Ranking rules. Open Library - open library of educational information

Features of ranking numerical characteristics:

1) The smallest numerical value is assigned rank 1.

2) The highest numerical value is assigned a rank equal to the number of ranked values.

3) If several initial values ​​turn out to be equal, then they are assigned a rank equal to the average value of the ranks that these values ​​would receive if they stood in order one after another and were not equal.

4) The total sum of real ranks must coincide with the calculated one, determined by the formula:

6) If it is necessary to rank a sufficiently large number of objects, they should be combined according to some criterion into fairly homogeneous classes (groups), and then the resulting classes (groups) should be ranked.

Example 1.1. Indicators of nonverbal intelligence were obtained from 11 subjects, which are presented in the table. Rank these indicators. Check the ranking for accuracy.

Solution: The third column of the table must be filled in. The numbers in brackets are auxiliary entries in case of equal values. In our case, this is the value 117. It occurs twice (eighth and ninth in order). Consequently, the rank of this value is equal to the arithmetic mean of the numbers 8 and 9, i.e. 8.5.

Examination:

1) Sum of ranks: 6+4+11+10+8.5+8.5+3+5+7+1+2=66

2) According to the formula: = =11 6 = 66

3) Compare the results: 66 = 66, therefore, the ranking was done correctly.

Issues for discussion

1. What is called a measurement, a unit of measurement? How does measurement in psychology differ from measurement in science and technology?

2. What is coding? At what stages of scientific research does a psychologist work with numerical codes?

3. What types of measurement scales are there? What are the fundamental differences between the types of scales?

4. What are the features, examples and special cases of the nominative scale? What are other names for this scale? What statistical methods are applicable to this scale?

5. Rank scale: its features, examples. Other names for the ranking scale. Statistical methods applicable to the ranking scale.

6. What is ranking? What are the ranking rules?

7. How to check the correctness of ranking?

9. Interval scale: features, examples. Interval and its size. Applicability of statistical methods to interval scales.

10. The ratio scale and its difference from the interval scale. Applicability of the attitude scale in psychology.

11. You are measuring the consent of ninth-graders to continue studying in a specialized class at the school. The student can answer “Yes” or “No”. On what scale is it carried out? given measurement?

12. The weight and height of younger schoolchildren are measured. On what scale is the measurement carried out?

13. You determine the reaction speed of military pilots. To do this, the time of the subject's response to the light signal is recorded. On what scale is this measurement taken?

14. What measurements can you take in your group so that they are carried out:

a) in the scale of names;

b) on an ordinary scale;

c) on an interval scale;

d) on a scale of equal relationships?

15. What psychological techniques allow for measurement on an interval scale?

Example

Limitations of the U criterion

1. Each sample must have at least 3 observations: n 1 n 2 ≥3; It is allowed that there are 2 observations in one sample, but then in the second there must be at least 5.

2. Each sample should contain no more than 60 observations; n 1 n 2 ≤60. However, already with n 1 n 2 >20, ranking becomes quite labor-intensive.

In our opinion, if n 1 n 2 >20, it is better to use another criterion, namely the angular Fisher transformation in combination with the λ criterion, which allows us to identify the critical point at which the maximum differences accumulate between the two compared samples (see paragraph. 5.4). .The formulation sounds complicated, but the method itself is quite simple. It is better for each researcher to try different paths and choose the one that seems more suitable to him.

Let's return to the results of a survey of students from the physics and psychology faculties of Leningrad University using D. Wexler's methodology for measuring verbal and non-verbal intelligence. Using Rosenbaum's Q criterion, in the previous paragraph we were able to determine with a high level of significance that the level of verbal intelligence in the sample of students from the Faculty of Physics is higher. Let us now try to establish whether this result is reproduced when comparing samples according to the level of nonverbal intelligence. The data is given in Table. 2.3.

Is it possible to say that one of the samples is superior to the other in terms of nonverbal intelligence?

Table 2.3

Individual values ​​of nonverbal intelligence in samples of students of physical (n=\4) and psychological (n2 = 12) faculties

	Physics students		Psychology students
Subject Name Code		Subject Name Code	Nonverbal Intelligence Index
1.	I.A.		1.	N.T.	FROM
2.	K.A.		2.	O.V.
3.	K.E.		3.	E.V.
4.	P.A.		4.	F.O.
5.	S.A.		5.	I.N.
6.	Art.A.		6.	I.Ch.
7.	T.A.		7.	I.V.
8.	F.		8.	K.O.
9.	C.I.		9.	P.P.
10.	TA.		10.	R.I.
11.	See A.		11.	O.K.
12.	K.An.		12.	N.K.
13.	B.L.
14.	F.V.

Criterion U requires care and attention. First of all, you need to remember the ranking rules.

1. A lower value is assigned a lower rank. The lowest value is assigned rank 1.

The highest value is assigned a rank corresponding to the number of ranked values. For example, if n=7, then the highest value will be rank 7, with the possible exception of those cases provided by rule 2.

2. If several values ​​are equal, they are assigned a rank that is the average of the ranks they would receive if they were not equal.

For example, the 3 smallest values ​​equal 10 seconds. If we measured time more accurately, these values ​​could differ and would be, say, 10.2 seconds; 10.5 sec; 10.7 sec. In this case, they would receive ranks, respectively, 1, 2 and 3. But since the values ​​​​we obtained are equal, each of them receives an average rank:

Let's say the next 2 values ​​are 12 seconds. They should have received ranks 4 and 5, but since they are equal, they receive an average rank:

3. The total sum of ranks must coincide with the calculated one, which is determined by the formula:

Where N- total number of ranked observations (values). A discrepancy between the actual and calculated rank sums will indicate an error made when calculating ranks or summing them up. Before you continue, you must find the error and fix it.

When calculating the U criterion, it is easiest to immediately accustom yourself to act according to a strict algorithm.

ALGORITHM 4 Calculation of the Mann-Whitney U test. 1. Transfer all test subjects’ data to individual cards. 2. Mark the cards of the subjects in sample 1 with one color, say red, and all the cards from sample 2 with another color, for example blue. 3. Arrange all the cards in a single row according to the degree of increase in the attribute, regardless of which sample they belong to, as if we were working with one large sample. 4. Rank the values ​​on the cards, assigning a lower rank to the lower value. There will be as many ranks as we have (n 1 + n 2). 5. Once again, arrange the cards into two groups, focusing on the color designations: red cards in one row, blue cards in another. 6. Calculate the sum of ranks separately on red cards (sample 1) and on blue cards (sample 2). Check whether the total sum of ranks matches the calculated one. 7. Determine the larger of the two ranking sums. 8. Determine the U value using the formula: Where n 1 - number of subjects in sample 1; n 2- number of subjects in sample 2; T x - the larger of the two rank sums; n x - the number of subjects in the group with a larger sum of ranks. 9. Determine the critical values ​​of U according to Table. II Appendix 1. If U emp.>U k p 005, N o is accepted. If U em ≤ U k p _ 005 , N o is rejected. The lower the value of U, the higher the reliability of the differences.

Now let's do all this work on the material this example. As a result of working on steps 1-6 of the algorithm, we will build a table.

Table 2.4

Calculation of rank sums for samples of students from the faculties of physics and psychology

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Physics students (n 1 =14)	Psychology students (n 2 =12)
Nonverbal Intelligence Index	Rank	Nonverbal Intelligence Index	Rank
	20,5
	20,5
	15,5		15.5
			14"
	11.5		11,5
	11,5
	11,5
	6.5		6,5
	4,5		4,5
Amounts
Average	107,2		111,5

Total amount of ranks: 165+186=351. Estimated amount:

The equality of real and calculated amounts is maintained.

We see that in terms of the level of nonverbal intelligence, the sample of psychology students turns out to be “higher” next to each other. It is this sample that accounts for the large ranking sum: 186.

Now we are ready to formulate hypotheses:

H 0: The group of psychology students is not superior to the group of physics students in terms of nonverbal intelligence.

H 1: A group of psychology students is superior to a group of physics students in terms of nonverbal intelligence.

In accordance with the next step of the algorithm, we determine the empirical value of U:

Because in our case p\FP2, let us calculate the empirical value U for the second rank sum (165), substituting the corresponding value into the formula p x:

According to Table. II Appendix 1 determine the critical values ​​for n 1=14, n 2 =12.

We remember that the U criterion is one of two exceptions to the general rule for deciding the reliability of differences, namely, we can state significant differences if U em ≤ U to p

Let's build a "significance axis".

U em = 60

U em > U to p

Answer: H 0 is accepted. A group of psychology students is not superior to a group of physics students in terms of nonverbal intelligence.

Let us note that for this case, Rosenbaum’s Q criterion is not applicable, since the range of variability in the group of physicists is wider than in the group of psychologists: both the highest and lowest values ​​of nonverbal intelligence occur in the group of physicists (see Table 2.4).

I've been doing it for several years now search engine promotion Evgeniy Popov's websites. For those who don’t know, Evgeny Popov is known as a successful information businessman and the author of numerous training courses on website creation and information business.

Recently, Evgeniy asked me to prepare an article about the most important ranking factors for Yandex and Google. I collected and analyzed information from many authoritative sources, plus additionally supported it with comments and explanations from my many years of experience in website promotion.

As a result, a rather useful PDF report was created, which was called “ 34 main ranking factors for Yandex and Google" This report was created at the end of 2016, but all of the factors listed are still relevant in 2018, as they are updated periodically. Especially taking into account the latest innovations from search engines. Launched not long ago new algorithms: Baden-Baden from Yandex and Google Fred.

For those who do not like to download something, I am posting below the full content of the analytical material entitled: “34 main ranking factors for Yandex and Google in 2016-2017.”

ABOUT THE SELECTION OF FACTORS

Reading hundreds of factors (that search engines take into account) is interesting, but not very useful in terms of practical application. Most of the existing materials on this topic are either already outdated or not initially adapted for the Russian-language Internet.

We analyzed many publications and studies of various factors in authoritative sources (links are provided below). Additionally, we checked all these statements with the statements of the presenters Google developers and Yandex. The result is a selection of the most important factors that modern search engines Yandex and Google take into account.

But we presented not only a description of the factors themselves, but also gave detailed explanations on them so that you can implement certain points on your sites and get real benefits in
form of growth of positions in search engines.

Please think for us. Remove the extra “water” and give us a sample closer to life,” this was the request made by one of the webmasters.

Let me emphasize right away that you should not try to find out and take into account absolutely all search engine ranking factors. This is a pointless waste of time. And after reading the text below, you will understand why.

According to data known from the developers Yandex takes into account more than 800 factors ranking, and Google (at least) 271 factors.

The data on Yandex was obtained from an interview with the head of Yandex search services, Alexander Sadovsky, for www.sostav.ru, as well as from other statements by officials.

Google data is based on research from northcutt.com.

Additionally, materials from an article by Brian Dean (online resource backlinko.com) were used. In his work, the foreign SEO specialist described more than 200 factors that Google takes into account when building search results.

The following is useful analytical material, but in no way does it claim to be the ultimate truth.

Additional explanation:

Dark color represents the Russian translation and description of the factor with in English(information was taken from an article by Brian Dean http://backlinko.com/google-ranking-factors).

Blue color indicates the decoding of a specific factor. You will be able to read not only a description that is adapted to the modern realities of the Russian-language Internet, but also receive valuable advice from 7 years of practical experience from SEO specialist Ruslan Savchenko.

FACTOR #1. DOMAIN AGE

« The difference between a six month old domain and a one year old one is actually not that big " - Matt Cutts, Head of Web Spam and Search Quality at Google.

Search engines certainly take into account the age of the domain... but this is not a very important factor.

Ruslan Savchenko: In fact, it is very important to distinguish between the concepts of “domain age” and “site age”. Many novice webmasters buy long-registered domain names, but sites on these domains have not developed.

Search engines take into account the “age of the site.” If the site was unavailable for a long time or there was a temporary page (“stub”), this does not count towards the age. In general, you should not focus much attention on the age of the domain; it is more important to work on the quality of the site.

P.S. When purchasing a new website (domain), be sure to check its history through the service https://archive.org/web/.

FACTOR #2. PRESENCE OF KEYWORDS IN THE DOMAIN

Doesn't have the same effect as before, but the presence of keywords in the domain name is still taken into account. After all, search engines still highlight in bold keywords that appear in the domain name.

Keywords in the domain name are taken into account, although this is far from the most important factor. But if it is possible to register a domain name with a key phrase that accurately reflects the name and theme of the site, then why not do it?

If there are keywords in the domain, they are highlighted. Accordingly, the click-through rate in search results increases. If a user sees the words he typed in the search bar highlighted in the site address, the likelihood of going to the site increases. This is a positive factor that is also taken into account.

FACTOR #3. DOMAIN HISTORY

A domain with frequent changes of ownership (via WHOIS) or with untimely renewal of registration (“drop”) can force search engines to “reset” the site’s history and stop taking into account links pointing to the domain.

It is highly desirable that the domain owner does not change frequently. Each change of ownership temporarily “freezes” the accumulated trust in the site. Search algorithms are waiting to see what the new owner will do with the site.

It is worth noting: if you suddenly change the content of the site (not the design, but the theme and the content itself), then search engines will also nullify the credibility of your site. Domain age will no longer have the same effect.

FACTOR #4. EXACT MATCH DOMAIN

Exact match domains (EMDs) can still give you an edge... if you have a quality site, that is. But when such a domain hosts a low-quality website, it is poorly protected from the EMD algorithm.

First, let's decipher what the so-called exact match domain (EMD) is.

EMD-domain (Exact Match Domain) - if translated literally, then this is a domain with an exact occurrence of keywords. When you register a domain name that consists solely of a popular keyword phrase, it may make search algorithms suspicious. The domains at greatest risk are:

• with the words in the title “buy, download, free, etc.”
• if the domain name contains only words from a popular key phrase, but there is no unique brand name, etc.
• If the domain consists of 3 or more keywords, for example, “buy real estate in Krasnodar inexpensively.” Google has developed a special EMD algorithm that fights so-called EMD domains.

The inclusion of keywords in the domain name has less and less influence on search results, but other things being equal, search engines will give preference to a site with a narrowly thematic name (containing keywords) than to a portal with a general topic.

Which site do you think best answers the query “BMW repair?” A website with the domain name AvtoMir.com or a website Remont.BMW-club.com? I am 100% sure that (without taking into account other factors) preference is given to the 2nd option. Google and Yandex think the same way.

By the way, it was not for nothing that I gave the example of the 3rd level subdomain Remont.BMW-club.com. The option with the 2nd level domain Remont-BMW.com would not be the most optimal.

Representatives of search engines noted that they are very distrustful of 2nd level domains, which consist exclusively of keywords. These are the domains that are at risk of being punished by the EMD algorithm. This is not surprising, because not so long ago, websites (“doorways”) that were useless to people were created on just such domain names.

But if the domain name is the name of your company or brand combined with a keyword, then this is a good option and is not at risk of EMD.

Moreover, if you have a choice: register a domain consisting of keywords or the name of your brand, then it is better to give preference to the second option.

After all, even if you are not afraid of the EMD algorithm, the links leading to your site will no longer be completely anchorless. And for this you can get punishment from other algorithms and filters. For example, the same Google Penguin and Minusinsk from Yandex, which punish sites for a large number of external links with direct inclusion of keywords in the anchor.

But this is a topic for another big conversation, so let’s move on to the next ranking factors.

FACTOR #5. PRESENCE OF KEYWORD IN THE “TITLE” TAG

The title tag is the second most important SEO parameter of a web page (after the content itself), and therefore has a strong impact on ranking for a specific page. search query.

Don’t forget that it is the contents of the “title” tag that Yandex and Google show in search results.

If we explain the work of search engines in the most simplified way, then the answer to the user’s request is formed based on the keywords that are present in the title tag, as well as in the text of the page itself. This is one of the most important SEO parameters.

Another thing is that in no case should you oversaturate the text and title of the page with keywords. For this, modern search engines have various sanctions: starting from the “uniqueness of headings” filter, ending with algorithms that punish overspam, excessive content of keywords in the page text, etc.

FACTOR #6. TITLE TAG STARTS WITH KEYWORD

It is important to understand that there is a page title (it is located in the title tag) that users see in search results.

But there is also a title for the text on the page (it is located in the H1 tag). Users see it after they have gone to the site page itself.

Both of these headings are very important for search engine optimization site. Therefore, the keyword phrase must be present in both tags.

FACTOR #9. KEYWORD IS FREQUENTLY USED IN THE TEXT OF THE DOCUMENT

If a keyword appears in the text of a page more often than any other, then this is a positive factor in the page's relevance to a specific search query.

That is why a few years ago, optimizers created SEO texts with a large number of keywords, highlighted them in bold, etc. In modern conditions, for a large number of keywords in the text, you can quickly get a “spam filter” than achieve any bonuses to the relevance of the page.

Therefore, write texts that people will be interested in reading, create pages that can solve a specific user problem. In modern conditions, even one occurrence of a key phrase in the text is enough for it to be relevant to a particular search query.

FACTOR #10. LATENT SEMANTIC INDEX OF KEYWORDS IN CONTENT (LSI)

LSI Keywords Help search engines determine the meanings of words with more than one meaning. For example, the word Apple is a computer company or a fruit. The presence or absence of LSI can also be an indicator of the quality of content on the site.

In recent years, the term LSI copywriting has even appeared. And compliance with certain requirements allows you to increase the relevance of a certain text and, accordingly, the entire page as a whole. Let's try to figure out what LSI is.

To begin with, I will give a quote that inexperienced people should never try to understand. If you are a beginner, it is better to skip this paragraph right away. But these are the concepts that are given when some authoritative sources try to explain such terms in a more “scientific” language: “ LSI is a singular value decomposition of a term-document matrix, which allows you to catch the key components of this matrix and ignore noise.»

Have you read it? Now forget it. I'll try to give a clearer explanation:

LSI is a way of determining the topic and quality of a text based on an analysis of the words it contains. Simply put, if the text contains the words “engine”, “wheel”, “steering wheel”, then most likely the text is about a car.

Search engines have begun to introduce algorithms that combat texts that are oversaturated with the same keywords. If the same key phrase is used very often in the text, then the search engines Yandex and Google have questions about the quality of the material.

Either this is an attempt to artificially increase the significance of the page for a certain search query, or the author is not very competent in this topic, since he cannot use synonyms and a generally richer vocabulary. Both the first and second options can lead to a lowering of the site’s page in search results.

The quality of text design, the absence of grammatical errors and many other parameters are also taken into account.

Texts that are written taking into account LSI requirements rarely fall under any filters and rise to high places in search much more easily. This is especially true in highly competitive areas.

P.S. Analyze your competitors who are in first place in Google and Yandex. Look at the design of their pages, what words they use in texts, etc. This will give you a lot of food for thought if your site is not yet in the TOP.

But this is a really big topic, and I don’t want to bore you, so let’s move on to the next factor.

FACTOR #11. LSI KEYWORDS IN “TITLE” AND “DESCRIPTION” TAGS

As with site content, LSI keywords in a page's meta tags help determine the correct meaning of synonymous words. This is also one of the relevance factors.

Based on the context, search engine algorithms understand what topic a word with several meanings relates to. For example, a headline appeared on the website: “A new pop star has been lit.” If the title did not contain the word “variety”, it would be unclear what topic this fragment of text should be classified in – astronomy or show business.

This is why it is important that the “title” and “description” tags always contain words that clearly define the topic of the page on your site.

FACTOR #12. HTML PAGE LOADING SPEED AND TECHNICAL ERRORS ON THE SITE

Search engines consider page loading speed as one of their ranking factors. Search engine bots can estimate the speed of your site quite accurately based on the page code and the size of the downloaded files.

This is not the most important factor. The same Alexander Sadovsky (head of Yandex search services) stated that algorithms do not punish the site for any technical errors and shortcomings.

But if there are no direct sanctions, then there is an indirect negative impact on the ranking. For example, if the pages of your site take a long time to load and errors constantly appear on them, this will irritate users.

Most often, dissatisfied visitors simply close your site and go to your competitors. Accordingly, your site’s so-called behavioral factors are deteriorating. And they already directly affect rankings. Moreover, there is a “bounce” rate. In particular, when the user spent less than 15 seconds on your site page and returned back to the search.

Accordingly, search engines will lower your site in search results not for the technical shortcomings of your site themselves, but for the consequences that they cause.

FACTOR #13. REPEATING CONTENT (INCLUDING DUPLICATE PAGES)

Identical content on the same site (even slightly changed) can negatively affect the site's visibility in search engines.

Duplicate pages and repeated content on different pages are quite negative factors. Thus, you take away the “weight” from your own pages.

Moreover, you force search engine robots to index unnecessary non-unique content (pages). And search bots have a strictly limited time for each site.

FACTOR #14. IMAGE OPTIMIZATION

Images on pages convey important information about their relevance. Search engines determine the subject of images by analyzing the file name of the image itself and the text that is in the tags: alt, title, description.

Ideally, you need to fill out all the tags and write captions for the pictures. Especially the alt tag (alternative text for the image). Search engines pay attention to its content first of all.

Therefore, sign what is shown in the pictures. It is also desirable that the image description tags contain keywords for which the page itself is optimized.

FACTOR #15. FREQUENCY AND SIZE OF CONTENT UPDATES

Search engines love recently updated content, especially for queries that are time sensitive.

Search engines love frequently updated sites. Of course, your old posts can also rank well, but if you make significant changes to them, add something, improve them - all this will only be a plus.

Keep your materials up to date, or write new posts and link to them from your old pages.

FACTOR #16. KEYWORD VISIBILITY

The presence of a keyword among the first 100 words of a page's content is considered a significant signal of relevance.

After all, if a user came to a website page and did not find an answer to his query at the beginning of the page, then he will most often close your site and go to search further. Search engines also understand this, so the presence of a keyword at the very beginning of the text has a double meaning.

FACTOR #17. QUALITY AND SUBJECT OF OUTGOING LINKS

Moreover, many novice webmasters have read the now outdated myths that outgoing links take away valuable weight from their site and therefore add the rel=“nofollow” parameter to all outgoing links. Thus, they not only do not save the weight of their pages, but simply give it away to nowhere.

Plus, this approach harms your site. After all, rel=“nofollow” should only be set if you are linking to a non-topic resource.

Experiments were conducted at various sites. So, pages from which there were links to high-quality thematic materials on the topic occupied higher places in searches than pages from which there were no outgoing links at all.

The logic here is simple. Even the incredibly authoritative Wikipedia, which has a TIC of 150,000 and enormous trust from search engines, always refers to sources and additional materials on the topic. You might say that all their outgoing links are closed with the rel=“nofollow” parameter. Yes, this is true, but this was done to protect against spammers. Since these measures had not yet been taken, many webmasters and optimizers tried to get a link from Wikipedia at any cost.

But the conclusion is simple. If you are not a well-known expert in your field and your Internet resource does not have much trust from search engines, then the Yandex and Google algorithms are unlikely to believe that you wrote a very high-quality article without using a single source and without ever citing anyone .

It’s even worse if you rewrote or, more simply put, rewrote someone else’s article in your own words. This is exactly what search engines are fighting against, and their algorithms have already become very good at identifying authors and plagiarists.

By the way, this is a little secret why large analytical articles with non-unique parts of the text, but with links to sources or other materials on the topic, rank high in searches. News aggregators are just as successful, publishing non-unique materials, but always providing active links to sources.

There are other practical secrets and nuances regarding outgoing links, but it’s time for us to move on to the next factor.

FACTOR #18. USEFUL SUPPORTING CONTENT

According to the now publicly available Google Rater Guidelines, useful supporting content is an indicator of page quality (and therefore an additional ranking factor). Examples include: interest and credit calculators, currency converters, interactive recipes, etc.

All additional features and functionality that benefit your site visitors also provide additional ranking bonuses. All additional “chips” affect not so much directly as indirectly. After all, while a site user is using a calculator or other function, he is spending additional time on your site.

Thus, by satisfying and interesting visitors to your site, you improve user factors - and this is very important in modern conditions. It is these factors that have a direct impact on the position of your site in Google search and Yandex.

FACTOR #19. MULTIMEDIA MATERIALS ON THE SITE

Images, videos, and other media can signal the quality of content.

In continuation of the previous factor. Thanks to beautiful pictures and high-quality videos, you can retain users of your site and improve behavioral data. Plus, search engines rank pages that contain images and videos better.

All other things being equal, a page that has at least one image will rank higher in searches than its text-only counterpart.

FACTOR #20. QUANTITY AND QUALITY OF INTERNAL LINKS POINTING TO THE PAGE

The number of internal links to a page shows its importance relative to other pages on the site.

The quality and quantity of links to the landing page is important. Each page of your site has a certain “weight”. It may grow if this page is directed to external links from other sites or there are links from pages on your site.

Accordingly, when you have written a new article on a certain topic, think about it: maybe you already have an article on a similar topic and it would be appropriate to link to it using the desired key phrase?

FACTOR #21. URL LENGTH

Search Engine Journal notes that URLs that are too long can harm a page's relevance.

There is such a trend. It is advisable to create short page URLs. Ideally, they should consist of 2-3 keywords written in transliteration.

FACTOR #22. LIVING PEOPLE ASSESSORS

Although it has not been confirmed, Google has filed a patent for a system that allows human editors to influence the SERP (search engine results page).

So-called assessors are indeed present in both Yandex and Google. Of course, there are millions of sites, and it is unrealistic to evaluate all search results manually. But the highest places (TOP 10) of search results in the most competitive topics are also assessed by special assessors.

That is why initially low-quality sites have very little chance of reaching the TOP of search results. Even if we assume that the owners of “bad” sites figure out the current search engine algorithms and come out on top in searches, there will be extremely little chance of staying there for a long time.

FACTOR #23. OPTIMIZATION OF THE SITE FOR MOBILE DEVICES

Creating adaptive websites in our time is no longer a tribute to “fashion”, but a real necessity. Sites that are not adapted for mobile devices, receive penalties from search engines and are greatly reduced in mobile search results.

It's no secret that most modern people search for goods and services on the Internet, including from tablets, mobile phones and so on.

In some areas, the percentage of users who access websites exclusively from mobile devices reaches 80%.

Therefore, if you have not yet made the design of your website responsive, then it’s time to do it urgently. You simply lose new visitors and potential clients.

FACTOR #24. COMMERCIAL FACTORS

If you have a commercial website, then modern commercial factors have a fairly serious impact on its position in search. These include: the presence of a contact page, a convenient order form, delivery availability, service availability technical support customers, breadth of product range, etc.

In fact, more than 30 of the most important commercial factors alone can be listed. This is a specific topic and there are many nuances here, so we will consider this issue in detail separately.

FACTOR #25. LINKS FROM OLD DOMAINS

I completely agree. But it's worth noting that getting links from authoritative domains is quite difficult (or expensive). Of course, there are certain interesting methods for obtaining high-quality and natural links (including without costs). But this is a large separate topic, so let’s move on.

FACTOR #26. NUMBER OF REFERING DOMAINS

The number of referring domains is one of the most important ranking factors in Google's algorithm, as you can see from this Moz graph (horizontal axis is position in the search results list):

My personal observations also confirm the information described above. It is better to have 10 backlinks from 10 different domains than 20 links from one domain.

FACTOR #27. LINKS FROM COMPETITOR SITES

Here we are talking about the following. For example, you are promoting according to the request: “buy a car in Moscow.” If you received links from sites that are in the TOP 10 for the same request, this would have a powerful effect.

But let's be realistic. In highly competitive topics, no one will want to link to a competitor. Unless you're a genius at threats or diplomacy.

Although in my practice there have been cases when I was able to get a non-anchor link (just by URL) from a competitor’s website in the TOP 10. But this is more of an exception to the rule.

However, it is not necessary to try to get links from direct competitors. Look at sites outside the TOP 10. Moreover, you can search for sites for related queries in the same topic.

By the way, in information topics there are several interesting approaches, thanks to which you can receive links from “indirect” competing sites. This is an important and large topic, so we will definitely consider it separately.

FACTOR #28. LINKS AND MENTIONS OF THE SITE IN SOCIAL NETWORKS

Links and mentions of your site name in in social networks provide both direct and indirect effects for promotion. By the way, some social networks work better for Yandex, and some for Google. And we’re not just talking about Facebook, Twitter and VKontakte.

Moreover, there is an approach that allows you not only to increase trust in the pages of your site (through links from social networks), but also to further promote specific search queries.

Also, now it is becoming increasingly important to work on obtaining not only links, but also reviews, mentions of your site on various forums, recommendation sites, and social networks. Including when on a particular Internet resource there is no backlink to your site at all, but only a mention of the brand or domain name in the text.

This direction is called crowd marketing and to achieve high results in competitive topics it is difficult to do without it.

FACTOR #29. QUALITY OF THE CONTENT THAT SURROUNDS THE LINK

Everything is logical here. If the donor page from which there will be a link to your site has high-quality and interesting content, beautiful design, useful pictures, videos, etc., then it can rank higher in search engines. And such a page will have more trust from Yandex and Google. Accordingly, links from such a page will have more weight and authority.

It's quite stupid to purchase a link to your site from a quality site, but post some uninteresting and poorly designed content. It’s even worse if this page is placed in some section with a large level of nesting. For example, it will be placed in very old material located in the archive.

Moreover, owners of high-quality Internet resources are unlikely to allow poor quality materials to be posted on their website. And if they allow bad articles with links to be published on their website, then questions immediately arise about the prospects and the value of such a donor site.

FACTOR #30. BACK RATE

Search engines may well use users as quality testers (if there are a lot of failures, the site is most likely not of very good quality).

A “bounce” is considered when the user spent less than 15 seconds on a specific page of the site and left back to the search results. This factor, combined with other behavioral data, allows search engines to further evaluate the quality of certain web pages.

FACTOR #31. REPEATED VISITS TO THE SITE

Search engines can also look at whether users return to a site after their first visit. Repeat traffic can improve your site's ranking in search results.

Not only repeat visits to the site are taken into account, but also many other actions. For example, how often do users save a site to their bookmarks, do they go to the site directly from a URL, do they enter the site name in a search, do they share links to the site, etc.

FACTOR #32. NUMBER OF COMMENTS ON THE SITE

Pages with a large number of comments can be a signal of user activity and indirect confirmation of the quality of the content.

The ranking procedure is quite simple, but errors can arise completely unexpectedly. Therefore, whenever ranking is carried out, it is necessary to check the correct implementation of this procedure. In the most general case, to check the correct ranking of a column (or row) of features, the following formula is used:

If ranked N characteristics, then the sum of all obtained ranks should be equal to:

Where N- number of ranked features.

This formula is widely used in the future, so it should be remembered well.

The coincidence of the results of calculating ranks according to formula (1.1) and the actual results of ranking experimental data is confirmation of the correctness of the ranking.

In the case of example 1, the number of ranked features was N=7, therefore, the sum of ranks calculated using formula (1.1) should be equal to 7*8/ 2= 28.

Let's add the rank values ​​separately for the left and right columns of Table 1.2:

7 + 1 + 3 + 2 + 5 + 4 + 6 = 28- for the left column and

1 + 5 + 7 + 6 + 4 + 3 + 2 = 28 - for the right column.

The sums of ranks calculated using formula (1.1) and as a result of real ranking coincided, therefore, the ranking was carried out correctly. A similar check should be done after each ranking.

In the future we will encounter several more different ranking options. For example, ranking a table of numbers. Such tables will be used quite often in the future, so you should thoroughly understand the rules for checking the correct ranking of tabular data.

Option 1. Let's assume that we tested two groups of subjects of 5 people in each group using the method of differential diagnosis of depressive states by V.A. Zhmurov and they received the following test scores, which we will immediately enter in Table 1.3:

Table 1.3

Let's check the ranking is correct. Since we have already obtained the sums of ranks for the columns, the total real sum of ranks can be obtained simply by adding these sums, so 31 + 24 = 55.

Therefore, the ranking was done correctly.

If the table has a large number of rows and columns, you can use a modification of formula (1.1) to calculate ranks; it will look like this:

Where k- number of rows, c - number of columns.

Let's calculate the sum of ranks using formula (1.2) for our example. We have 5 rows and 2 columns, therefore the sum of the ranks will be equal to

Option 2. In a number of statistical methods, the ranking of tabular data is carried out for each line separately. Let us illustrate this situation with the previous example by adding another group of 5 subjects. We will get table 1.5 in which we will rank by line:

Table 1.5

No. of subjects	Group 1	Ranks	Group 2	Ranks	Group 3	Ranks
Amounts

Please note that in Table 1.5 the minimum number is assigned a minimum rank.

In the case of such ranking, the sum of all ranks for each line should be equal to 6, since we only rank three values:

The calculation formula for the total sum of ranks for this ranking method is determined by the formula:

(1.3)

Where P- number of subjects in the column

With - number of columns (subject groups, measurements, etc.).

The correctness of the ranking is again determined by the condition that the calculated sums of real ranks obtained from the table and from the calculation formula (1.3) coincide.

Let's check the correctness of ranking for our example.

The real sum of ranks is: 8 + 10 + 12 = 30

According to formula (1.3) it is:

Therefore, the ranking was done correctly.

1.3.3. The case of identical ranks

When issuing expert assessments or in other ranking cases, situations arise when two or more qualities are assigned the same ranks. Consider this case in relation to example 1.2, in which seven personal qualities were ranked. To illustrate, let’s divide the first and second columns in Table 1.2 into two parts, presenting it in the form of Table 1.6:

Table 1.6

Suppose that when assessing the characteristics of the “real self,” the subject believes that such qualities as “perseverance” and “energy” should have the same rank. Then, when conducting ranking (see column No. 1 of Table 1.6), these qualities must be assigned conditional ranks, which must be in order one after another - and mark these ranks with parentheses - (). However, since these qualities, in the opinion of the subject, should have the same ranks, in the second column of Table 1.6, relating to the “Real Self,” the arithmetic average of the ranks in parentheses should be placed, i.e. (2+3)/2=2.5. Thus, the second column of Table 1.6 will be the final result of ranking the features of the “Real Self” for a given subject.

Let's check the ranking is correct. First, we add up the real ranks obtained in the second column of Table 1.6: 1 + 2, 5 + 2, 5 + 5 + 4 + 6 = 28

Suppose that when ranking the qualities related to the “Ideal Self,” the subject believes that such qualities as “sociability,” “energy,” and “cheerfulness” should be given the same ranks. In this case, he assigns conditional ranks to these qualities in order in parentheses in the last fifth column of Table 1.6.

The arithmetic mean of the conditional ranks (4 + 5 + 6)/3 = 5 is the desired rank, which is attributed to the three above-mentioned qualities, in the fourth column of Table 1.6

Let us emphasize once again that the conditional ranks should be arranged in order of magnitude, despite the fact that the qualities being ranked are not located next to each other.

Let's check again the correctness of the ranking by summing up the ranks obtained in the fourth column: 1 + 2 + 3 + 5 + 5 + 5 + 7 = 28

We remember that according to formula (1.1) the sum of ranks was also equal to 28. Therefore, the ranking was carried out correctly.

The same ranks can be assigned to any number of ranked values. In this case, they are also assigned the value of the arithmetic mean of the number of conditional ranks, assigned in order of their magnitude.

Let's consider the features of ranking quantitative characteristics. Despite the fact that ranking is widely used in relation to quantitative indicators, it should be remembered that in an ordinal scale, operations with numbers are essentially operations with ranks (orders), but not with the quantitative expression of properties (qualities, characteristics, etc.). ) as such.

In this case, the ranking rules are:

1. The smallest numerical value is assigned rank 1.

2. The highest numerical value is assigned a rank equal to the number of ranked values.

3. In case there are several initial numerical values turned out to be equal, then they are assigned a rank equal to the average value of the ranks that these values ​​would receive if they stood in order one after another and were not equal.

Note that this case may include both the first and last values ​​of the original series for ranking.

4. The total sum of real ranks must coincide with the calculated one, determined by formula (1.1).

6. If it is necessary to rank a sufficiently large number of objects, they should be combined according to some criterion into fairly homogeneous classes (groups), and then the resulting classes (groups) should be ranked.

Example 1.2. The psychologist obtained the following values ​​of nonverbal intelligence from 11 subjects: 113, 107, 123, 122, 117, 117, 105, 108, 114, 102, 104. It is necessary to rank these indicators, and it is best to do this in a table:

Table 1.7

In this table, conditional and real ranks were located in one column, which is more convenient and saves a lot of space.

Let's check the correctness of the ranking using formula (1.1): we substitute the initial values ​​into the formula, we get: 11∙12/2=66.

We sum up the real ranks, we get:

6 + 4 + 11 + 10 + 8,5 + + 8,5 + 3 + 5 + 7 + 1 + 2 = 66.

Since the amounts coincided, therefore, the ranking was carried out correctly.

The ranking scale uses a variety of statistical methods, some of which will be described below. The most commonly used correlation coefficients for measurements obtained on this scale are Spearman and Kendall, and a variety of difference tests are used for data obtained on this scale.

Interval scale

On a scale intervals, or interval scale, each of the possible values ​​of the measured quantities is located at an equal distance from the nearest one. The main concept of this scale is the interval, which can be defined as the proportion or part of the property being measured between two adjacent positions on the scale. The size of the interval is a fixed and constant value in all areas of the scale. For measurement using an interval scale, special units of measurement are established; in psychology these are walls and walls. When working with this scale, the property or item being measured is assigned a number equal to the number of units of measurement, equivalent to the amount of the property present. An important feature of the interval scale is that it does not have a natural reference point (zero is arbitrary and does not indicate the absence of the property being measured).

Thus, in psychology, the semantic differential of Charles Osgood is often used, which is an example of measuring on an interval scale various psychological characteristics of an individual, social attitudes, value orientations, subjective personal meaning, various aspects of self-esteem, etc.:

However, as S. Stevens and a number of other researchers emphasize, psychological measurements on an interval scale in essence often turn out to be measurements made on an order scale. The basis for this statement is the fact that functionality people change depending on different conditions. When measuring, for example, strength using a dynamometer or stability of attention using a stopwatch, the measurement results at the beginning and end of the experiment due to the fatigue of the subject will not be quantified at equal intervals.

Only a measurement using a strictly standardized test procedure, provided that the distribution of values ​​in a representative (see below) sample is sufficiently close to normal (see below), can be considered a measurement on an interval scale. An example of the latter is standardized intelligence tests, where the standard unit of measurement IQ is equivalent for both low and high intelligence values.

It is also fundamentally important that a fairly large number of statistical methods are applicable to the experimental data obtained on this scale.

Relationship scale

scale relations also called scale equal relations. A feature of this scale is the presence of a firmly fixed zero, which means the complete absence of any property or characteristic. The ratio jackal is the most informative scale, allowing any mathematical operations and the use of a variety of statistical methods.

The ratio scale is essentially very close to the interval scale, since if the starting point is strictly fixed, then any interval scale turns into a ratio scale.

It is on the ratio scale that precise and ultra-precise measurements are made in sciences such as physics, chemistry, microbiology, etc. Measurements on the ratio scale are also made in sciences close to psychology, such as psychophysics, psychophysiology, psychogenetics.

Chapter 2

THE CONCEPT OF SAMPLING

An experimental psychologist in most cases studies a specific sample of people, which is always selected from a larger group. Such an enclosing group is called in statistics the general population. Thus, general population - This is any group of people that a psychologist studies as a sample. Theoretically, it is believed that the size of the population is unlimited. In practice, the volume of the general population is always limited and can vary depending on the subject of observation and the task that the psychologist has to solve.

A sample is any subgroup of elements (subjects, respondents) selected from the general population to conduct an experiment. In this case, an individual from the sample with whom the psychologist works is called a subject (respondent).

The sample size, usually denoted by the letter I, can be any size, but not less than two respondents. In statistics, there are small (n ≤ 30), medium 30< n < 100 и большую выборку (n ≥ 100).

2.1. Full Study

If all representatives of the studied population are subjected to psychological research (observation, measurement, experiment), then such a study is called full, or continuous.

It is assumed that, in accordance with the objectives, hypotheses and plan, a complete survey of the general population allows us to obtain comprehensive information about the psychological patterns studied in it. However, a comprehensive study has never been carried out in domestic and foreign psychology for the reason that in practice, determining the size of a particular general population, much less studying it, is an unrealistic task and, moreover, to a certain extent redundant. If the sample of subjects is representative of the general population in its characteristics, then there is reason to extend the results obtained from its study to the entire general population. We must also not lose sight of the fact that the work of a psychologist is essentially a complex activity that requires high professional competence and often a lot of time to work with each subject.

2.2. Sample study

If a psychologist selects a limited number of elements from the studied (general) population, then such a study is called partial, or selective.

The sampling method is the main one in the experimental work of a psychologist when studying general populations. Its advantage over a complete (continuous) study of all elements of the general population is that it reduces both time and labor costs, and most importantly, it allows you to obtain information about such groups, a complete survey of which is fundamentally impossible or impractical.

MATHEMATICAL METHODS IN PSYCHOLOGY

Introduction

Currently, an interdisciplinary approach is becoming more common in the practice of training specialists. It is also widely used in the training of psychologists. It was at the intersection of mathematical and psychological subjects that a relatively new discipline, “Mathematical Methods in Psychology,” was born.

Thanks to the penetration of the mathematical apparatus into psychology, the latter was able to go beyond introspection and gained the opportunity to quantitatively describe and compare observed phenomena. Subsequently, some methods, such as correlation and factor analysis, appeared precisely thanks to the efforts of psychologists. It is the mathematical apparatus that is a convenient tool for describing and modeling certain phenomena in various branches of human activity.

For a modern psychologist, mastery of mathematical statistics is necessary primarily because without it, the psychologist will not be able to substantiate his reasoning and will not be able to prove the regularity of his conclusions. Knowledge of this subject is also necessary to be a good psychodiagnostician, mathematically correctly understand and interpret test results.

Topic 1 Problems of measurement in psychology and types of scales

Types of scales

Measurement is the assignment of numerical forms to objects. There are 4 types of measuring scales.

1. Nominative (nominal, categorical)
2. Ordinal (rank, ordinal)
3. Interval
4. Relationship scale

The last two types of scales are also called metric scales.

Nominative scale is a scale in which the quantitative characteristics of objects are not expressed. Only the property of objects that they are different is taken into account. This scale is used to classify objects. For example:

Thus, according to the criterion of completing or failing to complete a task, people can be classified into one of two categories. There may be more categories in the nominative scale.

Ordinal (rank) scale allows you to rank objects (assign ranks to them) according to any criterion. For example:

That is, on this scale it is already possible to quantitatively record the degree of expression.

There may be a zero mark on this scale, but it is chosen arbitrarily. Thus, on the Celsius temperature scale (interval scale), the melting temperature of water at a pressure of 1 atm is selected as 0°.

Absolute scale (ratio scale)- a scale that classifies according to the principle “more (less) by a certain number of times.

		Kor-v		Pan-in	You in	Mich-in

From this scale it is clear that Kor-v completed the task 2 times slower than Mikh-va and 0.6 times slower than Vas-va. This scale differs from the previous one in that it assumes the presence of absolute zero. For example, on the Kelvin temperature scale (ratio scale), 0° is set to the point where any thermal movement of molecules stops.

Interval and absolute scales are also commonly called metric scales.

Data types

Data are the basic elements that are to be classified or categorized for the purpose of processing. There are three types of data:

1. Metric data: quantitative data obtained from measurements. They can be distributed on an interval or ratio scale.
2. Rank data corresponding to the positions of these elements in the sequence obtained by arranging them in ascending order. These data can be represented as an ordinal scale.
3. Nominative data: Categorical (qualitative) data that represents specific properties of sample elements. For example, the eye color of the subjects. These data cannot be measured, but their frequency of occurrence can be estimated.

Ranking Rules

The use of an ordinal scale allows you to assign ranks to objects according to any criterion. Thus, metric values ​​are converted into rank values. At the same time, differences in the degree of expression of properties are recorded. There are 2 rules to follow during the ranking process.

Ranking order rule. It is necessary to decide who receives the first rank: the object with the greatest degree of expression of any quality or vice versa. Most often, this is absolutely indifferent and does not affect the final result. It is traditional to assign the first rank to objects with a greater degree of quality expression (a higher value means a lower rank). For example, the champion is awarded first place, and not vice versa. Although, even here if it were accepted reverse order, then the results would not have changed. So each researcher has the right to determine the ranking order himself. For example, E.V. Sidorenko recommends assigning a lower rank to a lower value. In some cases it is more convenient, but more unusual.

For example: there is an unordered sample whose data needs to be ranked. (2, 7, 6, 8, 11, 15, 9). After ordering the sample, we rank it.

The following should be said separately. There is a group of rarely used nonparametric tests (Wilcoxon T-test, Mann-Whitney U-test, Rosenbaum Q-test, etc.), when working with which you should always assign a lower rank to a smaller value.

Rule of related ranks. Objects with the same expression of properties are assigned the same rank. This rank is the average of the ranks they would have received if they had not been equal. For example, you need to rank a sample containing a number of identical metric data: (4, 5, 9, 2, 6, 5, 9, 7, 5, 12). After ordering the sample, the arithmetic mean of the related ranks should be calculated.