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7282 Statistics > 02 Basics of Statistics 2 > Flashcards

02 Basics of Statistics 2 Flashcards

1
Q

How do you test hypotheses?

A

build statistical models of the phenomenon of interest

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2
Q

simplest statistical model

A

mean

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3
Q

How do statistical models allow you to gain confidence in the alternative hypothesis?

A
  • fits the data well

- explains a lot of variation in the scores

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4
Q

Most models are:

A

linear - based on a straight line

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5
Q

Types of fits for statistical models

A
  • good fit
  • moderate fit
  • poor fit
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6
Q

interferential statistics

A

determines whether the alternative hypothesis is likely to be true

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7
Q

p-values

A

probability that the result is a chance finding

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8
Q

common threshold for confidence

A

95% confident that the result is genuine and not due to chance

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9
Q

What p-value is statistically significant?

A

P less than 0.05

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10
Q

easiest way to assess statistical models

A

look at the difference between the data observed and the model fitted

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11
Q

measures of how well the model fits the actual data

A
  • deviance
  • sum of squared erros (SS)
  • variance
  • standard deviation
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12
Q

deviance

A

difference between the observed data and the model of the mean

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13
Q

deviance =

A

observed score = mean value (x-bar)

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14
Q

disadvantages to using deviance

A
  • some values are negative and some positive

- can cancel themselves out

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15
Q

sum of squared errors (SS)

A

square the difference between observed score and mean value

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16
Q

disadvantage of using SS

A

SS value is dependent on the amount of data collected

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17
Q

With more data point, SS value is

A

higher

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18
Q

variance (s2)

A

average error between the mean and observed scores

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19
Q

variance equation

A

SS/(n-1)

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20
Q

What does variance build upon?

A
  • SS value

- takes amount of collected data into account

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21
Q

standard deviation (s)

A

square root of variance

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22
Q

benefit to using standard deviation

A

ensures that measure of average error is in the same units as the original measure

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23
Q

standard deviation equation

A

√(SS/(n-1))

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24
Q

What does a small s indicate?

A
  • data points are close to the mean

- the model is a good fit

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25
Q

What does a large s indicate?

A

the mean is not an accurate representation of the data

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26
Q

Standard deviation provides information about

A

how well the mean represents the sample data

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27
Q

If you take several samples from the same population, the samples will ____________, so it is important to understand _______________.

A
  • differ slightly

- how well the sample represents the population

28
Q

standard error related to standard deviation

A

standard error is similar measure to the population as standard deviation is to the sample

29
Q

sampling variation

A

samples from the same population will vary slightly because they contain different members of the population

30
Q

sampling distribution

A

frequency distribution of the sample means from the population

31
Q

average of the sample means =

A

mean of the population

32
Q

standard error of the mean

A

standard deviation of the sample means

33
Q

What does standard error of the mean measure?

A

variability between the means of different samples of the population

34
Q

standard error

A

√(standard error of the mean)

35
Q

central limit theorem

A

as samples get large, the sampling distribution has a normal distribution with a mean equal to the population mean

36
Q

central limit theorem applies to

A

more than 30 people in a sample

37
Q

Because it’s impossible to collect hundreds of samples, you must rely on

A

approximations of standard error

38
Q

What do confidence intervals provide?

A

another approach to assess the accuracy of the sample mean as an estimate of the population mean

39
Q

confidence interval - range of values

A

range (2) values within which the researchers think the population value falls

40
Q

What do you need to calculate confidence intervals?

A

must know

  • s
  • x-bar
41
Q

most common CIs

A

95%

99%

42
Q

95% CI means

A

95% likely that the population mean falls between the two values

43
Q

99% CI means

A

99% likely that the population mean falls between the two values

44
Q

What lies at the center of the CI?

A

mean

45
Q

small CI

A

sample mean must be very close to the true mean

46
Q

wide CI

A

sample mean is not similar to the true mean and thus is a bad representation of the population

47
Q

How can systematic variation be explained?

A

by the statistical model (IV)

48
Q

Can unsystematic variation be explained by the statistical model?

A
  • no

- not attributable to IV

49
Q

test statistic

A
  • variance explained by the model

- variance not explained by the model

50
Q

examples of test statistics

A

t-stat
f-stat
x2 stat

51
Q

larger test statistic

A

more unlikely it occurred by chance

52
Q

larger test statistic =

A
  • lower p-value

- more likely the test statistic is statistically significant

53
Q

A hypothesis can be ________ or _________

A
  • directional

- non-directional

54
Q

directional hypothesis

A

one-tailed test

55
Q

non-directional hypothesis

A

two-tailed test

56
Q

The prediction of direction must be made ______

A

prior to collecting data

57
Q

The one/two tailed test has a statistical advantage

A

one-tailed test

58
Q

Why does the one tailed test have a statistical advantage to a two-tailed test?

A
  • researcher needs a smaller test statistic to find significant results
  • must have research to support the use of a one-tailed test
59
Q

different effect sizes

A
  • Cohen’s D
  • Pearson’s correlation coefficient
  • response measures (MCID most common)
60
Q

Why do we need effect sizes?

A

A statistically significant finding does not mean that the finding is clinically useful or of a magnitude that is meaningful

61
Q

When can effect sizes be calculated?

A

post-hoc to determine the magnitude of a statistically significant effect

62
Q

power =

A

1-beta

63
Q

How can power be useful?

A
  • calculate sample size a priori

- calculate power of the study post-hoc

64
Q

g power

A

free program that can be downloaded to determine sample size to achieve a desired level of power

65
Q

higher test statistic = lower

A

p-value

7282 Statistics (17 decks)

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