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# Can I Believe It? Understanding Statistics in Published Literature - PowerPoint PPT Presentation

Can I Believe It? Understanding Statistics in Published Literature. Keira Robinson – MOH Biostatistics Trainee David Schmidt – HETI Rural and Remote Portfolio. Agenda. Welcome Understanding the context Data types Presenting data Common tests Tricks and hints Practice Wrap up.

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### Can I Believe It?Understanding Statistics in Published Literature

Keira Robinson – MOH Biostatistics Trainee

David Schmidt – HETI Rural and Remote Portfolio

• Welcome

• Understanding the context

• Data types

• Presenting data

• Common tests

• Tricks and hints

• Practice

• Wrap up

• Never consider statistics in isolation

• Consider the rest of the article

• Who was studied

• What was measured

• Why was that measure used

• Where was the study completed

• When was it done

• It is the author’s role to convince you that their results can be believed!

### Types of Data

Examples of data – Table 1Diamond et al. 2006

• Numeric

• Continuous (height, cholesterol)

• Discrete (number of floors in a building)

• Categorical

• Binary (yes/no, ie born in Australia?)

• Categorical (cancer type)

• Ordinal categorical (cancer stage)

• Represents continuous variables

• Areas of the bars represent the frequency (count) or percent

• Indicates the distribution of the data

• 6* 11

6* 2

6* 3333333

6* 44444444444

6* 555555555555

6* 66666666666666666666666

6* 777777777777777777777777777777

6* 8888888888888888

6* 99999999999999999999999999999999

7* 0000000000000000000000000

7* 1111111111111111111

7* 222222222222

7* 333333

7* 44

7* 55

• The average value:

• The observation in the middle

• Example- newborn birth weights

• 3100, 3100,3200,3300,3400,3500,3600,3650 g

• (3300+3400)/2 = 3350

• Not affected by extreme values

• Wastes information

• Mean is preferable

• Symmetric distributions mean ~ median

• Present the Mean

• Skewed distributions

• Mean is pulled toward the ‘tail’

• Present the Median

• The average distance between the observations and the mean

• Standard deviation :

• with original units , ie. 0.3 %

• Variance =

• With the original units squared

• Example, infant birth weight

• 3100, 3100,3200,3300,3400,3500,3600,3650, 3800

• Range = (3100 to 3800) grams or 700 grams

• Interquartile range: the range between the first and 3rd quartiles (Q1 and Q3)

• 3100, 3100,3200,3300,3400,3500,3600,3650 , 3800

• IQR = (3200 to 3600) grams or 400 grams

• Present standard deviation if the mean is used

• Present Interquartile range if the median is used

• Boxplot :

outlier

Maximum in

Q3

75th percentile (Q3)

IQR

Median

Minimum in Q1

25th percentile (Q1)

• Relative frequency for a categorical or discrete variable

Bar chart vs Histogram

• Histogram

• For continuous variables

• The area represents the frequency

• Bars join together

• Bar chart

• For categorical variables

• The height represents the frequency

• The bars don’t join together

• Areas of “slices” represent the frequency

• Tables should need no further explanation

• Means

• No more than one decimal place more than the original data

• Standard deviations may need an extra decimal place

• Percentages

• Not more than one decimal place (sometimes no decimal place)

• Sample size <100, decimal places are not necessary

• If sample size <20, may need to report actual numbers

### Statistical Inference

Inference

Sampling

• A statistic that is used as an estimate of the population parameter.

• Example: average parity

Population

Mean

Sample

Mean

• We are confident the true mean lies within a range of values

• 95% Confidence Interval: We are 95% confident that the true mean lies within the range of values

• If a study is repeated numerous times, we are confident the mean would contain the true mean 95% of the time

• How does confidence interval change as the sample size increases?

• Is our sample of babies consistent with the Australian population with a known mean birth weight of 3500 grams?

• Sample mean = 3800 grams, 95% CI of 3650 to 3950 grams

• 3800 lies outside of this confidence interval range, indicating our sample mean is higher than the true Australian population

• State a null hypothesis:

• There is no difference between the sample mean and the true mean: Ho = 3500

• Calculate a test statistic from the data t = 2.65

• Report the p-value = 0.012

• The probability of obtaining the data, ie a mean weight of 3800 grams or greater if the null hypothesis is true

• The smaller the p-value, the more evidence against the null hypothesis

• < 0.0001 to 0.05 – evidence to reject the null hypothesis (statistically significant difference)

• > 0.05 – evidence to accept the null hypothesis (not statistically significant)

• P –value: Indicates statistical significance

• Confidence interval: range of values for which we are 95% certain our true value lies

• Recommended to present confidence intervals where possible

• What are they used for?

• Analyse means

• Provide estimate of the difference in means between the two groups and the 95% confidence interval of this difference

• P-value – a measure of the evidence against the null hypothesis of no difference between the two groups

T tests- paired vs independent

• Paired:

• Outcome is measured on the same individual

• Eg: before and after, cross-over trial

• Pairs may be two different individuals who are matched on factors like age, sex etc.

• Calculate the difference for each of the pairs

• The mean weight at baseline was 93 kg and the mean weight at 3 months was 88 kg. The weight at 3 months was 5 kg less compared to the baseline weight 95% CI (-3, 12)

• There was no evidence that there was a significant change in weight after 3 months (p value = 0.19)

• Assumptions

• Bell shaped curve with no outliers

• Assess shape by graphing the difference

• Use a histogram or stem and leaf plot

• Two groups that are unrelated

• Eg: weights of different groups of people

• Same assumption as for paired t tests plus the assumption of independence and equal variance

• The mean weight in NW Public was 62 kg and the mean weight in SW Public was 61 kg

• The mean difference in weight between the two schools was 1 kg (-22, 24)

• There was no evidence of a significant difference in weight between the two schools (p=0.92)

• What happens when there are more than two groups to compare?

• Null hypothesis: means for all groups are approximately equal

• No way to measure the difference in means between more than two groups, so the variance between the groups is analysed

• Can measure variance within a group as well as variance between groups

• Comparing multiple groups

• There was evidence of a difference between the average student weight between the four schools p<0.05

• There was evidence of no difference between the average student weight between the four schools p>0.05

• Not advised to compare all means against each other because there is an increased chance of finding at least 1 result that is significant the more tests that are done

• Normality, - observations for all groups are normally distributed,

• Variance in all groups are equal

• Independence – all groups are independent of each other

• Two way-ANOVA:

• Multiple factors to be considered. Eg school and type of school (public/private)

• ANCOVA – Analysis of Covariance

• Tests group differences while adjusting for a continuous variables (eg. age) and categorical variables

• Measures the association between two continuous variables (weight and height)

• Or one continuous variable and several continuous variables (mutliple linear regression)

• What is the relationship between height and weight?

• Correlation between height and weight = 0.75

• Correlation between body fat and height = -0.23

• Fits a straight line to describe the relationship

• Assumes

• Independence for each measure (each person)

• Linearity (check with scatter plots)

• Normality (check residuals with a graph)

• Residuals are the difference between the data point and the regression line

• Homscedasticity

• Variability in weight does not change as height changes, ie

Multiple Linear Regression

• Extends the simple linear regression

• Example: Does smoking while pregnant affect infant birth weight?

• Outcome variable: infant birth weight

• Exposure variable: maternal smoking

• Covariates (other variables of interest):

• Sex of the baby, gestational age

• A variable (factor) associated with both the outcome and exposure variables

• Gestational age is associated with both smoking (exposure) and the outcome (birth weight)

• Confounders can be assessed by checking the correlation between the variable of interest and the outcome variable

• Correlation coefficient : -1.0 <r<1.0

• Rule of thumb: >0.5 or <-0.5 should be considered a confounder

Example of weight vs height adjusting for sex

• Comparing means from two group

• Use t- tests (paired for same person comparison, independent for independent groups comparison)

• Comparing means for more than two groups

• One-way ANOVA

• Comparing means for two or more groups and adjusting for other variables (ANCOVA)

• Assessing the relationship between two continuous variables

• Simple linear regression

• Assessing the relationship between two or more variables

• Multiple linear regression

### Chi-square tests

What can a chi-square test answer?

• 2x2 tables:

• Can be used for paired (same person under two different conditions) or independent samples (unrelated people in different groups)

• Used often in case-control studies where the outcome is categorical (or dichotomous)

• Tests no association between row and column factors

• Smoking and low birth weight association

• The study design defines the appropriate measure of effect

• Exposure is determined by

• Randomisation to different groups

• followed over time

• Outcome is determined at the end of follow up

• Rate of outcome can be estimated

• Eg. Rate of low birth weight in:

• Smokers: rate = 25/100 = 0.25 = 25%

• Non-smokers: = 5/105 = 5%

• Relative risk (RR) = 25/5=5 times higher risk of low birth rate in smokers relative to non-smokers

• Risk Difference (RD) = 25-5 = 20

• No relative difference between the low birth rate in smokers and non-smokers RR =1.0

• No absolute difference in the low birth rate in smokers and non-smokers = RD

• People observed at one point in time (questionnaire)

• Exposure and outcome are measured at the same time

• Causal associations cannot be deduced

• Rate ratio (RR) = 25/5=5 times higher risk of low birth rate in smokers relative to non-smokers

• Rate Difference (RD) = 25-5 = 20

• No relative difference between the low birth rate in smokers and non-smokers RR =1.0

• No absolute difference in the low birth rate in smokers and non-smokers = RD

• Use for rare outcomes (example: child prodigies)

• Children are selected based on being a prodigy

• Eg. 100 child prodigies and 100 children with normal intelligence

• Determine exposure retrospectively

• Cannot obtain a rate

• Must obtain the odds of the outcome and compare using an odds ratio

• Odds of being a prodigy:

• In exposed: 70/50 = 1.4

• In unexposed: 0.6

• Odds ratio:

• 1.4/0.6 = 2.3

• 2.3 times more likely to have a child prodigy if maternal fish oil supplements were taken during pregnancy

• Null hypothesis

• No association between the exposure and the outcome

• Odds Ratio = 1

• Both compare the relative likelihood of an outcome between 2 groups

• RR=1 or OR = 1

• Outcome is as likely in the exposed and unexposed groups

• RR>1 or OR >1

• The outcome is more likely in the exposed group compared to the unexposed group

• The exposure is a risk factor

• RR<1 or OR<1

• The outcome is less likely in the exposed group compared to the unexposed group

• The exposure is protective

• RR cannot be calculated for a case-control study

• OR ~ RR when the outcome is rare

• Small sample sizes

• Fisher’s exact test

• Recommended when n<20 or 20 <n<40 and the smallest expected cell count is <5

• Paired data

• Exact binomial test for small sample sizes

• McNemar’s test

• Multiple regression:

• Logistic regression

### Spurious statistics

• Vaccines and autism?

• Cell phones and brain tumours?

• 60.182 kg or 61kg?

• Reporting measurements with unnecessary precision

• Age divided into 20-44 years, 45-59 years, 60-74 years, 75+ years

• Dividing continuous data without explaining why or how

• Certain boundaries may be chosen to favour certain results

• Presenting Means and SD for non-normal data

• What should be presented instead?

• “The effect of more exercise was significant”

• “The effect of 40 minutes of exercise per day was statistically significant for decreasing weight (p<0.05)”

• “40 minutes of exercise per day lowered the mean weight of the group from 95 kg to 89 kg, (95% CI = 75-105 kg, p= 0.03)

• Checking the distribution of the data to determine the appropriate statistical test

• Using parametric tests when data is not normal

• Using tests for independent data when the data is paired

• Using linear regression without confirming linearity

• Not reporting what happened to all patients

• Leads to bias of the results

• Data dredging

• Multiple statistical comparisons until a significant result is found

• Not accounting for the denominator or adjusting for baseline

• Selection Bias

• Sampling from a bag of candy where the larger candies are more likely to be chosen

• On November 13, 2000, Newsweek published the following poll results:

• Other biases (measurement bias, intervention bias)

• Using cross sectional studies to infer causality

• More likely to have a c-section if attending a private hospital instead of a public hospital

• Working in groups quickly read the article provided

• Summarise

• What data they used

• What test

• Do you believe their findings?

• Can you explain why?

• Statistics must be understood in the context of the whole article

• Statistical tests must fit the data type

• Findings should be presented appropriately

• Beware flashy stats!

• It’s the author’s job to justify their choices

• If you don’t believe it- can you base your practice on it?