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if you want to finally understand
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statistics this is the place to be after
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this video you will know what statistics
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is what descriptive statistics is and
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what inferential statistics is so let's
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start with the first question what is
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statistics statistics deals with the
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collection analysis and presentation of
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data an example we would like to
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investigate whether gender has an
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influence on the preferred newspaper
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then gender and newspaper are our
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so-called variables that we want to
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analyze in order to analyze whether
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genda has an influence on the preferred
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newspaper we first need to collect data
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to do this we create a questionnaire
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that asks about gender and preferred
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newspaper we will then send out the
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survey and wait 2 weeks afterwards we
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can display the received answers in a
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table in this table we have one column
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for each variable one for gender and one
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for newspaper on the other hand each row
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is the response of one served person the
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first respondent is mail and stated New
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York Post the second is female and
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stated USA Today and so on and so forth
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of course the data does not have to be
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from a survey the data can also come
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from an experiment in which you for
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example want to study the effect of Two
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drugs on blood pressure now the first
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step is done we have collected data and
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we can start analyzing the data but what
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do we actually want to analyze we did
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not survey the entire population but we
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took a sample now the big question is do
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we just want to describe the sample data
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or do we want to make a statement about
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the whole population if our aim is
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limited to the sample itself I.E we only
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want to describe the collected data we
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will use descriptive statistics
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descriptive statistics will provide a
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detailed summary of the sample however
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if we want to draw conclusions about the
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population as a whole inferential
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statistics are used this approach allows
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us to make educated guesses about the
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population based on the sample data let
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us take a closer look at both methods
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starting with descriptive statistics why
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is descriptive statistics so important
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let's say a company wants to know how
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its employees travel to work so the
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company creates a survey to answer this
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question once enough data has been
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collected this data can be analyzed
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using descriptive statistics but what is
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descriptive statistics descriptive
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statistics aims to describe and
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summarize a data set in a meaningful way
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but it is important to note that
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descriptive statistics only describe the
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collection data without drawing
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conclusions about a larger population
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put simply just because we know how some
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people from one company get to work we
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cannot say how all working people of the
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company get to work this is the task of
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infuential Statistics which we will
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discuss later to describe data
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descriptively we now look at the four
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key components measures of central
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tendency measures of dispersion
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frequency tables and parts let's start
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with the first one measures of central
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tendency measures of central tendency
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are for example the mean the median and
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the mode Let's first have a look at the
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mean the arithmetic mean is the sum of
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all observations divided by the number
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of observations an example imagine we
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have the test scores of five students to
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find the mean score we sum up all the
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scores and divide by the number of
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scores the mean test score of these five
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students is therefore
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86.6 what about the median when the
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values in a data set are arranged in
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ascending order the median is the middle
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value if there is an odd number of data
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points the median is simply the middle
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value if there is an even number of data
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points the median is the average of the
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two middle values it is important to
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note that the median is resistant to
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extreme values or outliers let's look at
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this example no matter how tall the last
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person is the person in the middle
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Remains the person in the middle so the
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median does not change but if we look at
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the mean it does have an effect on how
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tall the last person is the mean is
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therefore not robust to outliers let's
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continue with the mode the mode refers
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to the value or values that appear most
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frequently in a a set of data for
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example if 14 people travel to work by
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car six by bike five walk and five take
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public transport then car occurs most
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often and is therefore the mode great
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let's continue with the measures of
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dispersion measures of dispersion
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describe how spread out the values in a
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data set are measures of dispersion are
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for example the variance and standard
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deviation the rate
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and the interquartile range let's start
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with the standard deviation the standard
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deviation indicates the average distance
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between each data point and the mean but
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what does that mean each person has some
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deviation from the mean now we want to
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know how much the person's deviate from
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the mean value on average in this
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example the average deviation from the
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mean value is 11.5 cm to calculate the
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standard deviation we can use this
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equation Sigma is the standard deviation
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n is the number of persons x i is the
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size of each person and xar is the mean
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value of all persons but attention there
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are two slightly different equations for
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the standard deviation the difference is
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that we have once 1 / by n and 1's 1 /
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nus 1 to keep it simple if our survey
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doesn't cover the whole population we
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always use this equation to estimate the
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standard deviation likewise if we have
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conducted a clinical study then we also
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use this equation to estimate the
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standard deviation but what is the
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difference between the standard
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deviation and the variance as we now
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know the standard deviation is the
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quadratic mean of the distance from the
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mean the variance now is the squared
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standard deviation if if you want to
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know more details about the standard
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deviation and the variance please watch
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our video let's move on to range and
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interquartile range it is easy to
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understand the range is simply the
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difference between the maximum and
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minimum value inter quartile range
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represents the middle 50% of the data it
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is the difference between the first
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quartile q1 and the third quartile Q3
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therefore 25% of the values are smaller
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than the interquartile range and 25% of
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the values are larger the inter quartile
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range contains exactly the middle 50% of
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the values before we get to the last two
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points let's briefly compare measures of
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central tendency and measures of
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dispersion let's say we measure the
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blood pressure of patients measures of
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central tendency provide a single value
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that represents the entire data set have
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helping to identify a central value
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around which data points tend to Cluster
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measures of dispersion like the standard
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deviation the range and the
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interquartile range indicate how spread
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out the data points are whether they are
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closely packed around the center or
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spread far from it in summary while
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measures of central tendency provide a
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central point of the data set measures
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of dispersion describe how the data is
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spread around Center let's move on to
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tables here we will have a look at the
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most important ones frequency tables and
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contingency tables a frequency table
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displays how often each distinct value
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appears in a data set let's have a
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closer look at the example from the
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beginning a company surveyed its
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employees to find out how they get to
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work the options given were car bicycle
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walk and public transport here are the
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results results from 30 employees the
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first answered car the next walk and so
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on and so forth now we can create a
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frequency table to summarize this data
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to do this we simply enter the four
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possible options car bicycle walk and
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public transport in the First Column and
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then count how often they occurred from
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the table it is evident that the most
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common mode of Transport among the
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employees is by car with 14 employees
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preferring it the frequency table thus
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provides a clear and concise summary of
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the data but what if we have not only
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one but two categorical variables this
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is where the contingency table also
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called cross tab comes in Imagine the
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company doesn't have one Factory but two
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one in Detroit and one in Cleveland so
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we also ask the employees at which
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location they work if we want to display
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both variables we can use a contingency
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table a contingency table provides a way
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to analyze and compare the relationship
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between two categorical variables the
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rows of a contingency table represent
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the categories of one variable while the
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columns represent the categories of
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another variable each cell in the table
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shows the number of observations that
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fall into the corresponding category
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combination for example the first cell
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show that car and Detroit were answered
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six times and what about the charts
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let's take a look at the most important
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ones to do this let's simply use
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data.net if you like you can load this
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sample data set with the link in the
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video description or you just copy your
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own data into this table here below you
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can see the variables distance to work
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mode of transport and site data daab
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gives you a hint about the level of
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measurement but you can also change it
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here now if we only click on mode of
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Transport we get a frequency table and
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we can also display the percentage
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values if we scroll down we get a bar
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chart and a pie chart here on the left
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we can adjust further settings for
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example we can specify whether we want
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to display the frequencies or the
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percentage values or whether the bars
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should be vertical or
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horizontal if you also select side we
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get a cross table here and a grouped bar
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chart for the diagrams here we can
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specify whether we want the chart to be
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grouped or stacked if we click on
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distance to work and mode of Transport
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we get a bar chart where the height of
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the bar shows the mean value of the
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individual groups here we can also
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display the
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dispersion we also get a histogram a box
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plot a violin plot and a rainbow plot if
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you would like to know more about what a
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box plot a violin plot and a rainbow
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plot are take a look at my videos let's
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continue with inferential statistics at
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the beginning we briefly go through what
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inferential statistics is and then I'll
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explain the six key components to you so
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what is inferential statistics
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inferential statistics allows us to make
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a conclusion or inference about a
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population based on data from a sample
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what is the population and what is the
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sample the population is the whole group
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we're interested in if you want to study
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the average height of all adults in the
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United States then the population would
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be all adults in the United States the
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sample is a smaller group we actually
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study chosen from the population for
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example 150 the adults were selected
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from the United States and now we want
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to use the sample to make a statement
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about the population and here are the
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six steps how to do that number one
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hypothesis first we need a statement a
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hypothesis that we want to test for
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example you want to know whether a drug
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will have a positive effect on blood
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pressure in people with high blood
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pressure but what's next in our
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hypothesis we stated that we would like
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to study people with high blood pressure
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so our population is all people with
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high blood pressure in for example the
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us obviously we cannot collect data from
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the whole population so we take a sample
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from the population now we use this
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sample to make a statement about the
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population but how do we do that for
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this we need a hypothesis test
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hypothesis testing is a method for
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testing a claim about a parameter in a
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population using data measured in a
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sample great that's exactly what we need
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there are many different hypothesis
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tests and at the end of this video I
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will give you a guide on how to find the
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right test and of course you can find
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videos about many more hypothesis tests
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on our Channel but how does a hypothesis
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test work when we conduct a hypothesis
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test we start with a research hypothesis
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also called alternative hypothesis this
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is the hypothesis we are trying trying
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to find evidence for in our case the
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research hypothesis is the drug has an
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effect on blood pressure but we cannot
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test this hypothesis directly with a
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classical hypothesis test so we test the
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opposite hypothesis that the drug has no
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effect on blood pressure but what does
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that mean first we assume that the drug
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has no effect in the population we
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therefore assume that in general people
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who take the drug and people who don't
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take the drug have the same blood
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pressure on average if we now take a
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random sample and it turns out that the
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drag has a large effect in a sample then
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we can ask How likely it is to draw such
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a sample or one that deviates even more
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if the drag actually has no effect so in
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reality on average there's no difference
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in a population if this probability is
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very low we can ask ourselves maybe the
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drug has an effect in the population and
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we may have enough evidence to reject
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the null hypothesis that the drug has no
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effect and it is this probability that
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is called the P value let's summarize
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this in three simple steps number one
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the null hypothesis states that there is
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no difference in the population number
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two the hypothesis test calculates how
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much the sample deviates from the null
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hypothesis number three the P value
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indicates the probability of getting a
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sample that deviates as much as our
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sample or one that even deviates more
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than our sample assuming the null
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hypothesis is true but at what point is
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the P value small enough for us to
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reject the Nile hypothesis this brings
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us to the next Point statistical
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significance if the P value is less than
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a predetermined threshold the result is
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considered statistic ically significant
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this means that the result is unlikely
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to have occurred by chance alone and
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that we have enough evidence to reject
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the N hypothesis this threshold is often
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0.05 therefore a small P value suggests
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that the observed data or sample is
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inconsistent with the null hypothesis
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this leads us to reject the null
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hypothesis in favor of the alternative
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hypothesis a large P value suggests that
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the obser serve data is consistent with
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the Nal hypothesis and we will not
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reject it but note there is always a
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risk of making an error a small P value
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does not prove that the alternative
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hypothesis is true it is only saying
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that it is unlikely to get such a result
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or a more extreme when the null
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hypothesis is true and again if the null
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hypothesis is true there is no
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difference in the population and the
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other way around a large p value does
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not prove that the N hypothesis is true
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it is only saying that it is likely to
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get such a result or a more extreme when
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the null hypothesis is true so there are
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two types of Errors which are called
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type one and type two error let's start
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with the type one error in hypothesis
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testing a type one error occurs when a
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true null hypothesis is rejected so in
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reality the null hypothesis is true but
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we make the the decision to reject the
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null hypothesis in our example it means
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that the drug actually had no effect so
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in reality there is no difference in
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blood pressure whether the drug is taken
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or not the blood pressure Remains the
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Same in both cases but our sample
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happened to be so far off the True Value
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that we mistakenly thought the drag was
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working and a type two error occurs when
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a full Sile hypothesis is not rejected
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so in reality the null hypothesis is
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false but we make the decision not to
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reject the null hypothesis in our
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example this means the drag actually did
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work there is a difference between those
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who have taken the drag and those who
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have not but it was just a coincidence
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that the sample taken did not show much
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difference and we mistakenly thought the
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drug was not working and now I'll show
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you how data helps you to find a
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suitable hypothesis test and of course
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calculates it and interprets the results
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for you let's go to data.net and copy
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your own data in here we will just use
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this example data set after copying your
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data into the table the variables appear
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down here data tab automatically tries
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to determine the correct level of
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measurement but you can also change it
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up here now we just click on hypothesis
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testing and select the variables we want
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to use for the calculation of a
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hypothesis test data tab will then
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suggest a suitable test for example in
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this case a Kai Square test or in that
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case an analysis of
00:19:46
variant then you will see the hypotheses
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and the results if you're not sure how
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to interpret the results click on
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summary inverts further you can check
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the assumptions and decide whether you
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want to calculate a parametric or a
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non-parametric test you can find out the
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difference between parametric and
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nonparametric tests in my next video
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thanks for watching and I hope you
00:20:13
enjoyed the
00:20:19
video
