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Language samples of words This study investigated the stability of five type-token ratios TTRs in utterance oral language samples segmented into nine lengths. The samples were obtained Area Tested: Expressive vocabulary; Method: Elicit a spontaneous speech sample. From the sample count the total number of Learn more. A Type-Token Ratio. Journal of Speech and Hearing Research, If a text is 1, words long Free download type token ratio engine Files at Software Informer - The Engine Expert used computer simulation to give builders of high performance engines a tool to Free download type token ratio software Files at Software Informer - Given the current high rate of identity theft and other online scams the world of Internet is Icon, KeyWords: calculation;..

Type-token ratios of different texts are not directly comparable as words in text usually follows a power law type of distribution First of all an overview about the Free download calculate type token ratio online Files at Software Informer - Ink Volume Setter can calculate image area ratio not only from prepress data containing TTR; 4. Blue lines: simple weighted moving average with an year window centered on the current value.

One common approach to avoid spurious correlations is to transform the series prior to the analysis, for example by detrending the series estimating the trend and subtracting it from the actual series. Another more general solution that often results in stationary series, that is a series in which the mean and the variance of the investigated series do not change as a function of time, is to correlate period-to-period changes instead of the actual levels of the two series [ 11 ]. It is worth emphasizing that this also re-formulates the research question as it excludes the upward trends of the correlated series [ 21 ].

It determines if period-to-period changes that are above or below the average of the first series correspond mainly to changes that are above or below the average of the second series. Therefore, [ 8 ] suggest as a rule of thumb to generally model data on a combination of both levels and changes. In our case, correlating year-to-year changes or decade-to-decade changes seems to be even better suited to answer our "research question": if the population increases from last year to this year, then—on average—lexical diversity should also increase from last year to this year, if both series are related.

To demonstrate why it is problematic to correlate two trending time-series, we have simulated 10, random walks with drift cf. Materials and Methods. Each resulting time-series has an average upward trend, but otherwise behaves in a completely random manner. This means that the random walks serve as a proxy for time series with a general upward trend. All series are then correlated with the annual global mean sea level.

This result is, of course, far from what we should actually expect for the distribution of correlation coefficients where one variable is a random quantity per definition : only a few series should—by chance—substantially correlate with the global mean sea level, while most correlation coefficients should be close to zero. Top: Histogram of the correlations between levels.

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Bottom: Histogram of the correlation between year-to-year changes. The height of the bars in both histograms represents the number of cases in the category. Blue lines: scaled normal density. This leaves little room for debate: Whenever two variables evolve through time, those variables will almost always look highly correlated even if they are not related in any substantial sense. The reason why standard statistical models fail when it comes to the analysis of time-series has to do with the fact that there is basically no such thing as a univariate time-series: analyzing univariate time series is always "the analysis of the bivariate relationship between the variable of interest and time.

In the Materials and Methods section, we demonstrate why temporal autocorrelation is problematic from a statistical point of view, if regular models for cross-sectional data that assume independence between individual observations are used.

Using the koRpus Package for Text Analysis

This model would also imply that every 10 new inhabitants of Spain are equal to 4. We believe that this would be an extraordinary result. In fact, this result would be so extraordinary that it seems wise to first ask: is this result plausible? Can we come up with any good theory regarding this relationship?

A few words on the Google Books data are in order here, as they are the basis of all but one [ 16 ] study quoted above. Here, we want to echo [ 22 ], p. After all, for n -grams where n is ranges from one single words to five five word units , the data consist of only year-wise aggregated overall frequencies of occurrence and the number of books each n-gram appears in. Since n-grams do not occur independently across distinct books, this aggregation of individual book frequencies means that we cannot account for the distributions of n-grams which can have profound consequences for the analysis of textual data [ 23 , 24 ].

In addition, it is a largely overlooked fact that the Google Books Ngram data only includes the counts for n-grams that occur at least 40 times across the entire corpus. At least from a corpus linguistic point of view, this certainly matters since most n-grams are very infrequent. To the best of our knowledge, the question of whether this arbitrary data truncation does not impose a systematic bias on the data is something that remains to be demonstrated empirically, given the fact that corpus size for each year strongly increases as a function of time.

At the same time, this means that we would have to further extend our analysis illustrated above: nearly every second new inhabitant of Spain is "responsible" for one new word type that occurs more than 40 times in the Spanish Google Books data. To check the plausibility of this result, we would have to face the fact that we still do not have any reliable information about the books included in the corpora.

This statement has not changed in the last few years and we are rather pessimistic that it will change anytime soon; but we would love to be proven wrong. This, in turn, means that we currently have no way of finding out whether the different diachronic book samples really represent similar things at different moments in time and, as the Culturomics team themselves pointed out [ 28 ], p. The lack of metadata can have important ramifications for any interpretation of potential results based on the Google Books Ngram data [ 29 , 30 ].

Returning to our research question—the correlation between population size and lexical diversity—population growth is affected by the birth of children and the influx of immigrants. Babies do not write books, and only a few immigrants publish books which are acquired by libraries shortly after immigration. So, the strong relationship between lexical diversity and population size would indicate that nearly every second new inhabitant babies and immigrants alike is "responsible" for one new word type that occurs more than 40 times in the Spanish Google Books data.

This would really be an extraordinary relationship. | Lexicon | Vocabulary

Our model predicts that with every 1, new inhabitants of China, we will find roughly 15 additional word types in the German Google Books data. If we use year-to-year changes instead of the actual levels, we obtain an insignificant correlation of 0. This implies that knowing the Chinese population size does not help in predicting the lexical diversity in the Google Books data, a result which we believe fits reality more closely. From a statistical point of view, this demonstrates why it can be a good idea to model a potential relationship between two trending time series with changes instead of levels.

This is also important from a methodological point of view: just because two series are trending, does not necessarily imply any substantial relationship [ 31 ]. Therefore we strongly advise against using the fact that two series are evolving in a predicted way as evidence in order to substantiate a specific theoretical claim. The general question concerning the Google Books data itself, whether the acquisition strategy of major libraries really can serve as an temporarily unbiased proxy for the evolution of subjective or even latent cognitive traits, is an open research question.

Again, we are rather skeptical. For example, a change in the acquisition strategy of one major library is not necessarily motivated by one of the factors we might be interested in; nevertheless in aggregation of the frequency counts of different n-grams, it might look like one. Once again, we want to refer to [ 22 ], p. Is the instrumentation actually capturing the theoretical construct of interest? Is measurement stable and comparable across cases and over time? Are measurement errors systematic? The outlined problems all have to do with the fact that—in making the data freely available which is a fantastic thing —Google wanted to avoid breaking any copyright laws, and it goes without saying that legal restrictions also have to be taken seriously in this case.

All recently published studies that we mentioned in the introduction do not explicitly model the underlying temporal structure of the data [ 12 — 18 ]. This certainly has to do with the fact that time series analysis is a relatively young statistical discipline [ 11 ], p. To improve the reliability of research [ 32 ], we hope that this paper will help both researchers and reviewers to understand why it is important to use special models for the analysis of such data.

Standard statistical models that work for cross-sectional data run the risk of incorrect statistical inference in time-series analysis, where potentially strong effects are meaningless and therefore can potentially lead to wrong conclusions. While our analysis indicates that type-token ratios do not dependent on population sizes, this does not imply, of course, that the increase of the type-token ratios over time is not interesting in itself as Harald Baayen personal communication points out, because this increase could reflect the fact that onomasiological needs increase with the complexity of modern societies [ 33 ].

Or put differently, new ideas and new technologies need new designations in order to efficiently communicate about related concepts. Thus, under the assumption that cultural adaption is cumulative [ 34 , 35 ], a rapid increase of technological innovations could result in an increase of the type-token ratio, independently of the population size.

This is certainly an interesting avenue for future research. S1 File contains the population data, compiled from [ 36 ]. The time-series of the global mean sea level was presented in [ 7 ] and is available at [ 37 ]. The type-token ratio, a common way to measure lexical diversity, is based on the Google Books datasets that were made available by [ 6 ] at [ 27 ]. The type-token ratio for each year and each language is calculated by dividing the number of unique strings by the total number of strings.

Higher type-token ratios are indicative of higher lexical diversity. Since this measure is known to be heavily text-length dependent [ 38 ] and given the fact that the corpus size based on the Google Books data strongly increases as a function of time, calculating the type-token ratio based on the actual corpus sizes would systematically bias the results. To solve this problem, random samples of 1,, tokens were drawn from the data as described in [ 39 ]. For each resulting series this means that the current value of the series depends on its previous value plus a positive drift term and a white noise error term.

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At each point in time, the series takes one random step away from the last position, but as result of the drift term, the series will have an upward trend in the long-run. From a statistical point of view, temporal autocorrelation is problematic because it biases our estimators. If, for example, we fit a simple time-series regression that can be written as:. In the presence of first-order autocorrelation, the OLS estimators are biased and lead to incorrect statistical inferences [ 41 ].

To see, why this is also the problem of our simulation, Fig 5 shows the correlation between current and lagged residuals of an OLS regression for each of the simulated random walks with drift on the annual global mean seal level. Top: Histogram for levels.

  • (Mean) type/token ratios.
  • Poetic Travel of Life : Book of Poetry and Short Stories;
  • Associated Data.

Bottom: Histogram for year-to-year changes. We would like to thank Sascha Wolfer for valuable comments on earlier drafts of this article and Sarah Signer for proofreading. Also, we are grateful to an anonymous reviewer for helpful suggestions and to Harald Baayen for insightful comments and additional inputs on the interpretation of our analyses as mentioned in the text. The publication of this article was funded by the Open Access fund of the Leibniz Association. All relevant data are within the paper and its Supporting Information files. National Center for Biotechnology Information , U.

PLoS One. Published online Mar 3. Karen Lidzba, Editor.