Statistics

Population / population parameters
1. Standard Error
  Annotations:
  - Standard error from population
2. population Mean
3. population variance
  1. population Stand Dev
Samples / Point Estimates
Annotations:
- 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
  Annotations:
  - Statistical hypothesis is a claim about a population parameter and determines what we actually test
  1. confidence interval
    Annotations:
    - 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%
      Annotations:
      - 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
    Annotations:
    - Population parameter equals a specified value or equals parameter from another population
    1. p-value t-value
      1. NULL = FALSE significant difference
        Annotations:
        rejection = significant evidence of difference between mean from sample and population mean
        reject null hypothesis
        Annotations:
        if we reject our results are statistically significant
        (NULL true) type 1 error
        Annotations:
        if null hypothesis is true and we reject it: type 1 error
        probability = alpha
        Annotations:
        reducing alpha increasing beta
        NULL false: correct decision
        Power (1 - Beta)
        sample size
        Annotations:
        sample increases, power increases. sample + ...... power +
        population differences
        Annotations:
        as the population diffrences decreases, power decreases as well
        variability
        Annotations:
        As variability increases, power decreases
        level Alpha
        Annotations:
        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
        Annotations:
        there is no evidence for difference between sample mean and population mean
        fail to reject the null hypothesis
        Annotations:
        it concludes that we have not enough evidence to claim that alternative hypothesis is true
        type 2 error
        Annotations:
        if null hypothesis is false and we fail to reject it: type 2 error
        probability = Beta
        Annotations:
        increasing beta reducing alpha
        NULL true : correct decision
  3. Alternative H1
    Annotations:
    - Population parameter does not equal specified value
  4. making decision
    1. 1-sample t-test
      Annotations:
      - determine whether the population mean is equal to a hypothesized value
      1. Numeric data
      2. Random Data
      3. hypothesed value = population mean
      4. procedure
        determine null
        Annotations:
        the null hypothesis is that the hyphotesiszed value is equal to population mean
        determine alternative
        Annotations:
        alternative is the opposite null
        collect sample from population
        sample mean
        sample standard deviation
        Graph
        Annotations:
        graph to take a sense of variability and information about the mean
        individual value plot
        interpret
        p-value
        T-value
        alpha level
  5. 2 variance test
    1. Numeric Data
    2. Random Data
    3. comparing two populations
    4. procedure
      1. determine NULL
        Annotations:
        null hypothesis state that two populations have the same variability
      2. determine alternative
        Annotations:
        there is not the same variance between two populations
      3. colect sample 2 population
        data continious
        cmes from 2 independet samples
        randomly taken
      4. graph data
      5. interpret test
        Bonett
        Leven
  6. 2 sample t-test
    1. procedure
      1. termine NULL
      2. determiane alternative
      3. collect samples
        Normally distributed
        randomly taken
        taken from 2 populations
        ndependent samples
        potentially unequal variationces
        probalility plot ?
      4. graph the data
        two individual value plot
      5. conduct test, interpret data
        p-value
  7. Paired t-test
    1. procedure
      1. NULL hypothesis
        Annotations:
        the population means are equal
      2. alternative hypothe
        Annotations:
        the population means are not equal
      3. collect paired samples
        Probability test required?
        Annotations:
        do we need to prove probability ? Are we sure that data are with normal distribution?
        dependent sample
        numeric
        random sample
        normally distributed
      4. graph the data
        Annotations:
        Individual value plot (values are substracted between both samples. We plot differences !
      5. conduct test interpretation
        Annotations:
        checking p-value, t-value and confidence interval. how calculated mean relate to confidence interval?
Normal Distribution
1. 1Sigma
2. 2 sigma
3. 3 sigma
4. Estimated Standard Error
  Annotations:
  - calculate sampling deviation
  1. Z-score
    Annotations:
    - calculate sigma level
    1. t-disctribution
      Annotations:
      - t-distribution applied to sampling and used only for normal distribution data
      1. Cumulative probability
        Annotations:
        cumulative probability for a single observation
Descriptive Statistics
1. Bar Chart
  Annotations:
  - 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
  Annotations:
  - Produced to identify the largest opportunities for improvements
3. Pie Chart
  Annotations:
  - 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
  Annotations:
  - Shows the distribution of the data set, shape of the distribution, symmetricity, numerate to large number of displayed data
5. Dotplot
  Annotations:
  - 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
  Annotations:
  - 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
  Annotations:
  - 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
  Annotations:
  - 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?,

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	Created by Raf Jablonsky about 6 years ago