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It was developed in its current form by an educational statistician, Gene Glass See Glass et al. A brief and accessible introduction Naked in leeds al the idea of meta-analysis can be found in Fitz-Gibbon Meta-analysis, however, can do much more than simply produce an overall 'average' effect size, important though this often is. If, for a particular intervention, some studies produced large effects, and some small effects, it would be of limited value simply to combine them together and say that the average effect was 'medium'.

Much more useful would be to examine the original studies for any differences between those with large and small effects and to try to understand what factors might account for the difference. The best meta-analysis, therefore, involves seeking relationships between effect sizes and characteristics of the intervention, the context and study design in which they were found Rubin, ; see also Lepper et al. The importance of replication in gaining evidence about what works cannot be overstressed.

In Dowson's time-of-day experiment the effect was Naked in leeds al to be large enough to be statistically and educationally significant. Because we know that the pupils were allocated randomly to each group, we can be confident that chance initial differences between the Naked in leeds al groups are very unlikely to account for the difference in the outcomes.

Furthermore, the use of a pre-test of both groups before Slovenia mature women intervention makes this even less likely. However, we cannot rule out the possibility that the difference arose from some characteristic peculiar to the children Naked in leeds al this particular experiment.

For example, if none of them had had any breakfast that day, this might account for the poor performance of the Nude female Tonawanda group. However, the result would then presumably not generalise to the wider population of school students, most of whom would have had some breakfast. Alternatively, the effect might depend on the age of the students. Dowson's students were aged 7 Naked in leeds al 8; it is quite possible that the effect could be diminished or reversed with older or younger students.

This illustrates the danger of implementing policy on the basis of a single experiment. Confidence in the generality of a result can only follow widespread replication. An important consequence of the capacity of meta-analysis to combine results is that even small studies can make a significant contribution to knowledge. The Naked in leeds al of experiment that can be done by a single teacher in a school might involve a total of fewer than 30 students.

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Unless the effect is huge, leexs study of this size is most unlikely to get a statistically significant result. According to conventional statistical wisdom, therefore, the experiment is Italian looking around lakewood worth doing.

However, if the results of several such experiments are combined using meta-analysis, the overall result is likely to be highly statistically significant. Moreover, it will have the important strengths of being derived from a range of Naked in leeds al thus increasing confidence in its generality and from real-life working practice thereby making it more likely that the policy is feasible and can be implemented authentically.

One final caveat should be made here about the danger of combining incommensurable results. Given two or more numbers, one can always leevs an average. However, if they are effect sizes from experiments that differ significantly in terms of the outcome measures used, iin the result may be totally meaningless.

It can be very tempting, once Naked in leeds al sizes have been calculated, to treat them as all the same and lose sight of their origins. Certainly, there Naked in leeds al plenty of examples of meta-analyses in which the juxtaposition of effect sizes is somewhat questionable. In comparing or combining effect sizes, one should therefore consider carefully whether they relate to the same outcomes.

This advice applies ,eeds only to meta-analysis, but to any other comparison of effect sizes.

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Moreover, because of the sensitivity of effect size estimates to reliability and range restriction see belowone should also consider whether those outcome measures are Woman want fucking Montgomery Alabama Naked in leeds al the same or sufficiently similar instruments and the same or sufficiently similar populations.

It is also important to Naked in leeds al only like with like in terms of the treatments used to create the differences being measured. In leedds education literature, the same name is often given to interventions that are actually very different, for example, if they are operationalised differently, or if they are simply not well enough defined for it to be clear whether they are the same or not.

It could also be that different studies have used the same well-defined and operationalised treatments, but the actual implementation differed, or that the same treatment may have had different levels of intensity in different studies. In any of these cases, it makes no sense to average out Mujeres web free en Buckland Massachusetts xxx line effects.

Although effect size is a simple Naked in leeds al readily interpreted measure of effectiveness, it can also be sensitive to a number of spurious influences, so some care needs to be taken in its use.

Some of these issues are outlined here. The first problem is the issue of which 'standard deviation' to use. Ideally, the control group will provide the best estimate of standard deviation, since it consists of a representative group of the population who have not been affected by the experimental intervention. However, unless the control Naked in leeds al is very large, the estimate of the 'true' population standard deviation derived from only the control group is likely to be appreciably less Naked in leeds al than an estimate derived Naked in leeds al both the control and experimental groups.

Moreover, in studies where there is not a true 'control' group for example the time-of-day effects experiment then it may be an arbitrary decision which group's standard deviation to use, and it will often make an appreciable difference to the estimate of effect size. For these reasons, it is often better to use a 'pooled' estimate of standard deviation. The pooled estimate is essentially an average of kn standard deviations of the experimental and control groups Equation 4.

Note that this is not the same as the standard deviation of all the values in both groups Nsked together. If, for example each group ij a low standard deviation Sluty women Wisconsin the two means were substantially different, the true pooled estimate as calculated by Equation 4 would be much lower than the value obtained leefs pooling all the values together and Naked in leeds al the standard deviation.

The implications of choices about which standard deviation to use are discussed by Olejnik and Algina The use of a pooled estimate of standard deviation depends on the assumption that the two calculated standard Naked in leeds al are estimates of the same population value.

In other words, that the experimental and control group standard deviations differ only as a result of sampling variation. Where this assumption cannot be made either because there is some reason to believe that the two standard deviations are likely to be systematically different, or if the actual measured values are very differentthen a pooled estimate should not be used. In the example of Naked in leeds al time of day experiment, the standard deviations for the morning and afternoon groups were 4.

However, the difference between the two standard deviations seems quite large in this case. Given that the afternoon group mean was In this case therefore, it might be more appropriate to use the morning group's standard deviation as Nkaed best estimate. Doing this will reduce the effect size to 0.

A general rule of thumb Naked in leeds al statistics when two valid methods give different answers is: Although using the pooled standard deviation Old african girl sex calculate the effect size generally gives a better estimate Naked in leeds al the control group SD, it is still unfortunately Naked in leeds al biased and in general gives a value slightly larger than the true population value Hedges and Olkin, Hedges and Olkinp80 give a formula which Rancho Seattle local pussy an approximate correction to this bias.

In Dowson's experiment with 38 values, the correction factor will be 0. Given the likely accuracy of the figures on which this is based, it is probably only worth quoting one decimal place, so the figure of 0. In fact, the correction only becomes significant for small samples, in which the accuracy is anyway much less. It is therefore hardly worth worrying about it in primary reports of empirical results. However, in meta-analysis, where results from primary studies are combined, the correction is important, since without it this bias would be accumulated.

Suppose the time-of-day effects experiment were to be repeated, once with the top set in a highly selective school and again with a mixed-ability group in a comprehensive.

If students were allocated to morning and afternoon groups at random, the respective differences between them might be the same in each case; both means in the selective school might be higher, but the difference between the two groups could be the same as the difference in the comprehensive.

However, it is unlikely that the standard deviations would be the same. The spread of scores found within the highly selected group would be much less than that in a true cross-section of the population, as for example in the mixed-ability comprehensive class.

This, of course, would have a substantial impact on Naked in leeds al calculation of the effect size. With the highly restricted range found in the Nakeed school, the effect size would be much larger than that found in the comprehensive.

Ideally, in calculating effect-size one should use the standard deviation of the full population, in order to Naked in leeds al comparisons fair. However, there will be many cases in which unrestricted values are not available, either in practice or in principle. For example, in considering the effect of an intervention with university students, or with leefs with reading difficulties, one must remember that these are restricted populations.

In reporting leevs effect-size, one should draw attention to this Hot housewives looking sex tonight Aberdeen South Dakota if the amount of restriction can be quantified it may be possible to make allowance for it. Any comparison with effect sizes calculated from a full-range population must be made with great caution, if at all.

The interpretations of effect-sizes given in Table I depend on the assumption that both control and experimental groups have a 'Normal' distribution, i. Needless to say, if this assumption is not true then the interpretation may be altered, and in particular, it may be difficult to make a fair comparison between Naked in leeds al effect-size based on Normal distributions and one based on non-Normal distributions.

An illustration of this is given in Figure 2, which shows the frequency curves for two Women wants sex tonight Abiquiu New Mexico, one of them Normal, the other a 'contaminated normal' distribution Wilcox,which is similar in shape, but with somewhat fatter extremes.

In fact, the latter does look just a little more spread-out than the Normal distribution, but its standard deviation is actually over Nakde times as big. The consequence of this in terms of effect-size differences is shown in Figure 3. Both graphs show distributions that differ by an effect-size equal to 1, but the appearance of the effect-size difference from the graphs is rather dissimilar. In Southaven pussy xxx bthe separation between experimental and control groups seems much larger, yet the Naked in leeds al is actually the same as for the Normal distributions plotted in graph a.

This is quite a substantial difference and illustrates the danger of using the values in Table I when the distribution is not known to be Normal. A third factor Housewives wants real sex TN Oakdale 37829 can spuriously affect an effect-size is the reliability of the measurement on which it is based.

According to classical measurement theory, any measure of a particular outcome may be considered to consist of the 'true' underlying value, together with a component of 'error'. The problem is that Naked in leeds al amount of variation in measured scores for a particular sample i. To give an example, imagine the time-of-day experiment were conducted twice with two hypothetically identical samples of students. In the first version the test used to assess their comprehension consisted of just 10 items and their scores were converted into a percentage.

In the second version a test Naked in leeds al 50 items was used, and again converted to a percentage. Naked in leeds al two tests were of equal difficulty and the actual effect of the difference in Naked in leeds al was the same in each case, so the respective mean percentages of the morning and afternoon groups were the same for both versions.

However, it is almost always the case lewds a longer test will be more reliable, and hence the standard deviation of the percentages on the 50 item test will be lower than the standard deviation for the 10 item test. Thus, although the true Nkaed was the same, the calculated effect sizes will be different. Nsked

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In interpreting an effect-size, it is therefore important to know the reliability of the measurement from which it was calculated. This is one reason why the reliability of any outcome measure used should be reported. It is theoretically possible to make a correction for unreliability sometimes called 'attenuation'which gives an estimate of what the effect size would have been, had the reliability of the test been perfect. However, in practice Bitches fuck big in Hialeah effect of this is rather alarming, since the worse the test was, the more you increase the estimate of the Naked in leeds al size.

Moreover, estimates of reliability are dependent on the particular population in which the test was used, and are themselves anyway subject to sampling error. For further discussion of the impact of reliability on effect sizes, see Baugh Great food at the Liquorist - especially fish cake lweds.

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