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# ### Difference of mean survey total
# ### Difference of mean survey total
#
# When considering only lakes the difference of medians is inversed, less litter was observed in 2020 than 2018 and the difference of means is much larger in favor of 2018. Suggesting that at the lake level there was a decrease in observed quantities.
#
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#
# The land use features were previously calculated to compare the survey locations. To test the statistical significance of land use on beach litter survey results the survey totals and locations from both projects were considered as one group. The survey results of the most common objects were tested against the measured land use features.
#
# Spearman"s $\rho$ oor Spearmans ranked correlation coefficient is a non-parametric test of rank correlation between two variables {cite}`defspearmans` {cite}`spearmansexplained`. The test results are evaluated at p<0.05 and 454 samples, SciPy is used to implement the test {cite}`impspearmans`.
# Spearmans $\rho$ or Spearmans ranked correlation coefficient is a non-parametric test of rank correlation between two variables {cite}`defspearmans` {cite}`spearmansexplained`. The test results are evaluated at p<0.05 and 454 samples, SciPy is used to implement the test {cite}`impspearmans`.
#
# 1. Red/rose is a positive association: p<0.05 AND $\rho$ > 0
# 2. yellow is a negative association: p<0.05 AND $\rho$ < 0
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#
# From 2018 - 2020 there was a statistically significant change, a decrease in the number of objects directly related to behavior at the survey site. This indicates that any perceived decreases were in locations that had a higher % of land attributed to buildings and lower % of land attributed to agriculture or woods.
#
# Locations with an opposing or different land use profile (less buildings, more agriculture or woods) will most likely not have experienced any decrease at all. For locations near river interchanges or major discharge points there would be no perceivable difference from 2018 - 2020 and increases in fragmented plastics, expanded foams and industrial sheeting were likely. Both the test of difference of medians of the most common objects and the results fromSpearmans $\rho$ oof survey results support this conclusion.
# Locations with an opposing or different land use profile (less buildings, more agriculture or woods) will most likely not have experienced any decrease at all. For locations near river interchanges or major discharge points there would be no perceivable difference from 2018 - 2020 and increases in fragmented plastics, expanded foams and industrial sheeting were likely. Both the test of difference of medians of the most common objects and the results from Spearmans $\rho$ of survey results support this conclusion.
#
# Both survey years show peak survey results in June - July (annex) and lows in November. The possible causes for the peaks and troughs are different depending on the object in question. Food and tobacco objects are more prevalent during the summer season because of increased use. Objects like fragmented plastics depend more on hydrological conditions and the peak discharge rate of the biggest rivers in this study are from May - July( _section [Shared responsibility](transport)_ ).
#
# Future surveys should include visible items of all sizes. Data aggregation can be done at the server using defined rules based on known relationships. The total count is a key indicator in all statistics that rely on count data, for modeling purposes it is essentia
# Future surveys should include visible items of all sizes. Data aggregation can be done at the server using defined rules based on known relationships. The total count is a key indicator in all statistics that rely on count data, for modeling purposes it is essential.

# ## Annex
#
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#
# Die Merkmale der Landnutzung wurden zuvor berechnet, um die Erhebungsorte zu vergleichen. Um die statistische Signifikanz der Landnutzung auf die Ergebnisse der Strandabfalluntersuchung zu testen, wurden die Gesamtzahlen und Standorte beider Projekte als eine Gruppe betrachtet. Die Umfrageergebnisse der häufigsten Objekte wurden mit den gemessenen Landnutzungsmerkmalen verglichen.
#
# Spearman"s $\rho$ orSpearmans Rangkorrelationskoeffizient ist ein nichtparametrischer Test der Rangkorrelation zwischen zwei Variablen {cite}`defspearmans` {cite}`spearmansexplained`. Die Testergebnisse werden bei p<0,05 und 454 Stichproben ausgewertet. Zur Implementierung des Tests wird SciPy verwendet {cite}`impspearmans`.
# Spearman's $\rho$ oder Spearmans Rangkorrelationskoeffizient ist ein nichtparametrischer Test der Rangkorrelation zwischen zwei Variablen {cite}`defspearmans` {cite}`spearmansexplained`. Die Testergebnisse werden bei p<0,05 und 454 Stichproben ausgewertet. Zur Implementierung des Tests wird SciPy verwendet {cite}`impspearmans`.
#
# 1. rot/rosa ist eine positive Assoziation: p<0.05 AND $\rho$ > 0
# 2. gelb ist eine negative Assoziation: p<0.05 AND $\rho$ < 0
# 3. weißen Medianen, die p>0,05 sind, gibt es keine statistische Grundlage für die Annahme eines Zusammenhangs
#
# An association suggests that survey totals for that object will change in relation to the amount of space attributed to that feature, or in the case of roads or river intersections, the quantity. The magnitude of the relationship is not defined and any association is not linear.
#
# *__Unten:__ Eine Assoziation deutet darauf hin, dass sich die Erhebungssummen für das betreffende Objekt im Verhältnis zu der diesem Merkmal zugewiesenen Fläche oder - im Falle von Straßen oder Flusskreuzungen - der Menge ändern. Das Ausmaß der Beziehung ist nicht definiert, und jede Assoziation ist nicht linear.*

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(PSI) Paul Scherrer Institute

(PC or pc) parent code

(pcs) pieces

(p/100m) Pieces per 100 meters
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Expand Up @@ -917,7 +917,7 @@ <h3><span class="section-number">14.2.3. </span>Confidence intervals (CIs)<a cla
</div></blockquote>
<div class="section" id="bootstrap-methods">
<h4><span class="section-number">14.2.3.1. </span>Bootstrap methods:<a class="headerlink" href="#bootstrap-methods" title="Permalink to this headline"></a></h4>
<p>Bootstrapping is a resampling method that uses random sampling with replacement to repeat or simulate the sampling process. Bootstrapping permits the estimation of the sampling distribution of sample statistics using random sampling methods. <span id="id10">[<a class="reference internal" href="references.html#id29">Wika</a>]</span> <span id="id11">[<a class="reference internal" href="references.html#id18">JLGC19</a>]</span> <span id="id12">[<a class="reference internal" href="references.html#id26">SS21</a>]</span></p>
<p>Bootstrapping is a resampling method that uses random sampling with replacement to repeat or simulate the sampling process. Bootstrapping permits the estimation of the sampling distribution of sample statistics using random sampling methods. <span id="id10">[<a class="reference internal" href="references.html#id29">Wika</a>]</span> <span id="id11">[<a class="reference internal" href="references.html#id18">JLGC19</a>]</span> <span id="id12">[<a class="reference internal" href="references.html#id26">Sta21b</a>]</span></p>
<p>Bootstrap methods are used to calculate the CIs of the test statistics, by repeating the sampling process and evaluating the median at each repetition. The range of values described by the middle 95% of the bootstrap results is the CI for the observed test statistic.</p>
<p>There are several computational methods to choose from such as percentile, BCa, and Student’s t. For this example, two methods were tested:</p>
<ol class="simple">
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<div class="section" id="method-of-moments">
<h5><span class="section-number">14.3.1.2.1. </span>Method of moments<a class="headerlink" href="#method-of-moments" title="Permalink to this headline"></a></h5>
<p>The method of moments assumes that the parameters derived from the sample are close or similar to the population parameters. In the case of beach-litter surveys that means the sample median, mean and variance could be considered close approximations of the actual values if all the beaches on all the lakes and streams were surveyed.</p>
<p>Concretely, the parameters of a probable distribution model are estimated by calculating them from the sample data. This method is easy to apply because most of the parameter calculations for the most common distributions are well known. <span id="id24">[<a class="reference internal" href="references.html#id17">MDG18</a>]</span> <span id="id25">[<a class="reference internal" href="references.html#id25">VGO+20</a>]</span> <span id="id26">[<a class="reference internal" href="references.html#id24">Ove</a>]</span></p>
<p>Concretely, the parameters of a probable distribution model are estimated by calculating them from the sample data. This method is easy to apply because most of the parameter calculations for the most common distributions are well known. <span id="id24">[<a class="reference internal" href="references.html#id17">MDG18</a>]</span> <span id="id25">[<a class="reference internal" href="references.html#id25">VGO+20</a>]</span> <span id="id26">[<a class="reference internal" href="references.html#id24">SO</a>]</span></p>
</div>
<div class="section" id="maximum-likelihood-estimation">
<h5><span class="section-number">14.3.1.2.2. </span>Maximum likelihood estimation<a class="headerlink" href="#maximum-likelihood-estimation" title="Permalink to this headline"></a></h5>
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