Evidence -Based Management (Some) statistics for managers who hate statistics

Postgraduate Course

Evidence-Based Management

(Some) statistics for managers who hate statistics

Postgraduate Course

Why do we need statistics?

1. How does my population look like?

2. Is there a difference?

3. Is there a model that ‘fits’?

Postgraduate Course

Some statistics

Some statistic terms

1. Sample vs population

2. Variables

3. Levels of measurement

4. Central tendency

5. Hypothesis

Some statistic models

6. Mean

7. Variance, standard deviation

8. Confidence intervals

9. Statistical significance

10. Statistical power

11. Effect sizes 12.Critical appraisal

Postgraduate Course

1. Sample vs population

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Sample vs population

We want to know about these(population: N)

We have to work with these(sample: n)

population mean: μ

selection

sample mean: X _

statistics

fit?

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Law of large numbers

The larger the sample size (or the number of observations), the more accurate the predictions of the characteristics of the whole population, and smaller the expected deviation in comparisons of outcomes.

As a general principle it means that, in the long run, the average (mean) of a large number of observations will be close to (or: may be taken as the best estimate of) the 'true mean’ of the population.


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Sample size: why does it matter?

Law of the large numbers: a reliable and accurate representation of the population

Statistical power: to prevent a type 2 error / false negative


Don’t confuse: representativeness and reliability

The sample size has no direct relationship with

representativeness; even a large random sample can be

insufficiently representative.

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2. VariablesPostgraduate Course

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VariablesPostgraduate Course

Variable: anything that can be measured and can differ across entities or time

Independent variable: predictor variable (value does not depend on any other variables)

Dependent variable: outcome variable (value depends on other variables)

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3. Level of measurementPostgraduate Course

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Level of measurementPostgraduate Course

Relationship between what is being measured and the numbers that represent what is being measured.

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Categorical

Continuous

Nominal

Ordinal

Interval

Ratio

Level of measurement

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Nominal scale

Classification of categorical data. There is no order to the values, they are just given a name (‘nomen’) or a number. The numbers can’t be used to calculate … (you can’t calculate the mean of fruit) .. only frequencies

1 = Apples2 = Oranges3 = Pineapples4 = Banana’s5 = Pears6 = Mango’s

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Ordinal scale

Classification of categorical data. Values can be rank-ordered, but the distance between the values have no meaning. The numbers can only be used to calculate a modus or a median

1. Full Professor2. Associate professor3. Assistant professor4. PhD5. Master6. Bachelor

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Interval scale

Classification of continuous data. Values can be rank-ordered, and the distance between the values have meaning. However, there is no natural zero point

1. John (1932)2. Denise (1945)3. Mary (19524. Marc (1964)5. Jeffrey (1978)6. Sarah (1982)

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Ratio scale

Classification of continuous data. Values can be rank-ordered, the distance between the values have meaning and there is a natural zero point.

1. Jeffrey (192 cm)2. John (187 cm)3. Sarah (180 cm4. Marc (179 cm)5. Mary (171 cm)6. Denise (165 cm)

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Nominal Ordinal Interval Ratio

Classification Yes Yes Yes Yes

Rank-order No Yes Yes Yes

Fixed and equal intervals No No Yes Yes

Natural 0 point No No No Yes

Nominal Ordinal Interval Ratio

Mode Yes Yes Yes Yes

Median No Yes Yes Yes

Mean No No Yes Yes

Levels of measurement

Categorical Continuous

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Levels of measurement

Ordinal or interval? Can I calculate a mean?

Q3: Every organization is unique, hence the findings from scientific research are not applicable.

☐ Strongly agree

☐ Somewhat agree

☐ Neither agree or disagree

☐ Somewhat disagree

☐ Strongly disagree

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4. Central tendency

The aim is to find a single number that characterises the typical value of the variable in the sample. Which one you use depends in part on the level of measurement of the variable.

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Central tendency

Central tendency of a set of data / numbers(what number is most representative of the dataset / population?)

7, 9, 9, 9, 10, 11,11, 13, 13

Mean = 10,2

Median = 10

Mode = 9

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Central tendency

Central tendency of a set of data / numbers(what number is most representative of the dataset / population?)

3, 3, 3, 3, 3, 3, 100

Mean = 16,9

Median = 3

Mode = 3

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5. Hypothesis

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“It is easy to obtain evidence in favor of virtually any theory,

but such ‘corroboration’ should count scientifically only if it

is the positive result of a genuinely ‘risky’ prediction, which

might conceivably have been false.

… A theory is scientific only if it is refutable

by a conceivable event. Every genuine test

of a scientific theory, then, is logically an

attempt to refute or to falsify it.”

Hypothesis: falsifiability

Carl Popper

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Hypothesis

Null hypothesis (H0): Big Brother contestants and members of the public will not differ in their scores on personality disorder questionnaires

Alternative hypothesis (H1): Big Brother contestants will score higher on personality disorder questionnaires than members of the public.

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Hypothesis: type I vs type II error

null hypothesis is true

& was rejected(type I error)

α

null hypothesis is false

& was rejected(correct conclusion)

null hypothesis is true

& was accepted(correct conclusion)

null hypothesis is false

& was accepted(type II error)

β

H0 is true H0 is false

reject H0

accept H0

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Statistic models

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Statistic models: prediction

likely not likely

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6. The mean

The most widely used statistic model

μX_

or

sample population

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The mean

EBMgt Lecturer

Num

ber o

f Frie

nds

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The mean

Assessing the fit of the mean

Sum of squared errors (SS): (-1,6) + (-0,6) + (0,4) + (0,4) + (1,4) = 5,2

Variance (s ): = = 1,3

Standard deviation (s): √s = 1,14

2 2 2 2 2

2 SSN-1

5,24

2

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The second most widely used statistic model

σs or

sample population

7. Standard Deviation

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Standard Deviation

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110IQ

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Standard Deviation

Which class would you prefer to teach?

130 170

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110 130IQ

S=10

S=20

S=60

170

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Standard Deviation

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Standard Deviation

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So, what does

“two standard deviations of the mean”

mean?

Standard Deviation

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8. Confidence intervalsPostgraduate Course

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A confidence interval gives an estimated range of values which is likely to include an unknown population parameter (e.g. the mean).

Confidence intervals are usually calculated so that this percentage is 95% (95% CI)

Confidence intervals

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When you see a 95% confidence interval for a mean, think of it like this: if we’d collected 100 samples and calculated the mean for each sample, than for 95 of these samples the mean would fall within the confidence interval.


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1,96!


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2008 2009

4,5

4,0

3,5

5,0

3,0

“According to the federal government, the unemployment rate has dropped from 4.3% to 3.8%.”

95% CI= 4,1 - 3,5.

This means the unemployment rate could have increased from 4.0 to 4,1 !


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When a point estimate (e.g. mean, percentage) is given, always check:

standard deviation

or

confidence interval


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9. Statistical significance

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Statistical significance

Sir Ronald A. Fisher1890 - 1962

Significant = the probability of incorrectly rejecting the null hypothesis (= Type I error, α)

p = 0,05 / p = 0,01

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(1 in 20 / 1 in 100)

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110 130

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1. Is there a difference / an effect?

2. How certain is it that the difference / effect found is not a chance finding?

X_

0 X_

1


Testing multiple hypothesis

When you test 20 different hypotheses (or independent variables), there is a high chance that at least one will be

statistically significant.

example:

Does apples, bacon, cheese, eggs, fish, garlic, hazelnuts, ice cream, ketchup, lamb, melons, nuts, oranges, peanut butter, roasted food, salt, tofu, vinegar, wine or yoghurt cause cancer?

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Significance testing:

always prospective, never retrospective

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Statistical significant ≠ practical relevant

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Effect size


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10. Statistical power

Sample size Effect size (Significant increase in IQ)

4 10

25 4

100 2

10.000 0,2

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Statistical power

The statistical power: the power to detect a meaningful effect, given sample size, significance level, and effect size.

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Overpowered: sample size too large, high probability of making a Type I error

Underpowered: sample size too small, high probability of making a Type II error.

Statistical power

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11. Effect size

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Effect size

Effect size: a standardized measure of the magnitude of effect, independent of sample size

standardized > makes it possible to compare effect sizes across different studies that have measured different variables, or have used different scales of measurement

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Effect sizes

Cohen’s d

Pearson’s r

other - Hedges’ g

- Glass’ Δ

- odds ratio OR

- relative risk RR

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Effect sizes

Cohen’s d

Effect size based on means or distances between/among means

Interpretation

< .10 = small

.30 = moderate

> .50 = large

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Effect sizes

Pearson’s r

Effect size based on ‘variance explained’

Interpretation

< .10 = small (explains 1% of the total variance)

.30 = moderate (explains 9% of the total variance)

> .50 = large (explains 25% of the total variance)

Postgraduate Course

12. Critical appraisal

When you critically appraise a study, what characteristics of the findings will you consider to determine its statistical significance and magnitude?

Postgraduate Course

Critical appraisal

When you critically appraise a study, what characteristics of the findings will you consider to determine its statistical significance and magnitude?

p-value

confidence interval

sample size / power

effect size

practical relevance

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Evidence -Based Management (Some) statistics for managers who hate statistics