What are statistical tests?

Statistical tests are techniques used to analyze and make decisions based on data. They provide a systematic and objective way to analyze data and make inferences about a population based on a sample of data. These tests are used to determine if there is a relationship between variables, or to compare the means or proportions of different groups. They are widely used in various fields such as business, finance, healthcare, psychology, and social sciences to answer research questions and make evidence-based decisions.

The results of statistical tests are often reported as p-values, confidence intervals, and effect sizes, and they must be interpreted carefully in the context of the research question and the limitations of the test. The appropriate test to use depends on the type of data and research question.

Types of statistical tests: Parametric and non-parametric

There are two broad categories of statistical tests: parametric tests and non-parametric tests. Parametric tests make assumptions about the data being normally distributed and are typically used for interval or ratio level data, which have a meaningful zero point and allow for meaningful comparisons. Examples of parametric tests include t-tests, ANOVA (Analysis of Variance), and regression analysis.

Non-parametric tests, on the other hand, do not make assumptions about the distribution of the data and are typically used for ordinal or nominal level data, which do not have a meaningful zero point and do not allow for meaningful comparisons. Examples of non-parametric tests include Wilcoxon signed-rank test, Mann-Whitney U test, and Kruskal-Wallis test.

Regardless of the type of test used, it is important to remember that statistical tests provide only a tool to make decisions, and they must be used in conjunction with other information and critical thinking to make informed decisions.

What is parametric tests? Common types of parametric tests

Parametric tests are a type of statistical test that make assumptions about the population distribution, including normality and equal variances. Some common examples of parametric tests include:

1. t-test: This test is used to compare the means of two groups and determine if there is a significant difference between them.
2. ANOVA (Analysis of Variance): This test is used to compare the means of more than two groups and determine if there is a significant difference among them.
3. Regression analysis: This test is used to model the relationship between a dependent variable and one or more independent variables.
4. Pearson’s correlation coefficient: This test is used to measure the strength and direction of the linear relationship between two continuous variables.
5. Chi-square test: This test is used to compare the observed frequencies in a categorical data set to the expected frequencies.

It is important to keep in mind that parametric tests make assumptions about the population distribution, and it is crucial to assess the assumptions before conducting these tests. When the assumptions are not met, alternative non-parametric tests should be used instead.

Introduction to T-test

A t-test is a type of parametric test used to compare the means of two groups and determine if there is a significant difference between them. It assumes that the data is normally distributed and has equal variances. The t-test calculates a t-statistic and a p-value, which are used to make inferences about the population mean. The t-statistic is a measure of the difference between the sample means and the population mean, and the p-value is the probability of observing a t-statistic as extreme as the one calculated from the sample data, given that the null hypothesis is true.

The null hypothesis in a t-test is usually that there is no difference between the means of the two groups. If the p-value is less than a predetermined level of significance (e.g. 0.05), the null hypothesis is rejected and it is concluded that there is a significant difference between the means. If the p-value is greater than the level of significance, the null hypothesis is not rejected and it is concluded that there is not enough evidence to support a difference between the means.

There are two types of t-tests: a dependent t-test (also known as a paired t-test) and an independent t-test (also known as a two-sample t-test). A dependent t-test is used when the same individuals are being compared before and after some intervention, while an independent t-test is used when comparing the means of two distinct groups.

Examples of when a t-test might be used include:

1. Comparing the mean height of two groups of individuals, one group who received a new growth hormone treatment and one group who received a placebo.
2. Comparing the mean test scores of two classes, one class taught by a traditional teacher and one class taught by an online teacher.
3. Comparing the mean weight loss of two diet programs, one low-carbohydrate diet and one low-fat diet.

In each of these examples, a t-test would be used to determine if there is a significant difference between the means of the two groups, and to make inferences about the population mean.

Introduction to ANOVA test

ANOVA (Analysis of Variance) is a statistical test used to determine if there is a significant difference among the means of two or more groups. It is an extension of the t-test and is used when there are more than two groups being compared. ANOVA tests the null hypothesis that the means of all groups are equal.

In ANOVA, the total variance in the data is partitioned into two components: between-group variability and within-group variability. The between-group variability measures the variation between the means of the different groups, while the within-group variability measures the variation within each group. If the between-group variability is large relative to the within-group variability, it suggests that the means of the groups are different.

There are several types of ANOVA tests, including one-way ANOVA, two-way ANOVA, and repeated measures ANOVA. The one-way ANOVA tests the differences between the means of two or more groups with a single independent variable. The two-way ANOVA tests the differences between the means of two or more groups with two independent variables. The repeated measures ANOVA tests the differences between the means of two or more groups with a single dependent variable and a within-subjects independent variable.

Example of when ANOVA might be used:

1. Comparing the mean scores of three different teaching methods (lecture, group discussion, and individual projects) on a standardized test.
2. Comparing the mean yields of four different fertilizer treatments (A, B, C, and D) on crop growth.
3. Comparing the mean scores of three different diets (low-fat, low-carb, and balanced) on a weight loss program.

In each of these examples, ANOVA would be used to determine if there is a significant difference among the means of the groups, and to make inferences about the population means.

Overview of non-parametric statistical tests

Non-parametric statistical tests are a type of statistical test that do not assume a specific distribution (such as normal distribution) of the data. They are used when the data is not normally distributed or when the sample size is small. Non-parametric tests are also known as distribution-free tests.

Some common non-parametric tests include the Wilcoxon rank-sum test, the Kruskal-Wallis test, the Mann-Whitney U test, and the Friedman test. These tests are used to compare the difference between two or more groups in terms of their central tendency or location.

For example, the Wilcoxon rank-sum test is used to compare the median of two groups. The Kruskal-Wallis test is used to compare the medians of more than two groups. The Mann-Whitney U test is used to compare the medians of two groups and the Friedman test is used to compare the medians of more than two groups with a single dependent variable and a within-subjects independent variable.

Non-parametric tests are typically more robust than parametric tests and are less sensitive to outliers or skewness in the data. However, they may have lower power (the ability to detect a difference when it exists) compared to parametric tests.

Example of when non-parametric test might be used:

1. Comparing the median salary of employees in two different departments (marketing and finance).
2. Comparing the median number of sales made by three different salespeople (A, B, and C).
3. Comparing the median weight loss of two different diets (low-fat and low-carb).

In each of these examples, a non-parametric test would be used to determine if there is a significant difference between the medians of the groups and to make inferences about the population medians.

Wilcoxon Rank-Sum Test: an comprehensive overview

The Wilcoxon Rank-Sum Test, also known as the Mann-Whitney U Test, is a non-parametric test used to compare two independent groups and determine if there is a significant difference in the central tendency (e.g. median) between the two groups. The test is used when the data is not normally distributed or the sample sizes are small.

The Wilcoxon Rank-Sum Test works by ranking all the observations from the two groups together and then comparing the sum of ranks for each group. If the sum of ranks for one group is significantly larger than the other group, we can conclude that the central tendency for that group is higher.

Suppose we want to compare the effectiveness of two different types of headache medication. We conduct a study where 20 patients are randomly assigned to either medication A or medication B and the severity of their headache is rated on a scale of 0 to 10, with 0 being no headache and 10 being the worst headache. The data collected is as follows:

Medication A: 6, 5, 4, 7, 8, 9, 5, 7, 6, 8, 4, 6, 7, 5, 6, 7, 8, 9, 5, 7 Medication B: 5, 8, 9, 6, 7, 4, 8, 6, 5, 7, 8, 9, 5, 7, 6, 5, 4, 7, 8, 9

To perform the Wilcoxon Signed-Rank Test, we first rank the difference in headache severity for each patient, giving a positive rank for an improvement and a negative rank for a worsening. Then, we sum the positive ranks and negative ranks separately and compare the sum of positive ranks to a critical value. If the sum of positive ranks is significantly larger than the critical value, we can conclude that medication A is more effective in reducing headache severity.

This is just one example of a non-parametric test. Non-parametric tests are widely used in a variety of research areas when the data does not meet the assumptions of parametric tests, such as normality. Other common non-parametric tests include the Kruskal-Wallis Test, the Friedman Test, and the Wilcoxon Rank-Sum Test.

What is Wilcoxon Rank-Sum Test

The Wilcoxon Rank-Sum Test, also known as the Mann-Whitney U Test, is a non-parametric test used to compare two independent groups and determine if there is a significant difference in the central tendency (e.g. median) between the two groups. The test is used when the data is not normally distributed or the sample sizes are small.

The Wilcoxon Rank-Sum Test works by ranking all the observations from the two groups together and then comparing the sum of ranks for each group. If the sum of ranks for one group is significantly larger than the other group, we can conclude that the central tendency for that group is higher.

For example, suppose we want to compare the height of a sample of men and women. We measure the height of 20 men and 20 women and the data is as follows:

• Men: 68, 70, 71, 72, 72, 72, 73, 73, 74, 74, 75, 75, 75, 76, 76, 77, 77, 78, 78, 79
• Women: 63, 64, 65, 66, 66, 67, 67, 68, 68, 69, 69, 69, 70, 70, 71, 71, 72, 73, 74, 75

To perform the Wilcoxon Rank-Sum Test, we first rank all the observations from both groups and compare the sum of ranks for each group. If the sum of ranks for men is significantly larger than the sum of ranks for women, we can conclude that men have a higher central tendency for height.

This is a simple example of the Wilcoxon Rank-Sum Test. It is widely used in fields such as medical research, social sciences, and engineering when the data does not meet the assumptions of parametric tests.Regenerate resp

How to perform statistical tests correctly

When conducting a statistical test, it is important to specify the null hypothesis and the alternative hypothesis. The null hypothesis represents the default assumption that there is no relationship between the variables, while the alternative hypothesis represents the opposite assumption. The goal of the statistical test is to determine whether the sample data provides sufficient evidence to reject the null hypothesis in favor of the alternative hypothesis.

The significance level of a statistical test is used to control the probability of making a Type I error, which occurs when the null hypothesis is rejected when it is actually true. The most common significance level used is 0.05, which means that there is a 5% chance of making a Type I error. This level can be adjusted based on the consequences of making a Type I error in a particular situation.

Choosing the appropriate statistical test is a critical step in the data analysis process. The type of data, research question, and number of variables involved all play a role in determining the appropriate statistical test. It is important to understand the assumptions and limitations of each test and to interpret the results with caution, in the context of the research question and the limitations of the test.

One of the key challenges in using statistical tests is understanding the results and interpreting them in a meaningful way. It is essential to understand the meaning of p-values, confidence intervals, and effect sizes, and how they can be used to draw conclusions about the data. It is also important to be aware of potential confounding variables that could affect the results and to take steps to control for these variables.

In conclusion, statistical tests are an important tool for analysing and interpreting data. However, they must be used appropriately and with caution in order to obtain meaningful results. A thorough understanding of the assumptions, limitations, and interpretations of each test is essential for accurate and meaningful results. It is important to use statistical tests in conjunction with other analytical tools and to consider the results in the context of the research question and the limitations of the test.

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In the code below, I find the H1 element on my page, and then perform triple click on it

from selenium import webdriver
from selenium.webdriver.common.keys import Keys
from selenium.webdriver.common.action_chains import ActionChains

driver = webdriver.Chrome()
driver.get(“https://vutung.com/2019/08/23/how-to-use-timer-in-gtm-to-track-real-time-on-page/”)

triple_click_element = driver.find_elements_by_tag_name(‘h1’)[1]
actions = ActionChains(driver)
for i in range(3):
actions.move_to_element(triple_click_element).click()
actions.perform()

You can try to change the find_element_by… function with any other function that suit your needs

How to triple click on Selenium with Python

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Recently, Google has made an unsurprising move when limit the Search terms report. Before September, 2020, all search terms having more than 1 clicks will be shown in the search terms report, but now, Google limit it to a new threshold.

Google’s statements “…Search Terms Report to only include terms that a significant number of users searched for…” and how significant is enough will remain as a question. Search Engine Land reported that 20% of the search terms will be invisible to the users. Read more here https://searchengineland.com/googles-search-terms-move-will-make-millions-in-ad-spend-invisible-to-advertisers-340182

However, I recently find out that we still can access these report from Google Analytics, as long as the auto-tag feature is turned on. The key idea here is Google hid the search terms in Google Ads, but they have not hidden them in Google Analytics

It should be noted here that Google Analytics and Google Ads are 2 totally different systems, and the data will not be accurate as the old search term report, but this is the best we can have right now.

How to see the search terms that has been filtered in Google Analytics

Now, these are the procedure you can follow to unblock the Google Search terms report:

Step 1: Make sure the auto-tag is turned on and Google Analytics and Google Ads are linked

Step 2: Visit Google Analytics, go to Acquisition, Google Ads, Campaign

Step 3: Choose secondary dimension, type search query, and click on search query.

Step 4: Click on sessions to sort the data by the number of sessions. These filtered search terms are likely to be the search terms having 0 clicks, 0 impressions and >1 sessions (it is not totally correct)

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Basically, they are all click triggers, which means it is based on clicks to determine the tag is fired or not.

Just link is specifically used for “click on link”, and All elements is used for every click on website. Link click is any clicks on <a href…>, which could be a link to other sites, or may be click to call

2 examples that you will frequently met are:

• <a href=”https://vutung.com/2020/10/09/the-difference-between-all-element-and-just-link/”>Click here</a>
• <a href=”tel:+84982129595″>0982129595</a>

Every link click can trigger both All element and Just link, however, if it is a normal click (for example, click on submit button) then it will only trigger All elements click.

To determine which one you should choose, just think that is the click you want to be tracked, are link click or not.

Click here to read more about how to track real time-on-page by Google Tag Manager

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For example: If a person entered the website, then spent around 20 minutes reading your page, and gather all the information he needed, then he exit the page. He  is an potential customer, but in Google Analytics, he is count as a bounce, and session duration is 0.

How to use Google Tag Manager to track user’s time on page

Now, we can use Google Tag manager, timer trigger to fix that problem, by identify the real time-on-page for a particular page.

*** This trick should only be use in some specific pages, such as blog pages, or key pages, since it will send multiple hits to GA, and send much more events than normal.

See more: Track every user behaviors by sending client ID

1, Send a hit after user spend 30 seconds on page.

Create the Timer trigger as follows:

1. Add a new trigger. Choose Timer as the event type.
2. Enter the desired timer interval in milliseconds, e.g. For a 30 seconds timer, enter 30000, and set the timer limit to 1 (only fire once per page)
3. At the conditions, you enter Page Url -> contains -> URL of the pages you want to track. Leave domain for all pages
4. This trigger fire on all timers

Now, you create a universal analytics event, with category and label as you wish. This will not affect any reports. The correct set up should look like this

2. Multiple timer on a page

What if you want to record multiple timer events from the same timer? A single 30 second timer is better than nothing, but what if visitors are spending 5, 10, or as much as 20 minutes on a single page before leaving your site? With only a 30-sec timer, your session duration metric could still be hugely misleading.

The set up will be quite the same, as following instructions below:

1, Create a timer trigger. Set up the same as above, but you should leave limit blank. This will allow the timer listener to fire indefinitely until the user leaves the page or closes their browser.

2, Create two new variables to capture the timerEventNumber and timerInterval auto-event variables as follows. At least right now, GTM does not create these macros by default:

Create a new variable named timerEventNumber, set to the value of the gtm.timerEventNumber variable in the data layer. This will return the count of the number of times that the timer listener has fired on the page.

Create a new variable named timerInterval exactly as above, but with gtm.timerInterval as the data layer variable name. This will return the timer interval that you have specified in the listener tag.

3, Configure a variable , custom javascript

Then input the following code into the custom Javascript

function() {
var elapsed = {{gtm.timerEventNumber}} * {{gtm.timerInterval}} / 1000;
var min = elapsed/60;
return min + ‘m ‘;
}

4, Configure your Universal Analytics event tag as follows.

Finally, in Google Analytics, it will look something like this

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Sending the Client ID as a Custom Dimension to Google Analytics is absolutely necessary. It’s the only way to get row-by-row reports split by user, and it’s the only way to query for data collected from any anonymous user.

The setup is really simple. You need a Custom Dimension setup in Universal Analytics, and then you simply need to add a new Field to set in your Page View tag (or whatever you want to use to send the data to GA)

1, Create Custom dimension in Google Analytics

Click on admin -> custom dimension

Name and choose the type. There are 3 scopes in Google Analytics: hit, session and user. Here, client ID is user scope, which related to each cookies.

Then click save. After creating the custom dimensions, there will be an associated index number with it. We will use this index number later.

2, Create a variable in Google Tag Manager

First, you navigate to Google Tag Manager, and create a new variable.

Then choose custom javascript

Name that client_id_setter, and input this script

function() {
     // Modify customDimensionIndex to match the index number you want to send the data to
     var customDimensionIndex = 5;
     return function(model) {
          model.set('dimension' + customDimensionIndex, model.get('clientId'));
}
}

REMEMBER TO CHANGE THE “customDimensionIndex” IN THE CODE TO THE INDEX NUMBER IN CUSTOM DIMENSION. Here, we must change it to 2

Then save.

3, Change Google Analytics variable

Refer to your Google Analytics variable

Click on More setting

Enter as below screenshot

Then save.

After all changes, you may see the client ID as secondary dimension

Good luck on your Digital Marketing career.

Source: https://www.simoahava.com/gtm-tips/use-customtask-access-tracker-values-google-tag-manager/

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