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Flashcards in Evidence Based Medicine Deck (171):
1

Allows us to draw from the sample, conclusions about the general population

Statistics

2

An efficient way to draw conclusions when the cost of gathering all of the data is impractical

Taking Samples

3

Assume that an infinitely large population of values exists and that your sample was randomly selected from a large subset of that population. Now use the rules of probability to

Make inferences about the general population

4

States that the sampling distribution of the mean of any independent, random variable will be normal or nearly normal, if the sample size is large enough

The Central limit theorem

5

What does the Central Limit Theorem say?

The sampling distribution of the mean of any independent, random variable will be normal or nearly normal, if the sample size is large enough

6

If samples are large enough, the sample distribution will be

Bell shaped (Gaussian)

7

Statistics come in what two basic flavors?

Parametric and Non-parametric

8

A class of statistical procedures that rely on assumptions about the shape of the distribution (i.e. normal distribution) in the underlying population and about the form or parameters (i.e. mean and std. dev) of the assumed distribution

Parametric Statistics

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A class of statistical procedures that does not rely on assumptions about the shape or form of the probability distribution from which the data were drawn

Non-parametric Statistics

10

Summarize the main features of the data without testing hypotheses or making any predictions

Descriptive statistics

11

Descriptive statistics can be divided into what two classes?

Measures of location and measures of dispersion

12

A typical or central value that best describes the data

Measures of location

13

What are the measures of location?

1.) Mean
2.) Median
3.) Mode

14

Describe spread (variation) of the data around that central value

Measures of dispersion

15

What are the measures of dispersion?

1.) Range
2.) Variance
3.) Std. Dev
4.) Std. Error
5.) Confidence Interval

16

No single parameter can fully describe the distribution of data in the

Sample

17

The sum of the data points divided by the number of data points

-More commonly referred to as "the average"
-Data must show a normal distribution

Mean

18

What are often better measures of location if the data is not normally distributed?

Median and Mode

19

The value which has half the data smaller than that point and half the data larger

Median

20

When choosing the median for odd number of data points, you first

Rank the order, then pick the middle #

21

When choosing the median for even number of data points, you

1.) Rank the numbers
2.) Find the middle two numbers
3.) Add the two middle numbers and divide by 2

22

Less sensitive for extreme data points and is thus useful for skewed data

Median

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The value of the sample which occurs most frequently

Mode

24

The mode is a good measure of

Central Tendency

25

Not all data sets have a single mode, some data sets can be

bi-modal

26

On a box plot, 50% of the data falls between Q1 (25th percentile) and Q3 (75th percentile), the area encompassing this 50% is called the

Interquartile range (= Q3-Q1)

27

Used to display summary statistics

Box plots

28

To find the quartiles, put the list of numbers in order, then cut the list into four equal parts, the quartiles are at the

Cuts

29

The second quartile is equal to the

Median

30

Do not provide information on the spread or variability of the data

Measures of location

31

Describe the spread or variability within the data

Measures of dispersion

32

Two distinct samples can have the same mean but completely different levels of

Variability

33

The difference between the largest and the smallest sample values

-Depends only on extreme values and provides no information about how the remaining data is distributed

Range

34

Is the range a reliable measure of the dispersion of the whole data set?

No

35

The average of the square distance of each value from the mean

Variance

36

Makes the bigger differences stand out, and makes all of the numbers positive, eliminating the negatives, which will reduce the variance

Squaring the Variance

37

When calculating the variance, what is the difference between using N vs. N-1 as the denominator?

N gives a biased estimate of variance, where as (N-1) gives an unbiased estimate

38

In the calculation for variance, what does N represent?

N = size of population (biased)

39

In the calculation for variance, what does (N-1) represent?

(N-1) = size of the sample (unbiased)

40

The most common and useful measure of dispersion

Standard deviation

41

Tells us how tightly each sample is clustered around the mean

Standard deviation

42

When samples are tightly bunched together, the Gaussian curve is narrow and the standard deviation is

Small

43

When the samples are spread apart, the Gaussian curve is flat and the standard deviation is

Large

44

Means and standard deviations should ONLY be used when data are

Normally distributed

45

How can we determine if the data are normally distributed?

Calculate the mean plus or minus twice the standard deviation. If either value is outside of the possible rage, than the data is unlikely to be normally distributed

46

Approximately what percentage of data lies within:
1.) 1 standard deviation of the mean
2.) 2 Standard deviations of the mean
3.) 3 Standard deviations of the mean

1.) 68.3%
2.) 95.4%
3.) 99.7%

47

If data is skewed, we should use

Median

48

What are two more sophisticated, yet more complex, methods of determining normality?

D'Agostino & Pearson omnibus and Shapiro-Wilk Normality tests

49

D'Agostino & Pearson omnibus and Shapiro-Wilk Normality tests are not very

Useful

50

What we want is a test that tells us whether the deviations from the Gaussian ideal are severe enough to invalidate statistical methods that assume a

-Normality tests don't do this

Gaussian distribution

51

How can we determine whether our mean is precise?

Find the Standard Error

52

A measure of how far the sample mean is away from the population mean

Standard error

53

The standard error of the mean (SEM) gets smaller as

Sample size gets larger

54

If the scatter in data is caused by biological variability and you want to show that variability, use

Standard Deviation (SD)

55

If the variability is caused by experimental imprecision and you want to show the precision of the calculated mean, use

Standard Error of the mean (SEM)

56

Say we aliquot 10 plates each with a different cell line and measure the integrin expression of each, would we want to use SD or SEM?

SD

57

Say we aliquot 10 plates of the same cell line and measure the integrin expresion of each, would we want to use SD or SEM?

SEM

58

An estimate of the range that is likely to contain the true population mean

-combine the scatter in any given population with the size of that population

Confidence intervals

59

Generates an interval in which the probability that the sample mean reflects the population mean is high

Confidence intervals

60

Means that there is a 95% chance that the confidence interval you calculated contains the true population mean

95% confidence interval

61

If zero is included in a confidence interval for a change in a disease due to a drug, then it means we can not exclude the possibility that

There was no true change

62

An observation that is numerically distant from the rest of the data

An outlier

63

Can be caused by systematic error, flaw in the theory that generated the data point, or by natural variability

An outlier

64

What is one popular method to test for an outlier?

The Grubbs test

65

How do we use the Z value obtained by the Grubbs test to test for an outlier?

Compare the Grubbs test Z with a table listing the critical value of Z at the 95% probability level. If the Grubbs Z is greater than the value from the table, then you can delete the outlier

66

To test for an outlier, we compare the Grubbs test Z with a table listing the critical value of Z at the 95% probability level. If the Grubbs Z is greater than the value from the table, then the P value is

Less than 5% and we can delete the outlier

67

What constitutes "good quality" data

Data must be: reliable and valid

68

What measurements assess data reliability?

Precision, accuracy, repeatability, and reproducibility

69

In order for the data to be valid, it must be

Compared to a "gold standard," generalisable, and credible

70

The degree to which repeated measurements under unchanged conditions show the same results

Precision

71

High precision results in lower

SD

72

The degree of closeness of measurements of a quantity to that quantity's true value

Accuracy

73

High accuracy reflects the true

Population mean

74

Repeatability is the same as

Precision

75

The ability of an entire experiment or study to be duplicated either by the same researcher or by someone else working independently

-The cornerstone of research

Reproducibility

76

The extent to which a concept, conclusion, or measurement is well-founded and corresponds accurately to the real world

Validity

77

Assuming that data collected on small samples are indicative of the population, sampling errors (bias, size, etc), and instrument errors are all threats to

Validity

78

The generalizability of a study is called it's

External validity

79

Thalidomide was tested on rodents and showed no effects on limb malformations. However, the effects on humans were very pronounced. This is an error in

External validity

80

Many studies using single cell lines are no longer

Acceptable

81

Are the methodologies acceptable? Do the investigators have the required expertise? Who paid for the research? What is the reputation of the investigators an the institution? These are all questions that challenge

Credibility

82

Caused by inherently unpredictable fluctuations in the readings of a measurement apparatus or in the experimenter's interpretation of the instrumental reading

Random Error

83

Random error can occur in either

Direction

84

Error that is predictable, and typically constant or proportional to the true value

Systematic Errors

85

Caused by imperfect calibration of measurement instruments or imperfect methods of observation

Systematic Error

86

Systematic error typically occurs only in one

Direction

87

Say you measure the mass of a ring three times using the same balance and get slightly different values of 17.46 g, 17.42 g, and 17.44 g. This is an example of

Random error

-can be minimized by taking more data

88

Say the electronic scale you use reads 0.05 g too high for all of your measurements because it is improperly tare throughout your experiment. This is an example of?

Systematic error

89

If the sample size is too low, the experiment will lack

Precision

90

Time and resources will be wasted, often for minimal gain, if the sample size is

Too large

91

Calculates how many samples are enough

Power analysis

92

The calculation of power requires which three pieces of information?

1.) A research hypothesis
2.) The variability of the outcomes measured
3.) An estimate of the clinically relevant difference

93

Will determine how many control and treatment groups are required

A research hypothesis

94

What is the best option for showing the variability of the outcomes measured?

SD

95

A difference between groups that is large enough to be considered important

Clinically relevant difference

-set as 0.8 SD

96

What is the affect on sample size (n) for the following scenarios:

1.) More variability in the data
2.) Less variability in the data
3.) To detect small differences between groups

1.) Higher n required
2.) Fewer n required
3.) Higher n required

97

What is the affect on sample size (n) for the following scenarios:

1.) To detect large differences between groups
2.) Smaller α used
3.) Less power (smaller β)

1.) Fewer n required
2.) Higher n required
3.) Fewer n required

98

An important part of the study design

Statistics

99

What is the null hypothesis (Ho)

Ho: µ1 = µ2

Ho = null hypothesis
µ1 = mean of population 1
µ2 = mean of population 2

100

Is presumed true until statistical evidence in the form of a hypothesis test proves otherwise

Null hypothesis

101

We want to compare our null hypothesis to the alternative hypothesis being tested. To do this, we must select the probability threshold, below which the null hypothesis will be rejected. This is called the

Significance level (α)

-Common values are 0.05 and 0.01

102

Once our significance level has been selected, we need to compute from the observations the

Observed value (tobs) of the test statistic (T)

103

Once we have calculated tobs, we need to decide whether to

Reject Null hypothesis in favor of alternative or not

104

The incorrect rejection of a true null hypothesis (false positive)

Type I error

105

Incorrectly retaining a false null hypothesis (false negative)

Type II error

106

What are the two ways to compare a sample mean to a population mean?

1.) z statistic: used for large samples (n > 30)
2.) t statistic: used for small samples (n less than 30)

107

Any statistical test for which the distribution of the test statistic can be approximated by a normal distribution.

z statistic

108

Because of the central limit theorem (CTL), many test statistics are approximately normally distributed for

Large samples (n > 30)

109

Very similar to the z statistic and uses the same formula

t statistic

110

When a statistic is significant, it simply means that the statistic is

-does not mean it is biologically important or interesting

Reliable

111

Indicates strong evidence against the null hypothesis

-so we reject the null hypothesis

A small p-value (typically p

112

Indicates weak evidence against the null hypothesis

-so we fail to reject the null hypothesis

A large p-value (typically p > 0.05)

113

P-values close to the cutoff (0.05) are considered to be marginal (could go either way), thus we should always

Report our p-value so readers can draw their own conclusions

114

Can strongly influence whether the means are different

Variability

115

Most useful when comparing two means and N

Students t-test

116

The degreesof freedom are very important in a

Students t-test

117

Given two data sets, each characterized by it's mean, SD, and number of samples, we can determine whether the means are significant by using a

t-test

118

A t-test is nothing more than a

Signal-to-noise ration

119

The degree of freedom is important in a t-test. How do we find degrees of freedom?

d.o.f. = N-1, but we have more than one N, so for a t-test, d.o.f. = 2N - 2

120

Will test either if the mean is significantly greater than x or if the mean is significantly less than x, but not both

One-tailed t-test

121

Provides more power to detect an effect in one direction by not testing the effect in the other direction

One-tailed t-test

122

Will test both if the mean is significantly greater than x and if the mean is significantly less than x

Two-tailed t-test

123

In a one-tailed t-test, the mean is considered significantly different from x if the test statistic is in either the

Top 5% or the bottom 5%, resulting in a p-value of less than 0.05

124

In a two-tailed t-test, the mean is considered significantly different from x if the test statistic is in the

Top 2.5% or bottom 2.5%, resulting in a p-value less than 0.05

125

If tcalc > than ttable, than we must

Reject the null hypothesis and conclude that the sample means are significantly different

126

We must reject the null hypothesis and conclude that the sample means are significantly different if

tcalc > than ttable

127

The observed data are from the same subject or from a matched subject and are drawn from a population with a normal distribution

Paired t-test

128

The observed data are from two independent, random samples from a population with a normal distribution

Unpaired t-test

129

If we are measuring glucose concentration in diabetic patients before and after insulin injection, we perform a

Paired t-test

130

If we are measuring the glucose concentration of diabetic patients versus non-diabetic patients, we perform an

Unpaired t-test

131

If you have more than two groups, than you must make more than two

Comparisons

132

If you set a confidence level at 5% and do repeated t-tests on more than 2 groups, you will eventually get a

Type I error

-i.e. reject the null hypothesis when you should not have

133

The more comparisons we have to make, the higher the

α value must be

134

Instead of doing multiple t-tests when we have more than two means to compare, we can do an

Analysis of Variance (ANOVA)

135

To compare three or more means, we must use an

Analysis of Variance (ANOVA)

136

In ANOVA, we don't actually measure variance, we measure a term called

"Sum of squares"

137

For ANOVA, what are the three sum of squares that we need to measure?

1.) Total sum of squares
2.) Between-group sum of squares
3.) Within-group sum of squares

138

Total scatter around the grand mean

Total sum of squares

139

Total scatter of the group means with respect to the grand mean

Between-group sum of squares

140

The scatter of the scores

Within-group sum of squares

141

ANOVA and t-test are both essentially just

Signal-to-noise ratios

142

To calculate the sums of squares, we first need to calculate

1.) Group means
2.) Grand mean

143

If Fcalc > Ftable,

We must reject the null hypothesis and conclude that the sample means are significantly different

144

We must reject the null hypothesis and conclude that the sample means are significantly different if

Fcalc > Ftable

145

When we have one measurement variable and one nominal variable, we use

One-Way ANOVA

146

When we have one measurement variable and two nominal variables, we use

Two-way ANOVA

147

If we measure glycogen content for multiple samples of the heart, lungs, liver, etc. We perform a

One-way ANOVA

148

If we measure a response to three different drugs in both men and women, we use a

Two-way ANOVA

149

Only tells us that the smallest and largest means differ from one another

ANOVA

150

ANOVA only tells us that the smallest and largest means differ from one another, if we want to test the other means, we have to run

Post hoc multiple comparisons tests

151

Post hoc tests are only used if the null hypothesis is

Rejected

152

Test whether any of the group means differ significantly

Post hoc tests

153

Don't suffer from the same issues as performing multiple t-tets. They all apply different corrections to account for the multiple comparisons

Post hoc tests

154

When normal distributions can not be assumed, we must consider using a

Non-parametric test

155

Make fewer assumptions about the distribution of the data

Non-parametric tests

156

Less powerful, meaning it is difficult to detect small diferences

Non-parametric tests

157

Useful when the outcome variable is a rank score, one or a few variables are off-scale, or you're sure that the data is non Gaussian (ex: response to drugs)

Non-parametric tests

158

What is the non-parametric alternative to the two-sample t-test?

Mann-Whitney U test

159

The Mann-Whitney U test does not use actual measurements, but rather it uses

Ranks of the measurements used

160

In the Mann-Whitney U test, data can be ranked from

Highest to lowest, or lowest to highest

161

Let's say we want to test the two tailed null hypothesis that there is no difference between the heights of male and female students. What is
1.) Ho
2.) Ha
3.) U1
4) U2

1,) male and female students are the same height
2.) male and female students are not the same height
3.) U statistic for men
4.) U statistic for women

162

How do we analyze the Mann-Whitney U test?

Compare the smaller of the two U statistics to a table of U values. If Ucalc is less than U table than we reject the null hypothesis

163

The extent to which two variables have a linear relationship with eachother

Correlation

164

Useful because they can indicate a predictive relationship that can be exploited in practice

Correlations

165

Correlation is used to understand which two things?

1.) Whether the relationship is positive or negative
2.) The strength of the relationship

166

A measure of the linear correlation between two variables, X and Y, which has a value between +1 and -!, where 1 is total positive correlation, -1 is total negative correlation, and 0 is no correlation

Pearson Correlation Coefficient (r)

167

The goal of linear regression is to adjust the values of slope and intercept to find the line that best predicts

Y from X

168

It's goal is to minimize the sum of the squares of the vertical distances of the points from the line

Linear Regression

169

Linear regression does not test whether your data are

Linear

170

A unitless fraction between 0.0 and 1.0 that measures the goodness-of-fit of your linear regresion

-only useful in the positive direction

r^2

171

An r^2 value of zero means that

Knowing X did not help you predict Y (and vice-versa)

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