Meta analysis is a method that combines two or more studies into one. Suppose there are several studies on the effectiveness of fertilisers on increasing rice production. One study was conducted in the eastern region of Indonesia, where n was 100, resulting in a 30 percent increase, while another was conducted in the western region of Indonesia, where n was 75, resulting in an increase of 60 percent (at the same level). A meta-analysis is needed to combine the two studies with n, which means 175 replications. Meta-analysis is very useful for policy analysts because it summarises primary research into a useful synthesis to produce a policy recommendation, both in the exact and social fields. Meta-analysis is used if you have an urgent need or lack of funds to conduct research from Sabang to Merauke.

Because this meta-analysis is a method of combining research, not many can use it. In the description of a research pyramid, this meta-analysis is at the top, meaning that there are fewer studies and must be supported by the number of primary studies below it. This means that if we find a paper on a particular topic using a meta-analysis approach, we may have to look for another topic.

Meta-analysis is also a justifiable method for combining several quantitative studies. For example, when we talk about rice productivity, we usually find productivity in the Java Island region to be higher than in other regions. Combining several studies on productivity will be scientifically justified with a meta-analysis approach.

## Types of meta-analysis.

Before directly practising using meta analysis, it is necessary to understand that meta analysis has dependent and independent variables; this is the hallmark of the quantitative method. Sometimes we find meta-analyses explaining one independent variable but many dependent variables. Example: the effect of giving black seed on the weight of the cow and the volume of the cow’s milk. There is only one independent variable, namely habattussaudah, and two dependent variables: the weight of the cow and the volume of the cow’s milk.

There are also examples of meta-analyses where there is one dependent variable but many independent variables. Example: differences in organic and conventional productivity in several food crops One dependent variable is productivity, and the two independent variables are organic and conventional. In this example, there is already a subgroup, namely food crops, which could consist of rice, corn, soybeans, and others.

In practise, even though there is one independent variable and several dependent variables, or vice versa, work on the relationship between these variables is done one by one. So in the example of giving black seed to the weight of the cow and the volume of milk, two meta-analysis runs were carried out, namely habattussaudah to the weight of the cow and habattussaudah to the volume of the cow’s milk. Likewise, examples on one dependent variable and several independent variables are still carried out one by one.

After running one by one, the data presentation can be arranged according to the discussion. Here’s an example:

I captured this image from an article entitled Comparing the Yields of Organic and Conventional Agriculture.

The article talks about the comparison of organic and conventional productivity, which is divided into subgroup a. Crop type b, plant type c, and crop species So it only discusses one dependent variable, namely productivity.

In Part A of the figure above, it is explained that the x-axis is the productivity comparison between organic and conventional. So if it has a value of 1, it means that organic productivity is the same as conventional productivity. If the value is 0.8, it means that organic productivity is only 80 percent of conventional productivity. If seen in Part A, it means that the types of organic vegetable plants have the lowest productivity compared to the organic productivity of fruits, cereals, and others. In parts B and C, please look at the meaning yourself.

OK, the next meta-analysis example is taken from a journal article entitled Effect of dietary black cumin seed (Nigella sativa) on performance, immune status, and serum metabolites of small ruminants: A meta-analysis. Please search Google Scholar to read the full article.

This meta-analysis has one independent variable, namely black cumin seed, but two dependent variables, namely DMI and ADG. The image shown is the meta-regression, which will be explained below. The emphasis in this sub-chapter is that the presentation of meta-analysis can vary (according to the shrewdness of the researcher and the topic raised), but basically, the analysis process is carried out one relationship at a time.

## Exact meta-analysis.

Come on, practise right away… I use free software called OpenME. Please extract and open the software.

Prior to operating the software, there are things that must be prepared. First, you have to collect as many papers as possible on the topic you want to raise. To help, you can do a systematic literature review (to be discussed in a different article). After having a paper with a topic according to the research question, the data that needs to be collected is n (amount of data), mean (average), and std dev (standard deviation) for each control and treatment.

An example of data that needs to be prepared is this:

Yellow shading is the control group, and blue shading is the treatment or experimental group. Each consists of n data points (the amount of data), X is the mean (which is usually notated with the letters a, ab, or b), and SD is the standard deviation. This standard deviation is useful for knowing the long horizontal range at each point in the organic and conventional comparison images above.

Then data location, survey, processing, and season are optional. They are groupings. For example, place is a grouping based on place; we will use this later for subgroups. Just like the organic and conventional examples above, where the subgroups consist of crop types, plant types, and crop species.

If you want to do meta-regression, then the grouping requires continuous data, which is exemplified in column F or level. For example, on the effect of liquid fertiliser on increasing rice production Level can mean fertiliser levels according to treatment; some are 5 percent, 10 percent, 15 percent, and others. Because this data is continuous, meta-regression can be done like in the previous black cumin seed example.

Save the data in CSV format. Then open openmee.

Import data until it’s finished. Select the CSV file, then click OK.

The next step is to identify the variable by right-clicking on the column title and selecting continuous or count. In my example, the settings are as follows:

study >> mark as study ID column

lev >> continuous

Nc and Ne >> count

Xc, Xe, SDc, and Sde >> continuous

Later, it will be colourful like this:

The next step is to calculate the size of the effect. This effect size differs from one study to another. In order to be the same, the effect size needs to be uniform. Like currency, we agree to use the rupiah. Then all currencies are converted to rupiah according to their respective exchange rates.

How to calculate effect size: Click effect size to calculate effect size.

Then:

Then fill in according to the data we have as follows:

Click Finish, and the results will come out:

MD There is the mean difference, and var is the variance, which has the same unit amount of data and is ready for further analysis.

Okay, there are 3 types of meta-analysis output that I will write about here: standard meta-analysis, cumulative analysis, and subgroup analysis. The menu in the software is in the image below (which I will not repeat):

Let’s discuss the output of all three: **Standard meta-analysis**: fill in the data like this:

Select all, click next and finish.

The estimate above is the mean difference of all processed papers. With a lower bound, an upper bound, and, of course, the p-value. If the p-value is below 5 percent, there is a significant difference between the control and the treatment.

The heterogeneous examination was calculated based on the tau statistic. The greater the value of tau squared and I squared, the smaller the p value (meaning it is feasible because the variance is large).

The next image is like the one above.The small blue diamond image is the total mean difference of all the papers processed (in the example, there are 17 papers).Note that there are black and red vertical lines.Then 17 points with the wings (standard deviation)—if these wings touch the same vertical line, it is not significant.For example, papers 10, 11, and 13 both touch the red vertical line, meaning that the three are not significantly different.But paper 16 is significantly different from paper 8 because it doesn’t touch the same vertical line.Likewise, the others

The next output is a **cumulative analysis**, the same as a standard meta-analysis; the difference is that each paper is analysed based on the sequence.Look at the picture below:

What’s different is the picture at the far right, where there is a cumulative value when paper 2 is entered, and the mean changes every time a new paper is entered, so on until the last paper.

The next output is a **subgroup analysis**.We will be asked to choose which grouping to use based on existing data; for example, this time I chose survey.

The result is as follows:

Besides the blue rectangles, there are also two yellow rectangles representing the farm subgroup and the basketball subgroup. So the difference from the analysis above is that the data is divided by group and analyzed for each group.

The last output is **meta-regression**.

Click next until the post where we choose the variable to be the covariate.

We enter lev as the covariate, and the result is:

How do I read it? It’s the same as reading ordinary regression. Here it can be seen that adding levels to the experiment will actually reduce the mean difference. The bulleted list shows the mean difference in the sample with the standard deviation. If the bullet is large, it means that the deviation is also large.

## Social meta-analysis

In the social case, the data collected is only n and r (correlation). If the paper found is not in the form of a correlation, for example, regression or SE, it is necessary to convert it to r.

The next step is to import and identify each variable. N setting to count and r setting to continuous. No or study are used as the ID columns.

When calculating the effect size, use the settings below:

The results are found as follows:

Then, for the next analysis, we only use this Fisher effect and its variance. Not using initial data. More clearly, see this picture:

I hope it’s useful.

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