Med Lit - Lecture 17 - Centrality and Dispersion and Hypothesis Review - King

observation value where total observations are divided equally, ie. same number of observations above as there are below

Median

what measure of central tendency is useful with SKEWED distributions when outliers might present a problem?

Median

Most frequent measurement

Mode

what is the highest peak in a frequency distribution graph?

Mode

what measure of central tendency is used for bimodal distributions?

Mode

what offers the LEAST information of the 3 basic measures of central tendency?

Mode

can you use parametric analysis in skewed distribution?

NO- you need a NORMAL distribution

The ___ hypothesis presumes NO relationship between the independent and dependent variable. Any relationship between variables must be due to CHANCE.

NULL ie. any relationship between the variables must be due to chance

what type of skewed distribution is typical of a learning curve?

Negative (left) skewed distribution

statistical significance involves a P values of _____ or less

0.05

what is the rule of thumb for SE error bars?

1. If the gap is about the size of one-sided error bar, the difference is significant at P < 0.05 2. If the gap is about the size of one entire error bar, the difference is significant at about p < 0.01

what are the 3 measures of central tendency?

1. Mean 2. Median 3. Mode

How do you calculate the Z-score?

1. Obtain Mean of data 2. Obtain difference between mean and the datum (x) 3. Divide this difference by the standard deviation of the data set

what are 2 types of error bars that are appropriate in most journals?

1. Standard Deviation 2. Confidence Intervals *SEM should NOT be used as an error bar!!!!

what are 4 analytical outcomes of statistical tests?

1. True Positive 2. True negative 3. False Positive (type 1 error alpha) 4. False negative (type 2 error Beta)

3 ways to increase the power of a statistical test

1. increase alpha 2. decrease Beta 3. increase sample size

how to calculate variance

1. obtain average of data 2. obtain differences between each datum and the mean 3. square each of these differences 4. add the squared values 5. divide by 1 less the sample size

what are 3 things that influence power?

1. sample size (directly related to power) 2. Alpha and beta error limits 3. Effect size

a ___ % change is considered significant effect size

10%

what is considered an significant effect size?

10% change

For any normal distribution: what % of values lie within +/- 1 SD of the mean? what % of values lie within +/- 2 SD of the mean

68% of values lie within 1 95% of values lie within 2

A z-score of what represents an element equal to the mean

=0

A z-score of what is greater than the mean?

> 0

what is the distance between means of groups?

Effect size

There is a ___ relationship between Beta and Power

INVERSE

what is the rule of thumb for 95% CI error bars?

If the overlap is about half of one one-sided error bar, the difference is significant at ~p < -.05 if the error bars just abut, the difference is significant at ~ p< 0.01

Is there a direct or inverse relationship between sample size and effect size?

Inverse you need a larger sample size to detect a small effect size

In general, the SMALLER the effect that must be demonstrated, the ___ the sample size that is required

LARGER

In a highly skewed distribution, what measure of central tendency may be misleading as it is affected by extremes?

MEAN

what may be a more useful expression of central tendency in highly skewed distributions?

MEDIAN

sum of all observations divided by the number of observations. represented by Greek mu

Mean

standard parametric statistics assumes that _____ is the appropriate measure of central tendency and ___ is a measure of variation within the group

Mean SD *this is only true if data is normally distributed

The mean of a set of z-scores are always = to what? The standard deviation of a set of z-scores is always = ?

Mean= 0 SD= 1

what are the units of Z-score?

None it is a relative measure that is independent of absolute units

what hypothesis forms the basis for all statistical tests?

Null Hypothesis

The ___ of a test is its ability to detect a real effect or difference

POWER

the null hypothesis is more likely to be accepted or rejected if the sample size is extremely large

REJECTED

Sample size is more dependent upon ___ and ___ than power

SD and effect size

SEM =

SD/ Square root of n

what estimates the accuracy with which the sample mean resembles the population mean?

SEM (standard error of the mean)

what is the width or breadth of curve?

Standard error

T or F: a statistically significant finding DOES NOT show that the demonstrated difference is clinically, scientifically, or practically meaningful

TRUE

T or F: a statistically significant finding may have absolutely NO practical importance

TRUE

Power of a test is defined as 1- B. T or F

TRUE Power= 1-B

what is the ability of the test to detect what the researchers are looking for?

The power of a test ( 1-beta)

In skewed populations, the median is between the mean and mode. T or F

True

T or F: outliers can be very valuable

True, some outliers may be the only individuals responding or not responding to the treatment they are seen to distort the essential nature of the sample but can be very valuable

Reject the null but null is true: what type of error?

Type 1 error (false positive alpha) (the test found a difference but there really is none )

Retain the null but the null is really false: what type of error?

Type 2 (beta): false negative (the test found no difference but there really is a difference)

Statistical tests generally assume that the experimental treatment will or will no have an effect?

WILL NOT- null hypothesis (forms the basis for all statistical tests)

the number of standard deviations a value is from the population mean

Z score (Z-stat)

Data can be normalized using what?

Z-scores this distributes the data equally around 0 and the SD is normalized to 1

What is a Type 2 error (beta)

a false negative: groups differ but test found no difference

what is a Type 1 error (alpha)?

a false positive: groups do not differ but test found a difference

what is the distance of the NULL mean to critical value?

alpha

By convention: alpha is often ___ %, Beta is ___ % and power is ____ %.

alpha= 5% Beta= 20% Power= 80%

The greater the overlap of error bars, the greater the likelihood that the 2 means are/are not significantly different

are NOT

Skew is an indication of ____

asymmetry *more than half of cases are above or below the mean

Mode is sometimes useful in describing what?

categories of subjects or data (qualitative data)

what is the distance of TEST mean to critical value?

determined by beta

ES= ?

difference in group means/ SD

Effect size =

difference in group means/ SD

Alpha and power are ____ related

directly

what is generally used for observations measured on a logarithmic scale?

geometric mean

CI and SE bars tend to decrease as sample size _____

increases

alpha and beta are ____ related

inversely

when you increase standard deviation what happens to the curve?

it flattens (broader distribution)

As 2 samples become less statistically significant, what happens to P value?

it goes up

why is range not an ideal measure of dispersion or variation in the data?

it is greatly affected by outliers

A z-score < 0 is less than the _____

mean

If no value repeats, there is no ____

mode

The mean, median, and mode are equivalent in what type of distribution

normal distribution

distribution if Mean= Median

normal distribution (symmetric)

The mean is used for what type of data?

numerical data and symmetric (NOT skewed) distributions

The position of any given datum or value relative to all of the others is described by its ___ value

percentile

Mean is only for what type of data?

quantitative

what are 3 measures of dispersion?

range standard deviation standard error

Variability (reduces/improves) certainty

reduces

what does the area under the curve of any graph represent?

relative frequency or probability

what hypothesis: 1. states the point of the study 2. states the objective of the measurements and analyses 3. Includes indication of practically significant effect size 4. refers to the sample under study 5. is directly tested

research hypothesis

In a positive skew, the longer tail is to the ___ of the peak

right

It is of the ___ of the distribution that determines the best choice for the measure of central tendency

shape

distribution if Median > Mean

skewed to the left (Negatively skewed)

distribution if Mean > Median

skewed to the right (positively skewed)

Small effect = Medium effect= large effect=

small = 0.0-0.2 medium= 0.2-0.5 large = > 0.5

Beta errors (Type II errors/False negatives) most commonly arise because of

small sample size

The narrower the curve the ___ the standard deviation

smaller

the SEM is always (smaller/larger) than the SD and is (more/less) dependent upon sample size

smaller, more dependent

the square root of the variance

standard deviation

What are Z scores?

the Standard Deviation

what measures how the observations are spread around the mean?

the variance of a sample

T or F: SD does NOT change with sample size

true

measures of data dispersion or spread

variability measures

a ____ variation will have a broader curve

wider standard variation will have a broader curve