Funnel plots are typically used to display:
Bias is the term used to describe an error at any stage of the study that was not due to chance. Bias leads to the systematic difference between the results from a study and the true states of affair. Bias may be introduced at all stages of the research process, from study design, through to analysis and publication. Bias can create a spurious association or mask a real association.
Good research design can reduce the effect of bias (e.g. blinding, randomisation) but they cannot eliminate it completely. Increasing the sample size does not reduce bias.
Selection bias occurs when patients included in the study are not representative of the population to which the results will be applied. It may be sampling bias, introduced by the researches, or response bias, introduced by the study population. Selection bias can happen not only at the recruitment stage of a study but also when subjects are allocated to different arms.
Sampling bias:
Response bias:
Allocation bias:
Attrition bias occurs where those who drop-out or are lost to follow-up in a longitudinal study differ in a systematic way from those not lost to follow-up. Thus those left at the end of the study might not be representative of the study sample that was randomised at the start.
Bias may also occur after performing a study.
Funding bias is where there is a tendency to report findings in the direction favoured by the funding body and publication bias is where there is a tendency to publish only those papers that report positive, statistically significant or topical results. Excluding studies in a foreign language is another form of reporting bias.
Funnel plots are used to demonstrate the existence of publication bias in meta-analysis. Funnel plots are scatter plots of treatment effects estimated from individual studies on the x axis and some measure of study size on the y axis. Each point on the graph represents one of the studies. A symmetrical inverted funnel shape indicates an absence of publication bias. If there is publication bias, there will be asymmetry of the open wide end due to the absence of small negative results.

Funnel plot on right side demonstrating publication bias, funnel plot on left side in absence of bias.
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| Biochemistry | Normal Value |
|---|---|
| Sodium | 135 – 145 mmol/l |
| Potassium | 3.0 – 4.5 mmol/l |
| Urea | 2.5 – 7.5 mmol/l |
| Glucose | 3.5 – 5.0 mmol/l |
| Creatinine | 35 – 135 μmol/l |
| Alanine Aminotransferase (ALT) | 5 – 35 U/l |
| Gamma-glutamyl Transferase (GGT) | < 65 U/l |
| Alkaline Phosphatase (ALP) | 30 – 135 U/l |
| Aspartate Aminotransferase (AST) | < 40 U/l |
| Total Protein | 60 – 80 g/l |
| Albumin | 35 – 50 g/l |
| Globulin | 2.4 – 3.5 g/dl |
| Amylase | < 70 U/l |
| Total Bilirubin | 3 – 17 μmol/l |
| Calcium | 2.1 – 2.5 mmol/l |
| Chloride | 95 – 105 mmol/l |
| Phosphate | 0.8 – 1.4 mmol/l |
| Haematology | Normal Value |
|---|---|
| Haemoglobin | 11.5 – 16.6 g/dl |
| White Blood Cells | 4.0 – 11.0 x 109/l |
| Platelets | 150 – 450 x 109/l |
| MCV | 80 – 96 fl |
| MCHC | 32 – 36 g/dl |
| Neutrophils | 2.0 – 7.5 x 109/l |
| Lymphocytes | 1.5 – 4.0 x 109/l |
| Monocytes | 0.3 – 1.0 x 109/l |
| Eosinophils | 0.1 – 0.5 x 109/l |
| Basophils | < 0.2 x 109/l |
| Reticulocytes | < 2% |
| Haematocrit | 0.35 – 0.49 |
| Red Cell Distribution Width | 11 – 15% |
| Blood Gases | Normal Value |
|---|---|
| pH | 7.35 – 7.45 |
| pO2 | 11 – 14 kPa |
| pCO2 | 4.5 – 6.0 kPa |
| Base Excess | -2 – +2 mmol/l |
| Bicarbonate | 24 – 30 mmol/l |
| Lactate | < 2 mmol/l |