Exam 2 Flashcards

Question

Concurrent Validity (Empirical)

Answer 1

Measures the extent to which the measures taken by the instrument correspond to a known Gold Standard Correlation statistics are also used to measure the validity

Answer 2

For an instrument or test to be useful it must be both valid and reliable

Answer 3

Formula: Sensitivity = TP/TP+FN Definition: the probability that a symptom is present (or screening test is positive) given that the person does have the disease Patient Relevance\*: “I know my patient has the disease. What is the chance that the test will show that my patient has it?”

Answer 4

Formula: Specificity = TN/TN+FP Definition: the probability that a symptom is not present (or screening test is negative) given that the person does not have the disease Patient Relevance: “I know my patient doesn’t have the disease. What is the chance that the test will show that my patient doesn’t have it?”

Answer 5

Formula: TP/TP+FP Definition: the probability that a person has the disease given a positive test result Patient Relevance: “I just got a positive test result back on my patient. What is the chance that my patient actually has the disease?”

Answer 6

Formula: TN/TN+FN Definition: the probability that a person does not have the disease given a negative test Patient Relevance: “I just got a negative test result back on my patient. What is the chance that my patient actually doesn’t have the disease?”

Answer 7

Statistics used to characterize shape, distribution, central tendency & variation (variability) of a population or sample

Answer 8

Parameter –is the individual value or data point Statistic – calculated descriptive index

Answer 9

•Distributions described as the variation pattern around the point of central tendency Measures of central tendency: * Mean – the arithmetic mean which is the sum of all values in the distribution divided by the number of values * Median – the middle value in a distribution of values; half way in number from the lowest to highest numbers * Mode – value in the distribution with the highest frequency – most common number in the distribution

Answer 10

Frequency distribution – rank order of how many times a particular value occurred Can be displayed as percentage value and cumulative percentage Data can be grouped into classes or ranks

Answer 11

Can be displayed as histogram or frequency polygon

Answer 12

There will always be some errors in clinical research; confidence intervals attempt to allow for this by giving a +/- range of values. CI 95% means that the researcher is 95% confident that the true value is between a given range. Confidence intervals are defined in the research paper

Answer 13

Pattern of values of a set of scores with n = total number

Answer 14

Representation of tabulated frequencies, shown as adjacent rectangles, in discrete intervals, with height equal to the frequency of the observations in the interval

Answer 15

Intervals represented as points and level on vertical axis represents the frequency of the observations in the interval

Answer 16

Variation of the distribution pattern around the point of central tendency: Symmetric distribution of values of around the point of central tendency Mode, median & mean all the same point

Answer 17

Asymmetric distribution of values of around the point of central tendency Described as positive or negative skew based upon where majority of values are compared to the mode Use “tail” of distribution to determine skew Median & mean deviate from the mode in skewed distributions Mean is most sensitive to skew Therefore mean should be used ONLY in normal distributions as a measure of central tendency

Answer 18

Highest to lowest value of the distribution – 58 to 75 in illustration No measure of how much each value deviates from point of central tendency

Answer 19

Assess deviation of each score from the mean – deviation score Sum of these deviation scores = 0 so take sum of deviation scores squared – called the sum of squares (SS) Divide the SS by the number of scores (n) to get the SAMPLE VARIANCE also called mean square (MS) Better estimation of the POPULATION VARIANCE is to divide the sum of squares by n-1

Answer 20

Standard Deviation (s or SD) is derived from the mean value Mean is only meaningful in normal distribution so mean & SD should be used only with normal distributions Mode is best measure of central tendency & range is a good measure of variability in skewed distributions

Answer 21

Equals the square root of the variance (s2) Has a meaning in normal distributions –± 1 SD represents 68% of total # values in distribution –± 2 SD represents 95% of total # values –± 3 SD represents 99.7% of total # values Excellent discussion of variance & standard deviation can be found at: http://www.mathsisfun.com/data/standard-deviation.html

Answer 22

Value represents what percent of the total number of values in a data set In a data set of 40 values – the 10th value from the lowest in the set is the 25th percentile The median value (20th of 40 values) is the 50th percentile Commonly reported quartiles, quintiles or deciles * Quartiles - each group comprises a quarter of the entire data set * Quintiles – ranked data set are the four points that divide the data set into five equal groups * Deciles – ranked data set are the nine points that divide the data set into ten equal groups

Answer 23

Quartiles of a ranked data set are the three points that divide the data set into four equal groups - 25th percentile, 50th percentile & 75th percentile Each group comprises a quarter of the entire data set Different Quartiles: * Lower (bottom) quartile – \< 25th% * Lower middle quartile − 25th% − 50th% * Upper middle quartile − 50th% − 75th% * Upper (top) quartile − \> 75th% Interquartile range is from 25th% − 75th%

Answer 24

Common display in graphs of mean as a point and an error bar showing one SD around that mean Allows for easy comparison between groups

Answer 25

Box & Whisker Plot: * Line at center of box - Median * Box - Interquartile range (IQR) * Whiskers (bars) - 1.5 x IQR – approximates range Box & Whisker plots allow for easy comparison between groups when using median, quartiles and ranges

Answer 26

Independent of units (cancel out) so can compare distributions using different units Expresses SD as a proportion to the mean which account for differences in the mean so is a relative variation

Answer 27

Z-score = Mean divided by SD ((X)/SD) Normalizes mean to the variability of the data set

Answer 28

Allow investigators to make decisions from sample data about the larger population

Answer 29

Likelihood that an event will occur given all possible outcomes Single Coin Toss: * 2 sides with both having an equal chance of coming face up when tossed * So probability = 0.5 Probability of Single Die Toss * Six sides so probability = 0.167

Answer 30

Applied to Groups of Data The greater the deviation from mean the greater the probability of NOT being in the group Critical when comparing two groups – what is the probability of 2 groups being from different populations * 68% of all values are within 1 SD of mean * 95% of all values are within 2 SD of mean * 99% of all values are within 3 SD of mean * \> deviation from mean less probability of being in the group

Answer 31

value of 2 - 1/36 – p=.028 * value of 3 – 2/36 – p=.056 * value of 4 – 3/36 - p=.083 * value of 5 – 4/36 - p=.111 * value of 6 – 5/36 - p=.139 * value of 7 – 6/36 - p=.167 * value of 8 – 5/36 - p=.139 * value of 9 – 4/36 - p=.111 * value of 10 – 3/36 - p=.083 * value of 11 – 2/37 – p=.056 * value of 12 – 1/36 - p=.028

Answer 32

In statistics, sampling error is the error caused by observing a sample instead of the whole population. The sampling error is the difference between a sample statistic used to estimate a population parameter and the actual but unknown value of the parameter

Answer 33

The standard error of the mean (SEM) (i.e., of using the sample mean as a method of estimating the population mean) is the standard deviation of those sample means over all possible samples (of a given size) drawn from the population. The smaller the standard error, the more representative the sample will be of the overall population.

Answer 34

The standard error is inversely proportional to the sample size; the larger the sample size, the smaller the standard error because the statistic will approach the actual value.

Answer 35

Experimental error is the difference between a measurement and the true value,or between two measured values. Within group variance due to experimental error or error variance Experimental error unexplained variation including personal differences between individuals, methodological inconsistencies, behavior differences between individuals & environmental factors Not mistakes just unexplained variation

Answer 36

Applied to Groups of Data Distributions of outcome measure before (blue) & after (red) an intervention What probability that the intervention produced a change in the outcome? What probability that the difference between these two distributions is due to chance alone and not the result of the intervention?

Answer 37

Difference between group before and after intervention produces two hypotheses: Null Hypothesis: * No difference between the pre & post- intervention groups * No treatment effect * Any difference just due to chance * Any difference is functionally 0 * NOT SIGNIFICANT difference Alternative – Experimental Hypothesis * Difference between pre & post groups is large enough so that the difference is not due to chance alone * Functional difference * SIGNIFICANT difference

Answer 38

Reject or not reject the experimental or null hypothesis – 4 possible outcomes ## Footnote Correctly reject null hypothesis – experimental hypothesis is true Correctly reject experimental hypothesis – null hypothesis is true Incorrectly reject null hypothesis – null hypothesis is true, called Type I error Incorrectly reject experimental hypothesis – experimental hypothesis is true – Type II Error

Answer 39

Incorrect rejection of null hypothesis – null hypothesis is true Example: * Decide that a treatment works when it really doesn’t * Early studies of radical mastectomy versus lumpectomy reported superiority of radical mastectomy in certain forms of breast cancer * Incorrectly as it turned out – so many women had unnecessary disfiguring surgery

Answer 40

Incorrectly reject experimental hypothesis – experimental hypothesis is true – Type II Error Example: * Decide that a treatment does not work when it really does * Investigators wish to avoid this to enhance chance for publication

Answer 41

Level of significance – alpha (α) level – is set before beginning a study This is the risk the investigator is willing to take in making a Type I error Usual risk\* is considered being wrong 1 in 20 times, a 5% error rate or an α = 0.05 Can make it harder or easier to make a type I error If set risk at 1 in 100 times, a 1% error rate or an α = 0.01 – harder to make Type I error If set risk at 1 in 10 times, a 10% error rate or an α = 0.1 – easier to make Type I error When it is made harder to make a Type I error it becomes easier to make a Type II error – so there is a trade off

Answer 42

Type II Error – Statistical power Incorrect rejection of the experimental hypothesis Probability of making a type II error is beta (β) β= 0-1-0.2 are commonly accepted levels Which is the probability or likelihood that we will be unable to determine statistically significant differences 1-β is the statistical power of a test –is the probability that the test can determine a significant difference if it exists \> power means \> ability to determine a significant difference 0.8-0.9 is 80-90% 80% are commonly used levels

Answer 43

Significance is determined by using a statistical test and it provides a “p” (probability) level When p \< 0.05, the test shows a significant difference between group – that this difference did not occur by chance alone When p ≥ 0.05, the test shows that there was not a significant difference between groups – that this difference could have occurred by chance alone Once significance level is set cannot change for that study Dichotomous decision – significant or not significant, never say “highly significant” or “more significant” * If statistical test shows a p \<.001 you can have a high confidence that there is a significant difference, it is not “highly significant” * If p=0.04 you may have less confidence in the significant difference

Answer 44

Significance criterion Variance of the data Sample size Effect size

Answer 45

α & β are logical, not mathematical, opposites Risk of type I error when the risk of type II error so peril in changes

Answer 46

Increase power of statistical test when data variance decrease When variability within groups increase harder to tell difference so decrease power Variance decrease & power increase by: * Using repeated measures * Homogeneous subjects * Controlling sources of random measurement error Sometimes methodological changes can be done to reduce the variance of the data set – change population used or exclusion criteria Increasing size of the sample – more potential values clustered around mean and less influence of outliers

Answer 47

Small samples are * Less likely to reflect the population therefore decreases true differences between groups * Increases effect of outliers so increases variability * Decreases effect size THIS IS THE PRINCIPLE WAY TO INCREASE STATISTICAL POWER IN A STUDY TO AVOID A TYPE II ERROR

Answer 48

Factor that assesses true difference between groups If means of 2 groups very different but groups have a high variability – there may not really be a difference between the 2 groups If there is small difference between the means of two groups, but each group is very homogeneous, then could have a true difference between the groups Effect size involves variability within groups & mean difference between groups Effect size equals difference between means of two groups divided by the pooled standard deviation Cohen states that ES \< 0.2 is small, around 0.5 is medium & \> 0.8 is large Power Analysis is done before the study (a priori) to determine the needed sample sizes

Answer 49

Are the two groups just different or are they different in a particular way – one group \> or \< other Non-directional hypothesis – states only that there is a difference and does not predict which is \> or \< Directional hypothesis – predicts which is \> or \< Statistical Tests must reflect directionality or non-directionality of hypothesis

Answer 50

2-tailed test used for non-directional hypotheses * 2-tailed test the critical region of α = 0.05 is divided between upper & lower part of the curve so in each region α/2 1-tailed test used for directional hypothesis * 1-tailed test the entire critical region is in the region in the direction of the predicted difference so full critical region of α = 0.05 in that direction 1-tailed test more powerful & less likely to make a Type II error, but more likely to make a type I error 1-tailed test reflects placement of full critical region in one direction

Answer 51

Degree of freedom = # values -1 5 numbers which add up to 30 – if you change the values of 4 of those to add up to 30 the fifth can only have a preordained value and NOT one you can change So 5 numbers have 4 degrees of freedom * Used in most statistical calculations

Answer 52

Used to make inferences about a population Use requires assumption of a Normal distribution Large populations of interval or ratio (metric) data of often normally distributed “Goodness of fit” or “homogeneity of variance” tests used to determine normality of distribution Non-parametric tests when assumption of normality not met Parametric tests have \> statistical power so prefer to use those if possible

Answer 53

Statistics are tools and should not be substituted for clinical knowledge or judgment There may be a statistically significant change in say ROM which has no clinical implication – that is not producing a functional difference Conversely, a sizable change in a number of subjects can be produced, but because of variability of the result, there is not a significant difference Not enough # of subjects to avoid a type II error Responders versus non-responders – non-responders in the experimental group will act like control group So with subgroups may have a true difference Important considerations in interpreting statistical results: * What do your numbers mean? – understand the phenomenon * Don’t confuse statistical significance with size of treatment effect – statistical significance is only the probability of change NOT a reflection of the size of the effect What is a meaningful change? * Don’t confuse significance with a meaningful change - a statistically significant change may not be a meaningful change

Answer 54

Within group differences is the experimental error Between group difference includes both intervention + experimental error In RCTs the random assignment should equally distribute the characteristics that give rise to experimental error between the two groups; therefore should not contribute to between group comparisons Relative magnitude of between group differences & within group variability give rise to overlap or not between groups Two groups not different –reject experimental (alternative) hypothesis Two groups different – reject null hypothesis

Answer 55

Relative magnitude of between group differences & within group variability give rise to overlap or not between groups

Answer 56

Ratio of between groups to within groups–Between groups difference has both treatment effect + experimental error Within groups variability due sole to experimental error * So if no treatment effect the ratio is 1 Desired outcome is a \>\> a number as possible when treatment effect \>\>\>\> experimental error Think of it like a signal to noise ratio – lot of signal compared to noise wanted

Answer 57

Within group differences is the experimental error Between group difference includes both intervention + experimental error Compare between group differences to within group variability to calculate a T value and compare it to the critical T-value (T-value for p \< 0.05) to determine significance

Answer 58

Developed by William Gossett – Guinness Brewery –pseudonym was Student, so often called Student T-test Compare between group differences to within group variability to calculate a T value and compare it to the critical T-value (T-value for p \< 0.05) to determine significance Comes in two forms: * Unpaired T-test - for independent groups * Paired T-test - for dependent groups One & Two-tailed Tests * 1-tailed versions of both T-tests used with directional comparisons * 2-tailed versions of both T-tests used with non-directional comparisons * So need to use both terminologies when describing what test is used

Answer 59

(Used for two group comparisons, so if more than two groups being compared would have to use multiple T-tests) Use of multiple T-tests (or any test for that matter) higher risk of committing a Type I error For \> 2 group comparisons use the general analysis of variance (ANOVA) T-test is a specialized form of ANOVA for 2 group comparisons only

Answer 60

Look at the interval between the two means and potential variations of that interval if the study was repeated If the possible variation of intervals between the two means includes 0 that indicates there is the potential for no difference – and the experimental hypothesis can be rejected

Answer 61

T-test shows significant difference CI demonstrates statistical significance but also estimates the size of the effect as well

Answer 62

Independent because two different groups of individuals with two different levels of within group variability Use to compare control group with experimental group

Answer 63

Dependent because it compares two measurements for the same group of people with very similar within group variability because they are the same people Test compensates for the similarity of variances Use includes comparison of pre-post changes in a single group

Exam 2 Flashcards

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