6.8.2. Input Data Types
UNISTAT classifies commonly used data types into four groups:
1) 2 x 2 Tables
2) Ratios
3) Unpaired Samples
4) Paired Samples
Once the columns of the data matrix to be used in the analysis are selected as [Variable]s in the Variable Selection Dialogue, a second dialogue facilitates assigning a specific input data type and a task to each variable.
This threelevel menu system allows you to combine almost any type of study result entered in a simple spreadsheet format. Once the selections are made, you can save them to a file so that the selection process is not unnecessarily repeated. The default extension for meta analysis template file is .MTA.
The full extent of selection possibilities for these six data groups are given in the following tables.
2 x 2 Tables 
Ratios 
Unpaired Samples 
Paired Samples 
Label 
Label 
Label 
Label 
Group 
Group 
Group 
Group 
Cells 
Odds Ratio 
Number of Cases 
Number of Pairs 
A 
Odds Ratio 
Cases A 
Mean 
B 
Ln(Odds Ratio) 
Cases B 
Mean A 
C 
Risk Ratio 
Mean 
Mean B 
D 
Risk Ratio 
Mean A 
Mean Diff 
Sums 
Ln(Risk Ratio) 
Mean B 
Standard Error 
A+B 
Rate Ratio 
Mean Diff 
Std Err A 
C+D 
Rate Ratio 
Standard Error 
Std Err B 
Ratios 
Ln(Rate Ratio) 
Std Err A 
Std Err Diff 
A/(A+B) 
Hazard Ratio 
Std Err B 
Std Err Corr 
C/(C+D) 
Hazard Ratio 
Std Err Pooled 
Standard Deviation 
ChiSquare 
Ln(Hazard Ratio) 
Std Err Overall 
Std Dev A 
ChiSquare 
Risk Difference 
Standard Deviation 
Std Dev B 
Number of Cases 
Rate Difference 
Std Dev A 
Std Dev Diff 
Sign 
Observed – Expected 
Std Dev B 
Std Dev Corr 
Pairs 
Standard Error 
Std Dev Pooled 
Variance 
P pair 
Standard Error 
Std Dev Overall 
Var A 
Q pair 
Ln(Std Err) 
Variance 
Var B 
R pair 
Variance 
Var A 
Var Diff 
S pair 
Variance 
Var B 
Var Corr 
Rho 
Ln(Variance) 
Var Pooled 
Test Statistic 
Confidence Interval 
Var Overall 
tstat 

Lower Bound 
Test Statistic 
Fstat 

Upper Bound 
tstat 
Zstat 

Confidence Level 
Fstat 
Pvalue 

Zstat 
P (tdist) 

Pvalue 
P (Fdist) 

P (tdist) 
P (normal) 

P (Fdist) 
Tails 

P (normal) 
Confidence Interval 

Tails 
Lower Bound 

Confidence Interval 
Upper Bound 

Lower Bound 
Confidence Level 

Upper Bound 
Correlation 

Confidence Level 
Fisher’s Z 

Regression Coeff 
Std Mean Diff 

Standardised 
Sign 



Unstandardised 



Point Biserial Corr 



Std Mean Diff 



Hedges’ g 



Sign 

6.8.2.1. 2 x 2 Tables
Normally, cell frequencies from a 2 x 2 table are entered for each study. However, UNISTAT also accepts data in the form of sums and ratios. If one or more cell frequencies are zero, 0.5 is added to all four frequencies. Optionally, if the data is paired, an external correlation ρ (rho) can be entered.
The commonly used effect sizes for 2 x 2 tables are as follows:
Odds ratio:
Peto odds ratio:
where:
Risk ratio:
Risk difference:
Standardised mean difference:
Correlation from a chisquare statistic and sample size for a 2 x 2 table:
If a chisquare statistic and sample size from a 2 x 2 table is reported by a study, the correlation and its standard error are calculated as:
Event pairs:
Define each cell frequency from pairs data as:
A = P + Q
B = P + R
C = R + V
D = Q + V
For the calculation of other effect size measures based on d, see 6.8.2.3. Unpaired Samples.
6.8.2.2. Ratios
Given the odds ratio and its dispersion measure, the standardised mean difference d is calculated as above. Other ratios can only be compared within their own group.
6.8.2.3. Unpaired Samples
Select this option if the individual study is based on unpaired (or unmatched or independent or unequal size) samples consisting of continuous data.
The following data entry combinations are possible to calculate the standardised mean difference d, which is one of the most commonly used summary effect size for continuous data.
Sample sizes and means are given:
When the standard deviations are given, the standardised mean difference is calculated as:
where s_{p} is the pooled standard deviation:
The standard error of d is calculated as:
When standard errors or variances are given for samples A and B, standard deviations are calculated first.
UNISTAT also accepts data where difference in means is given instead of individual means and pooled or overall standard deviation is given instead of individual standard deviations.
When the overall standard deviation is given, the pooled standard deviation is calculated as:
The overall standard error and variance are converted into overall standard deviation first.
Sample sizes and the test statistic are given:
tstatistic is given:
The standard error of d is calculated as above.
Fstatistic from a oneway ANOVA is given:
Find tstatistic as:
and use the formula for tstatistic to calculate the standardised mean difference.
Zstatistic is given:
The Zstatistics can be used instead of tstatistic:
and the formula for tstatistic is used to calculate the standardised mean difference.
Sample sizes and the pvalue are given:
Pvalue from a ttest and its tail (1 or 2) are given: The tvalue is found using the inverse tdistribution with n_{A} + n_{B} – 2 degrees of freedom. If the tail value is not specified, a twotailed test is assumed.
Pvalue from an Ftest is given: The Fvalue is found using the inverse Fdistribution with 1 and n_{A} + n_{B} – 2 degrees of freedom.
Pvalue from a Ztest and its tail (1 or 2) are given: The Zvalue is found using the inverse normal distribution. If the tail value is not specified, a twotailed test is assumed.
Standardised regression coefficient:
Enter the standard deviation of dependent variable as Sample B standard deviation (or standard error or variance).
where b is the standardised regression coefficient and the pooled standard deviation is calculated as:
The standard error of d is calculated as in the Sample sizes and means are given option above.
Unstandardised regression coefficient:
Enter the standard deviation of dependent variable as Sample B standard deviation (or standard error or variance). Standard deviation of sample A (which is assumed to be a binary variable containing 0s and 1s only) is calculated as:
Given the unstandardised regression coefficient β, the standardised regression coefficient b and d are calculated as:
where the pooled standard deviation is as calculated as above. The standard error of d is calculated as in the Sample sizes and means are given option above.
Point Biserial Correlation:
where:
The standard error of d is calculated as in the Sample sizes and means are given option above. If a pvalue is given for point biserial correlation, select the Pvalue from a ttest option above.
Other effect sizes based on standardised mean difference are calculated as follows.
Mean Difference:
and its standard error is:
Hedges’ g:
Hedges’ correction factor for standardised mean difference d is:
where:
Hedges’ g is defined as:
The standard error of Hedges’ g can be calculated in one of the two following ways, which can be selected from the intermediate inputs dialogue. The default and recommended SE is:
and the alternative definition is:
Odds Ratio:
The correction factor for log odds ratio is:
The log odds ratio and its standard error can be calculated from standardised mean difference as:
The odds ratio is:
Correlation:
Given standardised mean difference and its standard error, the correlation and its SE are calculated as:
where:
and:
Fisher’s Z:
Fisher’s Z and its standard error are calculated from a given correlation as:
6.8.2.4. Paired Samples
This option should be selected when the individual study is based on paired (or matched or equal size) samples consisting of continuous data. This group also includes correlation coefficients and pre/post correlations. If the correlation value is not available, the imputed r value is used instead. The default value for imputed r is 0.5.
When only a tstatistic and the sample size are given, there are two ways of calculating the effect size. If the tstatistic was originally reported for a correlation coefficient, then in the intermediate inputs dialogue choose Yes for Use paired ttest box.
The following data entry combinations are possible to calculate the standardised mean difference d. Other effect sizes based on standardised mean difference are calculated as in unpaired samples above.
Sample size, means and standard deviations are given:
The standardised mean difference is calculated as:
where:
When r is not available and it is substituted by the imputed r value of 0.5, the correction factor for the correlation (i.e. the term in square brackets) simply disappears and the standardised mean difference formula becomes identical to the unpaired samples case.
The standard error of d is calculated as:
When standard error or variance is given for the paired differences, standard deviations are calculated first.
UNISTAT also accepts mean difference and standard deviation instead of individual means and standard deviations.
Sample size and the test statistic are given:
tstatistic is given:
The standard error of d is calculated as above.
Fstatistic from a oneway ANOVA is given:
Find tstatistic as:
and use the above formula to find d.
Z statistic is given:
Sample size and the test statistic are given (paired ttest):
To use paired ttest for correlations you need to select this option from the intermediate inputs dialogue first. The correlation is calculated as:
The standard error of d is calculated as.
where:
Sample sizes and pvalues are given:
Pvalue from a ttest and its tail (1 or 2) are given: The tvalue is found using the inverse tdistribution with n_{A} + n_{B} – 2 degrees of freedom. If the tail value is not specified, a twotailed test is assumed.
Pvalue from an Ftest is given: The Fvalue is found using the inverse Fdistribution with 1 and n_{A} + n_{B} – 2 degrees of freedom.
Pvalue from a Zstatistic and its tail (1 or 2) are given: The Zvalue is found using the inverse normal distribution. If the tail value is not specified, a twotailed test is assumed.