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Foundations Week 6 > Statistical Inference > Flashcards

Statistical Inference Flashcards

0
Q

What is a two-tailed alternative hypothesis?

A

simple expect a difference to exist (group A and B will differ)

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1
Q

What is the null hypothesis H0?

A

there will be no difference

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2
Q

What is a one-tailed alternative hypothesis?

A

expect a difference and state in which direction

e.g., group A will do better than group B

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3
Q

What is the significance level (alpha)?

A

criteria to decide whether to accept/reject H0

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4
Q

What does a significance level (alpha) of 0.05 signify?

A
  • minimum established by scientific community
  • when you find sufficient evidence to reject null you can be 95% certain that it is due to a true difference in data, not because of experimental manipulation
  • accept that 5% of time results occurred by chance alone
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6
Q

What does an alpha of 0.01 (significance level) signify?

A
  • stricter level significance
  • when find sufficient evidence to reject null you can be 99% certain truly is difference in data because of experimental manipulation
  • but accept that 1% of time results occurred by chance alone
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7
Q

What is the study flow?

A
  • estimate number of subjects needed to get reliable answer
  • obtain sample(s) and assign to conditions
  • collect data
  • calculate basic summary statistics (central tendency and dispersion)
  • choose statistical test based on types of variables and types of questions being asked
  • apply the STATISTICAL TEST and obtain test statistic
  • COMPARE test statistic to theoretical sampling distribution derived for the particular test you are using with a particular alpha-value as your criterion
  • obtain a P-VALUE = the likelihood that the result observed is due to chance if H0 is correct (alpha is the value of p at which you are willing to reject H0 even if it is correct)
  • -> p < 0.05 indicates statistical significance
  • decide to accept or reject H0
  • derive conclusion that answers hypothesis
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7
Q

What are two types of Decision Errors?

A
  • Type I (alpha)

- Type II (beta)

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8
Q

What is the study flow (includes early steps)?

A
  • state H1 (alternative hypothesis)
  • define population and variables
  • identify outcome variables
  • state H0, null hypothesis
  • declare significance level (alpha)
  • estimate number of subjects needed to get reliable answer
  • obtain sample(s)
  • collect data
  • calculate summary stats (central tendency and dispersion)
  • choose statistical test based on types of variables and types of questions being asked
  • apply stat test and obtain test stat
  • compare test stat to theoretical sampling
  • obtain p-value
  • decide to accept/reject H0
  • derive conclusion
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9
Q

What is Type I (alpha) error?

A

reject H0 when it’s true (more serious of two errors)

say something happened when it just happened by chance

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10
Q

What is Type II (beta) error?

A

accept H0 when it’s false (less serious)

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11
Q

How can errors be minimized?

A
  • by good design
  • sufficient power
  • but error cannot be eliminiated
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23
Q

What is the t-test used for?

A

when comparing means for two samples

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24
Q

What is the unpaired t-test?

A
  • typically have control and treatment/experimental groups, each with different subjects
    e. g., one group of hypertensive patients gets a new drug (treatment group) and the other gets sugar pills (control/placebo) group
  • has less power than paired t-tests
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25
Q

How can errors be minimized?

A
  • by good design
  • sufficient power
  • but error cannot be eliminiated
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26
Q

What are some characteristics of the t-test?

A
  • want to determine if the difference between means for each of two groups occurred because of the treatment or chance
  • -> H0: no significant difference between means
  • -> H1: can be either 1 (treatment group will have a higher mean score than control group) or 2-tailed (there is a significant difference between means)
  • t-test calculation basically gets the difference between 2 means and divides by standard error of the difference (square root of the average standard deviation of the two groups) - this takes into account the central tendency of the 2 groups and an estimate of the average dispersion of the data
  • formula yields single value called t-statistic
  • compare calculated t-statistic with theoretical sampling distribution for the t-distribution (tables are found in statistics books or online) to decide if accept/reject H0
  • ->need alpha value and degrees of freedom (number of subjects minus number of parameters (2))
  • -> if t-stat > table reject H0; if T-stat < table accept H0
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27
Q

What is the trade-off between the two types of error?

A

as you decrease the probability of making a Type I Error you increase the probability of making a Type II Error

*as Type I is more serious most people set the Type I Error (typically at 0.05)

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28
Q

When you reject H0, but H0 is true, what type of error is this?

A

Type I

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29
Q

When you accept H0 but H0 is not true, what type of error is this?

A

Type II

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30
Q

What does a confidence limit attempt to do?

A
  • capture population parameters
  • range of values around mean (or other measure of central tendency) that says X% sure that it will fall int his range using confidence levels/limits
  • this is used because sample statistics only estimate population statistics, can’t actually get population statistics
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31
Q

What do confidence limits depend on?

A
  • standard deviation of sample data (smaller yields narrower margin error)
  • sample size (larger yields narrower margin error)
  • level of confidence desired (95% o5 99%)
  • -> 95% tighter (narrower margin error) than 99% (to be more certain, 99% needs bigger margin of error)
  • formula to calculate confidence limits depend son type of data and test
32
Q

What is statistical power?

A

Power (1-B) = probability that you correctly reject H0 when H1 true

  • typically set at 80% : power of 80% means that when H0 is truly false and there is a true treatment/experimental effect, a significant difference will be detected 80% of the time
  • increase power reduces the probability of making Type II error
33
Q

Increasing power reduces the probability of making which type of error?

A

Type II

34
Q

What are methods of increasing power?

A
  • lower alpha to 0.1: easier say difference significant - generally not accepted as 0.05 is minimum
  • 1-tailed instead of 2-tailed H1 - sometimes feasible
  • increase effect size (differences between means) - can’t control
  • decrease variance/standard deviation - can’t control
  • increase sample size = best and most effective method
  • can work backwards before starting experiment and calculate what sample size would give you sufficient power
  • -> need significance level (alpha)
  • -> estimated std dev (from literature)
  • -> estimated effect size (from literature)
35
Q

What is the best way to increase power?

A

increase sample size

38
Q

What are some characteristics of a paired t-test?

A
  • typically have same subjects in both groups
    for example, in a pre-post (before and after) design
    e.g., single group of hypertensive patients has BP measured before going on any drug, go on the drug for 6 weeks then measure blood pressure again and compare pre and post levels

*takes into account that same subjects measured twice and thus there are correlations or common relationships between the two sets of data

39
Q

What is ANOVA used for?

A

comparing 3+ means

*analysis of variance

40
Q

What does the ANOVA do?

A
  • compares variability of each treatment/experimental group across all subjects (between variance) to variability individual subjects across all treatment conditions (within subject variance)
  • assumes data normally distributed and similar variances
  • F-statistic examined for significance using F-distribution
  • H0 = 3+ means do not differ; H1 = 3+ means differ
  • -> if reject null all you can say is the means differ - cannot say exactly which ones differ
  • -> need to conduct follow-up tests that then compare the means to determine which ones differ
  • numerous variations of ANOVA depending on study design and variance relationships
41
Q

What is the Chi-Squared or Goodness of Fit test used for?

A
  • do observed (collected) data fit expected pattern (chance) or are trends observed in distribution
42
Q

positive correlation

A

0 < r =< 1

  • score high on 1 variable and score high on the other
  • score low on 1 variable score and score low on the other
  • positive slope when plot the data
  • 1 = perfect correlation (can’t exceed 1)
43
Q

negative correlation

A
  • 1 =< r < 0
  • score high on 1 variable and score low on the other
  • negative slope when plot the data
  • -1.0 = perfect correlation, can’t exceed
44
Q

no correlation relates to what correlation coefficient?

A

r = 0

- no correlation or no linear relationship (other relationships exist, but correlation only measures linear)

45
Q

What are some characteristics of correlation and correlation coefficient?

A
  • correlation does NOT equal causation
  • interpreting r values
    |r| < 0.29 small correlation, weak relationship
    |r| 0.3 - 0.49 medium correlation/relationship
    |r| 0.5 - 1.0 large correlation, strong relationship
  • calculate the Spearman r if have ranked data
46
Q

What is the one-variable chi-square (X^2) test used for?

A
  • used with typical survey questions whether subject picks from set of pre-set categorical answers
    e. g., how much do you agree with the statement “compared to 5 years ago I take better care of myself” strongly disagree, disagree, neutral, agree, strongly disagree
  • -> with 20 subjects by chance would expect 4 people to answer in each one - do the observed responses differ significantly from 4 in each: H0 = no, H1 = yes
47
Q

What is coefficient of determination (r^2)?

A

gives the proportion of 1 variable explained by the other
e.g., if correlation between height and weight = 0.80, then r^2 = 0.64 meaning 64% of weight is explained by height and 36% is explained by other variables

48
Q

What is a multi-variable X^2 test used for?

A
  • proportions/frequencies/percents of observed categorical values for 2+ groups (minimum = 2x2) in 2+ conditions
  • -> is there a difference in the proportion of males vs females benefitting from low dose aspirin in terms?
  • -> calculating expected values more complicated than single-variable situation but still finding “goodness of fit” between expected and observed
49
Q

What is Fisher’s Exact Test?

A
  • version of Chi-square test when outcome of interest occurs infrequently and thus data are “lopsided” and one variable has too few counts (i.e., e.g., does alcohol reduce the rate of cardiac disease?
  • -> formula to get probabilities is complicated but still finding what would have occurred by chance compared to observed
50
Q

In what studies is an Odds Ratio (OR) used?

A

used in case-control study
*case-control study = group of cases/patients (those with disease and those without) assembled and exposure histories ascertained to compute measures of association between exposure and risk

51
Q

What is a case-control study?

A

group of cases/patients (those with disease and those without) assembled and exposure histories ascertained to compute measures of association between exposure and risk

52
Q

What are the characteristics of an Odds Ratio?

A
  • used in case-control studies
  • looking at retrospective data for the most part
  • outcome = lung cancer or no lung cancer; history = cigarette exposure or not
  • odds = probability exposure to cigarettes/probability no exposure to cigarettes
  • calculate for cancer and no cancer groups
  • Odds Ratio (OR) = cancer ratio/no cancer ratio
  • OR > 1 = association exists (Farther from 1 = stronger association)
53
Q

Odds vs. Odds Ratio?

A

Odds are easier to report to public

Odds Ratio is a way of normalizing things towards 1

54
Q

What is Relative Risk used for?

A

used more in cohort studies than case control in association with OR

55
Q

What are characteristics of Relative Risk?

A
  • outcome = probability that particular event will happen over time
  • can only be determined prospectively
  • RR = incidence of disease in exposed/incidence of disease in non-exposed
  • RR > 1 = risk exists (farther form 1 = greater risk)
  • used more in cohort studies than case control
56
Q

RR vs OR?

A

RR: prospective
OR: retrospective

57
Q

What is correlation?

A

examines strength and direction of relationship between 2 variables
–> can extend to 3+ variables using multiple correlation

58
Q

What is the correlation coefficient (r)?

A

measure used to express extent or strength of relationship; often referred to as Pearson r
- positive correlation: 0 < r < 1; score high on 1 variable and score high on the other; score low on 1 variable score and score low on the other; positive slope when pllot the data; 1.0

59
Q

What is regression (r)?

A

using correlation in models of prediction

  • if linear relationship exists between 2 variables can use that to calculate equation of line that best represents relationship, then use to predict what one variable (weight) would be if know value for other (height)
  • can use multiple regression techniques with 3+ variables
60
Q

What is inferential statistics?

A

estimating parameters of a population from a sample

61
Q

Example:
sample mean for BMI = 20.4
calculated 95% Confidence Interval = 3.5
What is the confidence interval? What does it mean?

A

16.9 - 23.9

We can be 95% certain the population mean falls between these limits

62
Q

What are three possible inferential tests for categorical data?

A
  • Chi-square
  • Fisher’s Exact
  • OR vs RR
63
Q

If have ranked data, what type of correlation coefficient do you find?

A

Spearman r

Foundations Week 6 (12 decks)

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