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Stats > Module 3 > Flashcards

Module 3 Flashcards

1
Q

statistical inference

A

idea of using sample data to provide evidence about population parameters

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2
Q

what can we use to estimate unknown population parameters?

A
  1. Point estimates
  2. confident intervals
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3
Q

point estimate

A

single value used as an estimate of a population parameters

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4
Q

Xbar

A

sample mean

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5
Q

u

A

population mean

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6
Q

________ the sample mean is a point estimate of _________

A

xbar sample mean is a point estimate of u the population mean

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7
Q

s^2

A

sample variance

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8
Q

o^2

A

population variance

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9
Q

_______ the sample variance is an estimate of ______________

A

s^2 the sample variance is a point estimate of the o^2 the population variance

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10
Q

s

A

sample standard deviation

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11
Q

____ the sample sd is a point estimate of ______________________

A

s the sample sd is a point estimate of o the population sd

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12
Q

what are point estimates influenced by ?

A

sampling error

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13
Q

the variation of a point estimate from one sample to another represents the extent of ___________________

A

sampling error

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14
Q

Sampling error in relation to sample size

A

Smaller samples have more sampling error than larger samples so we expect point estimates from small samples to have more sampling error than point estimates from larger samples

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15
Q

formula for the standard error of the mean

A

represents the amount that the sample means are spread around the population mean of a variable - or amount that a sample mean is expected to differ from the population mean on average

oxbar = o/sqrtN

the bigger N gets the smaller oXbar gets - mean has less sampling error with larger N

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16
Q

confidence interval

A

range of values or an interval that is expected to capture a population parameter of interest with some prespecified level of confidence

presents a range of plausible or reasonable values for the population parameter

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16
Q

Confidence limits

A

specify the particular range of values for a confidence interval

smallest value = lower limit
biggest value = upper limit

17
Q

confidence intervals in relation to sample size

A

confidence intervals from small samples are wider than confidence intervals from larger samples

18
Q

central limit theorem tells us that the sample means can be treated as observations from a _____________

A

normal distribution

19
Q

95% of all sample means fall within _______ standard error units of the population mean

A

1.96 standard error units of the population mean

20
Q

the 95% confidence interval is expressed as what formula

A

Xbar +/- 1.96*oxbar

where 1-alpha is the level of confidence

oxbar is also (o/sqrtN)

21
Q

Zalpha is what

A

critical valye

22
Q

Critical value for a 95% confidence interval

A

1.96

23
Q

Assumptions for a confidence interval calculated using the standard normal distribution

A
  1. Independent observations
  2. The sample data come from a normal population
  3. The population standard deviation is known
24
Q

Assumptions for CI

  1. Independent observations
A
  • Having info about one participant provides no further info about another participant
25
Q

Assumptions for a CI

  1. The sample data come form a normal population distribution
A

Because of the central limit theorem, this assumption can be ignored as long as the sample size is large. How large depends on the extend of non-normality of the population distribution of individuals.

26
Q

the width of a confidence interval represents _________

A

the precision of a point estimate with respect to its estimation of the corresponding parameter

27
Q

Does the population mean change?

A

The population mean is a constant, fixed, but unknown value that does not change.

28
Q

Does the confidence interval change?

A

The lower and upper confidence limits are random variables meaning they do change from sample to sample

29
Q

If you have calculated a 95% confidence interval how do you phrase it

A

if the exact sampling procedure were repeated an infinite number of times and a 95% confidence interval were calculated around each sample, 95% of those intervals would contain u. The interval of blank to blank is one of these infinitely many intervals.

Easier:

The interval captures u with 95% confidence
The interval blank to blank captures the population mean number of drinks per week with 95% confidence

30
Q

Factors affecting the width of a confidence interval that are under the researcher’s direct control

A
  1. Level of confidence - larger values of 1- alpha have wider intervals
  2. Sample Size - larger samples lead to narrower confidence intervals
31
Q

Null hypothesis

A

represents another method for researchers to describe sample evidence about the true value of a population mean

“We reject the null hypothesis that the population mean equals 0 with probability = alpha that we are incorrect

32
Q

want to know whether a mean is different enough to conclude what

A

conclude that the population mean of home schooled 4th graders is likely to be different from 250

if the population mean is u=250 how unlikely is a sample mean of xbar=272 or more extreme

33
Q

Formal steps of a null hypothesis testing procedure

A
  1. Specify the null hypothesis
  2. Specify an alpha level
    - 0.05
  3. Calculate a test statistic
    - convert sample mean to z score xbar-uo/o/sqrtN
  4. Calculate a P-value
    - probability of obtaining a score greater or equal to the one we are comparing to
  5. Compare the p-value alpha/2 to reach a decision about the null hypothesis
    - two tailed test = have to divide alpha by 2
34
Q

alternate hypothesis example

A

the population mean achievement score of home-schooled 4th graders does not equal 250

Non-directional which implies a two-tailed test

35
Q

alpha level

A

probability of rejecting a true null hypothesis

36
Q

test statistic

A

value calculated from a sample descriptive statistic that is used to evaluate the descriptive statistic relative to the population value specified by the null hypothesis

37
Q

Does the p-value demonstrate the probability that the null is true?

A

NO

38
Q

Correct interpretation of the p-value

A

Probability of obtaining the current sample mean or one that is more extreme under the assumption that the null is true.

39
Q

Assumptions of one sample z-test

A
  1. independent observations
  2. sample data come from a normal population distribution
  3. the population SD is known
40
Q

Effect size

A

difference between the sample mean compared to the hypothetical population mean

idea of by HOW MUCH a null hypothesis is likely to be wrong

41
Q

Does statistical significance convey practical importance?

A

no, effect size does

Stats (9 decks)

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