the mean within a set of measurements (spread of the data points).

SE- tries to quantify the variation of the MEANS of several sets of data

Question 38

What is the term for data which can take one of two values?

Answer 38

binary

Question 39

What is a proportion?

Answer 39

A fraction.

The proportion of mothers with hypertension was 329 / 1310 = 0.251

Expressed as a percentage this is

0.251 x 100 = 25.1%