Statistics

1. Standard Error

   Anmerkungen:

   • Standard error from population
2. population Mean
3. population variance
   1. population Stand Dev

Anmerkungen:

• use sample statistic to estimate the population parameters. Point estimates - single value that approximates the true value of a population parameter

1. Mean x
2. Variance
   1. Stand Dev S
3. Hypothesis tests

   Anmerkungen:

   • Statistical hypothesis is a claim about a population parameter and determines what we actually test
   1. confidence interval

      Anmerkungen:

      • A range of likely values for a population parameter. Using CI we can say: it is likely that the population parameter is somewhere within this range.
      1. confidence level 99%

         Anmerkungen:

         • how sure we are that confidence interval containts the actual population parameters
      2. confidence level 95%
      3. confidence level 90%
      4. practice
         1. compare to samples
         2. compare sample to industry std.
   2. Null H0

      Anmerkungen:

      • Population parameter equals a specified value or equals parameter from another population
      1. p-value t-value
         1. NULL = FALSE significant difference

            Anmerkungen:

            • rejection = significant evidence of difference between mean from sample and population mean
            1. reject null hypothesis

               Anmerkungen:

               • if we reject our results are statistically significant
               1. (NULL true) type 1 error

                  Anmerkungen:

                  • if null hypothesis is true and we reject it: type 1 error
                  1. probability = alpha

                     Anmerkungen:

                     • reducing alpha increasing beta
               2. NULL false: correct decision
                  1. Power (1 - Beta)
                     1. sample size

                        Anmerkungen:

                        • sample increases, power increases. sample +  ......  power +
                     2. population differences

                        Anmerkungen:

                        • as the population diffrences decreases, power decreases as well
                     3. variability

                        Anmerkungen:

                        • As variability increases, power decreases
                     4. level Alpha

                        Anmerkungen:

                        • common 0.05 level mean that we are willing to accept  a 5% chance that we incorrectly rejected the null hypothesis if alpha is set higher we are more likely to correctly reject the null hypothesis if alpha has smoller value is easier to see difference between sample mean and population mean
         2. NULL = TRUE no difference evidence

            Anmerkungen:

            • there is no evidence for difference between sample mean and population mean
            1. fail to reject the null hypothesis

               Anmerkungen:

               • it concludes that we have not enough evidence to claim that alternative hypothesis is true
               1. type 2 error

                  Anmerkungen:

                  • if null hypothesis is false and we fail to reject it: type 2 error
                  1. probability = Beta

                     Anmerkungen:

                     • increasing beta reducing alpha
               2. NULL true : correct decision
   3. Alternative H1

      Anmerkungen:

      • Population parameter does not equal specified value
   4. making decision
      1. 1-sample t-test

         Anmerkungen:

         • determine whether the population mean is equal to a hypothesized value
         1. Numeric data
         2. Random Data
         3. hypothesed value = population mean
         4. procedure
            1. determine null

               Anmerkungen:

               • the null hypothesis is that the hyphotesiszed value is equal to population mean
            2. determine alternative

               Anmerkungen:

               • alternative is the opposite null
            3. collect sample from population
               1. sample mean
               2. sample standard deviation
            4. Graph

               Anmerkungen:

               • graph to take a sense of variability and information about the mean
               1. individual value plot
            5. interpret
               1. p-value
               2. T-value
               3. alpha level
   5. 2 variance test
      1. Numeric Data
      2. Random Data
      3. comparing two populations
      4. procedure
         1. determine NULL

            Anmerkungen:

            • null hypothesis state that two populations have the same variability
         2. determine alternative

            Anmerkungen:

            • there is not the same variance between two populations
         3. colect sample 2 population
            1. data continious
            2. cmes from 2 independet samples
            3. randomly taken
         4. graph data
         5. interpret test
            1. Bonett
            2. Leven
   6. 2 sample t-test
      1. procedure
         1. termine NULL
         2. determiane alternative
         3. collect samples
            1. Normally distributed
            2. randomly taken
            3. taken from 2 populations
            4. ndependent samples
            5. potentially unequal variationces
            6. probalility plot ?
         4. graph the data
            1. two individual value plot
         5. conduct test, interpret data
            1. p-value
   7. Paired t-test
      1. procedure
         1. NULL hypothesis

            Anmerkungen:

            • the population means are equal
         2. alternative hypothe

            Anmerkungen:

            • the population means are not equal
         3. collect paired samples
            1. Probability test required?

               Anmerkungen:

               • do we need to prove probability ? Are we sure that data are with normal distribution?
            2. dependent sample
            3. numeric
            4. random sample
            5. normally distributed
         4. graph the data

            Anmerkungen:

            • Individual value plot (values are substracted between both samples. We plot differences !
         5. conduct test interpretation

            Anmerkungen:

            • checking p-value, t-value and confidence interval. how calculated mean relate to confidence interval?

1. 1Sigma
2. 2 sigma
3. 3 sigma
4. Estimated Standard Error

   Anmerkungen:

   • calculate sampling deviation
   1. Z-score

      Anmerkungen:

      • calculate sigma level
      1. t-disctribution

         Anmerkungen:

         • t-distribution applied to sampling and used only for normal distribution data
         1. Cumulative probability

            Anmerkungen:

            • cumulative probability for a single observation

1. Bar Chart

   Anmerkungen:

   • Compare categorical data, display counts of several categories, shows the frequency of each categories, easy to spot differences between two or more groups in count, 
2. Pareto Chart

   Anmerkungen:

   • Produced to identify the largest opportunities for improvements 
3. Pie Chart

   Anmerkungen:

   • Shows relation of parts to a whole, shows differences in percentage between categories in group or groups, (proportions of each categories relative to the whole), 
4. Histogram

   Anmerkungen:

   • Shows the distribution of the data set, shape of the distribution, symmetricity,  numerate to large number of displayed data
5. Dotplot

   Anmerkungen:

   • Dotplot, displays dot for each data value in the bin, useful for small  set of numeric data, we can see how the data is clustered (density in the bin), and shows the outliers
6. Individual Value Plot

   Anmerkungen:

   •    Displays individual variables for single group or groups of variables, (for example data for two production lines) The individual value plot is graph with one dot representing each individual value.   
7. Boxplot

   Anmerkungen:

   • Help to see larger patterns in the set distribution, Summarize the distribution of data,  Shows distribution of data, can be used to compare distribution of two groups (for example morning and evening shifts)   
8. Time Series Plot

   Anmerkungen:

   • Shows patterns over time, (increasing or decreasing variation over time), time related questions about variable, change in the process in the time scale or change in the data collection, variation over time is consistent?,