SE, CI and T-test

Question 1

SE

Answer 1

o/ root n. Variability of u from u standard error of the mean (Analytic tool)

As the sample size increases the dispersion of the sample mean reduces

Question 2

CI

Answer 2

Confidence that calculating CI for 100 samples 95/100 would contain the true population mean. u = point estimate of m hence u is estimated using an interval

CI = (m - 2(s/rootn)

Question 3

Why is SE used

Answer 3

SD of a hypothetical distribution which is never observed

Inferential tool measuring the precision of estimates in population. SD = descriptive measuring the dispersion of the data

Question 4

Why is mean +/-SE in correct

Answer 4

95% of values lie between u +/- 2o

Question 5

Precision of SE

Answer 5

It should be noted that the SE decreases as the sample size increases, because the denominator in the ratio n
σ gets larger.

Standard deviation, which does not have a tendency to get larger or smaller as n increases – the
sample standard deviation, s, simply becomes a better estimate of σ as n increases.

However, the square root in the formula means that the SE does not decrease withsample size as quickly as might be hoped: in order to halve the SE the sample size must quadruple.

Question 6

Central limit theorem

Answer 6

The distribution for a sample will get closer and closer to a normal distribution as the sample size increases even if the original population isn’t normal itself

Question 7

Increasing width of CI

Answer 7

Higher interval ie 99% large than 95%, low sample size = larger width

Question 8

Null hypothesis

Answer 8

usually u1=u2 or u=0 ie no effect of treatment to wild type control

Population assumed to be identical

Question 9

Why hypothesis test

Answer 9

We know the difference between the two groups and can compute a SE from. Aim to prove that the difference between the groups is not down to random chance

NB if hypothesis testing concludes a difference may be due to chance it doesn’t mean it is due to chance

Question 10

Logic of hypothesis testing

Answer 10

Null hypothesis = false or seen an event that occurs with a given probability p

Value of P small say that event happens 5% of the time due to random chance

Question 11

Small p value

Answer 11

p =0.05 provides evidence against null hypothesis. Smaller p value = more confident

Question 12

Type I error

Answer 12

Incorrect rejection of the null hypothesis hence concluding a relationship exists when infact there is no causal relationship. Controlled by the level of significance set for test

False positive

Question 13

Type II error

Answer 13

Failure to reject the null hypothesis hence a relationship exists. Controlled by power of the experiment

False negative

Question 14

T-test

Answer 14

reliable assessment = difference in means/SE

NB This ignores: precisely how likely are particular values of the above ratio, how is the SE calculated and how are large positive and large negative values handled.

Question 15

Paired T-test

Answer 15

Linked data format must be conserved dependent - absolute differences used d (mean of sample differences)/SE

Assumed normal distribution of differences. SE = variation of the sample differences hence much lower than the SE used in unpaired t-test

Question 16

Unpaired t-test

Answer 16

Independent data. Assumes both samples have normal distribution with common SD - o

Question 17

Unpaired t-test null hypothesis

Answer 17

u1=u2

NB
If the populations are non-Normal, but the departure from Normality is slight then this violation of the assumptions is usually of little consequence

b) The assumption of equal standard deviations may seem to constitute a rather severe restriction usually true in practise

c) It should be remembered that a Normal distribution is characterised by its mean and standard deviation: a test that assessed the equality of means and paid no heed to the standard deviations would not be all that useful. It is often of interest to assess whether or not the samples are from the same population and assuming that the means are the same does not specify that the populations are the same unless
the standard deviations are also the same.

Question 18

Pooled estimate of SE

Answer 18

Estimate of variance in two separate populations with different means but similar SD. Increased precision over SD hence SE of individual

Question 19

Inferential statistics ie t-tests

Answer 19

Allow generalisation findings beyond sample testing

Question 20

P=0.2

Answer 20

Does not prove NH is true (just: it provides no evidence against NH

Question 21

One sample t-test

Answer 21

Assumes u=0

Question 22

Assumptions of [aired t-test

Answer 22

• The dependent variable must be continuous (interval/ratio).
• The observations are independent of one another.
• The dependent variable should be approximately normally distributed.
• The dependent variable should not contain any outliers.

Question 23

Z-score

Answer 23

Difference between mean and data points in SD