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Deze samenvatting is gebaseerd op het studiejaar 2013-2014.
Chapter 1
Descriptive statistics | Deals with methods of organizing, summarizing and presenting data in a convenient and informative way |
Inferential statistics | Body of methods used to draw conclusions or inferences about characteristics of populations based on sample data |
Exit polls | For example: voters in the USA. A random sample of voters who exit the polling booth are asked for whom they voted. |
Population | Group of all items of interest to a statistical practioner |
Parameter | Descriptive measure of a population |
Sample | Set of data drawn from studied population |
Statistic | Descriptive measure of a sample |
Statistical inference | Process of making an estimate, prediction or decision about a population based on sample data. |
Confidence level | Proportion of times that an estimating procedure will be corrected |
Significance level | How frequently a conclusion will be wrong |
Chapter 2
Variable | Some characteristic of a population or sample |
Value (of a variable) | Possible observations of the variable |
Data | Observed values of a variable |
Interval data | A real number, such as weight / height. Also referred to as quantative or numerical |
Nominal data | Values are categories, there is no meaning in their order. They can also be called qualitative or categorical |
Ordinal data | The order of values has a meaning |
Frequency distribution | Summarize data in a table which presents the categories and their counts |
Relative frequency distribution | Lists the categories and the proportion with which each one occurs |
Bar chart | A chart with rectangular bars with lengths proportional to the values that they represent. Used to display frequencies |
Pie chart | A circular chart divided into sectors, illustrating numerical proportion. It shows relative frequencies |
Univariate | Techniques applied to single sets of data |
Bivariate | Techniques applied to depict a relationship between variables |
Cross-clarification (cross-tabulation) table | Used to describe the relationship between two nominal variables |
Chapter 3
Classes | Number of observations that fall into a series of intervals (that cover a complete range of observations) |
Histogram | A graph, created by drawing rectangles whose bases are the intervals and whose heights are the frequencies |
Class width | Calculated by subtracting the smallest observation from the largest observation and dividing that number by the number of classes |
Symmetric histogram | When you draw a vertical line in the centre, the two sides of the histogram are identical in shape and size |
Skewness | A histogram is skewed when it has a long tail extending to the right (positively skewed) or the left (negatively skewed) |
Mode | Observation that occurs with the greatest frequency |
Modal class | Class with the largest number of observations |
Unimodal histogram | A histogram with a single peak |
Bimodal histogram | A histogram with two peaks, which can be unequal in height |
Bell-shape | A special type of a symmetrical unimodal histogram |
Stem-and-leaf display | A device for presenting quantitative data in a graphical format, similar to a histogram, to assist in visualizing the shape of a distribution. Observations must be placed in ascending order. Each observation will be divided into a stem and a leaf. Typically, the leaf contains the last digit of the number and the stem contains all of the other digits. |
Ogive | Graphical representation of the cumulative relative frequencies |
Cumulative relative frequency distribution | A tabular summary of a set of data showing the relative frequency of items less than or equal to the upper class class limit of each class. Relative frequency is the fraction or proportion of the total number of items. |
Credit scorecards | Used by banks and financial institutions to determine whether the applicant will receive a loan |
Time-series data | Represent measurements of successive points in time |
Cross-sectional data | The observations are measured at the same time |
Line chart | A type of chart which displays information as a series of data points called 'markers' connected by straight line segments. |
Scatter diagram | A type of mathematical diagram using Cartesian coordinates to display values for two variables for a set of data. |
Dependent variable | Variable depends to some degree on the other variable |
Linear relationship | A straight line is drawn in the scatter diagram. There is a linear relationship if most points fall close to this line |
Positive linear relationship | If one variable increases when the other does |
Negative linear relationship | When two variables tend to move in the opposite direction |
Graphical excellence | Is achieved when certain characteristics apply |
Chapter 4
Measures of central location | Mean, Median, Mode |
Arithmetic mean | Often called mean or average. Computed by summing the observations and dividing by the number of observations |
Median | Calculated by placing all observations in order. The middle observation is the median. When there are two middle observations, you take their average to calculate the median |
Mode | Observation which occurs with the greatest frequency |
Geometric mean | A type of mean or average, which indicates the central tendency or typical value of a set of numbers by using the product of their values (as opposed to the arithmetic mean which uses their sum). |
Measures of variability | Range, variance, standard deviation and coefficient of variation |
Range | The largest observation minus the smallest observation |
Variance | Measures how far a set of numbers is spread out. |
Mean absolute deviation (MAD) | The average absolute value of the deviations |
Standard deviation | Shows how much variation or dispersion from the average exists. Computed by the positive square root of the variance |
Empirical Rule | Only used if the histogram is bell-shaped. Approximately 68% of all observations fall within one standard deviation of the mean. 95% is within two standard deviations of the mean and 99.7% is within three standard deviations of the mean |
Chebycheff’s Theorem | The proportion of observations in any sample or population that lie within k standard deviations of the mean is at least 1-(1/k²) for k > 1 – If k=2, at least 75% of all observations lie within two standard deviations of the mean |
Coefficient of variation | The standard deviation of observations divided by their mean. |
Measures of relative standing | Designed to provide info about the position of particular values relative to an entire data set |
Percentile | The Pth percentile is the value for which P percent are less than that value and (100-P)% are great than that value |
Quartiles | The first quartile is the 25th percentile. The median is the 50th percentile. The upper quartile is at the 75th percentile. |
Interquartile range | Spread of the middle 50% of observations; the 75th percentile minus the 25th percentile |
Box plots | A graphical representation of five statistics: the minimum and maximum observations plus the 25th, 50th and 75th percentile |
Whiskers | Lines extending vertically from the boxes, indicating variability outside the upper and lower quartile |
Outliers | Unusually large or small observations, any point that lies outside the whiskers |
Measures of linear relationship | Covariance, coefficient of correlation, coefficient of determination |
Covariance | A measure of how much two random variables change together. |
Coefficient of correlation | Covariance divided by the standard deviations of the variables |
Breakeven analysis | How much sales volume your company needs to start making profit |
Least squares method | A standard approach to the approximate solution of over determined systems, i.e., sets of equations in which there are more equations than unknowns. 'Least squares' means that the overall solution minimizes the sum of the squares of the errors made in the results of every single equation. |
Coefficient of Determination | Measures the amount of variation in the dependent variable that is explained by the variation in the independent variable. Denoted as R² (R-squared) |
Chapter 6
Random experiment | Action or process that leads to one of several possible outcomes |
Exhaustive | All possible outcomes are included |
Mutually exclusive | No two outcomes can occur at the same time |
Sample space (of a random experiment) | List of all the possible outcomes of the experiment. They must be exhaustive and mutually exclusive |
Classic approach | To assigning probabilities, associated with game or chance. For example, to flip a coin or toss a die |
Relative frequency approach | To assigning probabilities, defines probability as a long run relative frequency with which an outcome occurs. |
Subjective approach | To assigning probabilities, defines probability as a degree of belief that we hold in the occurrence of an event |
Event | A collection or set of one or more simple events in a sample space |
Simple event | The individual outcome of a sample space |
Probability of an event | Sum of probabilities of the simple event that constitute the event |
Joint probability | The probability of the intersection of events A and B, that is, the event that occurs when both A and B occur |
Marginal probability | Computed by adding across rows or down columns, named so because they are calculated in the margins of the table |
Conditional probability | Probability of one event given the occurrence of another related event |
Independent events | Two events are independent if the probability of one event is not affected by the occurrence of another event |
Union | The union of events A and B is the event that occurs when either A or B or both occur |
Complement rule | The complement of event A is the event that occurs when event A does not occur. The probability of an event and the probability of an event’s complement must sum to 1. |
Multiplication rule | Used to calculate the joint probability of two events |
Addition rule | Used to calculate the probability of the union of two events |
Probability tree | Shows all the possible events. The first event is represented by a dot. From the dot, branches are drawn to represent all possible outcomes of the event. The probability of each outcome is written on its branch. |
Bayes’s Law | Method for computing conditional probabilities. |
Prior probability | Determined prior to a decision |
Likelihood probability | Conditional probability |
Posterior (Revised) probability | Prior probability that is revised after a decision is taken |
False-positive result | In medicine, the patient does not have the disease, the test shows positive |
False-negative result | In medicine, the patient has the disease, the test shows negative |
Chapter 7
Random variable | A function or rule that assigns a number to each outcome of an experiment |
Discrete random variable | Countable number of values |
Continuous random variable | The values are uncountable |
Probability distribution | A table, formula or graph that describes the values of a random variable and the probability associated with these values |
Expected value | The population mean is the weighted average of all of its values. The weights are probabilities. Represented by E(X) |
Population variance | Weighted average of squared deviations from the mean |
Bivariate distribution | Provides probabilities of combinations of two variables |
Bivariate probability distribution | Of X and Y, table of formula that lists the joint probabilities for all pairs of values of x and y |
Binomial distribution | Result of binomial experiment, which consists of a fixed number of trails, n. The outcome of each trail is either success or failure. The trails are independent. |
Bernoulli process | If all properties of a binomial experiment are satisfied |
Binomial random variable | The number of successes in n trails |
Cumulative probability | The probability that a random variable is less than or equal to a value |
Poisson distribution | Result of Poisson experiment |
Poisson random variable | The number of successes that occur in a period of time or an interval of space in a Poisson experiment |
Chapter 8
Probability Density Function | Since a continuous random variable can take an uncountable number of values, we take the probability of a range of values, which results in the probability density function |
Uniform (rectangular) probability distribution | Used to find the area under the curve that describes a probability density function |
Normal density function | Probability density function of a normal random variable |
Standard normal random variable | Denoted as Z. Standardization of a random variable, calculated by subtracting its mean and dividing by its standard deviation. The probability of Z can be found in a table |
Exponential distribution | The probability distribution that describes the time between events in a Poisson process. The exponential distribution has no memory. |
Student t distribution | A family of continuous probability distributions that arises when estimating the mean of a normally distributed population in situations where the sample size is small and population standard deviation is unknown. |
Degrees of freedom | the number of values in the final calculation of a statistic that are free to vary |
Chi-Squared distribution | With k degrees of freedom is the distribution of a sum of the squares of k independent standard normal random variables. |
F distribution | A continuous statistical distribution which arises in the testing of whether two observed samples have the same variance. |
Chapter 9
Sampling distribution | Created by sampling |
Standard error of the mean | Standard deviation of the sampling distribution, calculated by the standard deviation of the population divided by the sample size |
Central Limit Theorem | The sampling distribution of the mean of a random sample drawn from any population is approximately normal for a sufficiently large sample size. The larger the sample size, the more closely the sampling distribution will resemble a normal distribution |
Sample proportion | The estimator of a population proportion of successes. |
Continuity correction factor | When using a normal approximation to the binomial distribution, draw rectangles whose bases where constructed by adding/subtracting 0.5 to the values of X. Omit the factor when computed a range of values of X |
Chapter 10
Point estimator | Draws inference about a population by estimating the value of an unknown parameter using a single value or point |
Interval estimator | Draws inferences about a population by estimating the value of an unknown parameter using an interval |
Unbiased estimator | Of a population parameter, is an estimator whose expected value is equal to that parameter |
Consistency | Of an unbiased estimator. Consistency is there if the difference between the estimator and the parameter grows smaller as the sample size grows larger |
Relative efficiency | The one of the two unbiased estimators of parameter with a smaller variance is relative efficient. |
Confidence level | The probability of 1-α |
LCL | Lower confidence limit, calculated with the confidence interval estimator |
UCL | Upper confidence limit, calculated with the confidence interval estimator |
Confidence interval (CI) | A type of interval estimate of a population parameter and is used to indicate the reliability of an estimate. |
Error of estimation | The difference between an estimated value and the true value of a parameter or, sometimes, of a value to be predicted. |
Bound error of estimation | Labelled as B, the maximum error of estimation we are willing to tolerate |
Chapter 11
Hypothesis test | Refers to the formal procedures used by statisticians to accept or reject statistical hypotheses. |
Statistical hypothesis | Assumption about a population parameter |
Null hypothesis | Denoted by H0, is usually the hypothesis that sample observations result purely from chance. |
Alternative (research) hypothesis | Denoted by H1, is the hypothesis that sample observations are influenced by some non-random cause. |
Type | error | To reject a true null hypothesis |
Type || error | To not reject a false null hypothesis |
Significance level | The probability of a type | error, α |
Test statistic | Criterion on which we base our decision about the hypothesis |
Rejection region | Range of values such that if the test statistic falls into that range, we decide to reject the null hypothesis in favour of the alternative hypothesis |
Standardized test statistic | Denoted as z, calculated by a formula |
Statistically significant | When H0 is rejected, a test is said to be statistically significant at whatever significance level it was conducted |
p-value | Of a test is the probability of observing a test statistic at least as extreme as the one computed given that the null hypothesis is true |
Highly significant | p-value less than 0.01 – overwhelming evidence to infer that H1 is true |
Significant | p-value between 0.01 and 0.05 – strong evidence to infer that H1 is true |
Not statistically significant | p-value between 0.05 and 0.10 – weak evidence to indicate that H1 is true. If the p-value > 0.1, there is little to no evidence. |
One tail test | Whenever H1 specifies that the value is bigger or smaller than the value stated in H0. |
Two tail test | Whenever H1 specifies that the value is not equal to the value stated in H0 |
Power of a test | The probability that the test will reject the null hypothesis when the alternative hypothesis is true. Denoted as 1-β, where β is the probability of a type || error |
Chapter 12
t-statistic | A ratio of the departure of an estimated parameter from its notional value and its standard error. |
Robust | A student t distribution is robust; which means that if the population is nonnormal, the results of the t-test and confidence interval estimator are still valid provided that the population is not extremely nonnormal. |
t-test | Any statistical hypothesis test in which the test statistic follows a Student's t distribution if the null hypothesis is supported. |
Large populations | Populations at least 20 times the sample size |
Chi-squared statistic | Estimator of the sample variance |
p-test | A statistical method used to test one or more hypotheses within a population or a proportion within a population. |
Wilson Estimator | Used when there are zero successes in a sample |
Studiegids bij Managerial Statistics van Keller
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