Basic Data Analysis: Descriptive Statistics

1. Basic Data Analysis:Descriptive Statistics

2. Disposition for afrapportering • Om undersøgelsens tilblivelse • Undersøgelsens hovedresultater • Materialets sammensætning • Elevernes faglige profiler • Mhp. en bestemt videreuddannelse? • Supplering inden studiestart? • Hvad skal der ske efter sommerferien? • Faglige interesset • Opdelt på hum, samf og tek-nat hovedområder • Kriterier for valg af studium • Faglige dimensioner • Sociale dimensioner • Praktiske forhold

3. Disposition for afrapportering(fortsat) • Valg af studieby • Plan for valg • Opfattelsen af forskellige studiebyer • Alt-i-alt-vurdering af studiebyer • Om matematik-økonomi-uddannelsen • Hørt om denne • Kendskab til, hvor man kan få uddannelsen • Overvejet at påbegynde mat-øk? • Specielt om studiet ved AAU • Kendskab • Kílde til kendskab • Påbegyndelse af studium? • Sandsynligheden for at begynde efter sommerferien.

4. Types of Statistical Analyses Used in Marketing Research • Data summarization: the process of describing a data matrix by computing a small number of measures that characterize the data set • Four functions of data summarization: • Summarizes the data • Applies understandable conceptualizations • Communicates underlying patterns • Generalizes sample findings to the population

5. Types of Statistical Analyses Used in Marketing Research

6. Types of Statistical Analyses Used in Marketing Research Five Types of Statistical Analysis: • Descriptive analysis: used to describe the data set • Inferential analysis: used to generate conclusions about the population’s characteristics based on the sample data • Differences analysis: used to compare the mean of the responses of one group to that of another group • Associative analysis: determines the strength and direction of relationships between two or more variables • Predictive analysis: allows one to make forecasts for future events

7. Types of Statistical Analyses Used in Marketing Research Hvis vi ændrer en bys image på en række dimensioner, hvor meget stiger vurderingen af byen så med? Hvis vi ændrer en bys image på én dimension, hvor meget stiger – alt andet lige - vurderingen af byen så med? Hvilken betydning haropfattelsen af studiebyer for valget heraf? • Test af sammenhænge mellem • undersøgelsesspørgsmål og kriterier • undersøgelsesspørgsmål indbyrdes Vurdering af repræsentativitet fx ved test mod en kendt populationsfordeling på køn og alder • Materialets sammensætning • kriterier som køn og alder • undersøgelsesspørgsmål

8. Understanding Data Via Descriptive Analysis • Two sets of descriptive measures: • Measures of central tendency: used to report a single piece of information that describes the most typical response to a question • Measures of variability: used to reveal the typical difference between the values in a set of values

9. Understanding Data Via Descriptive Analysis • Measures of Central Tendency: • Mode: the value in a string of numbers that occurs most often • Median: the value whose occurrence lies in the middle of a set of ordered values • Mean: sometimes referred to as the “arithmetic mean”; the average value characterizing a set of numbers

10. Understanding Data Via Descriptive Analysis • Measures of Variability: • Frequency distribution reveals the number (percent) of occurrences of each number or set of numbers • Range identifies the maximum and minimum values in a set of numbers • Standard deviation indicates the degree of variation in a way that can be translated into a bell-shaped curve distribution

11. Understanding Data Via Descriptive Analysis • Measures of Variability:

12. When to Use a Particular Statistic

13. Hvornår bruges hvad?Eksempler fra casen

14. Datamatricen i Studievalgsundersøgelsen

15. Hvornår bruges hvad?Eksempler fra casen

16. Hvornår bruges hvad?Eksempler fra casen

17. Hvornår bruges hvad?Eksempler fra casen

18. Hvornår bruges hvad?Eksempler fra casen

19. Hvornår bruges hvad?Eksempler fra casen

20. Generalizing a Sample’s Findings to Its Population and Testing Hypotheses About Percents and Means

21. Statistics Versus Parameters • Statistics:values that are computed from information provided by a sample • Parameters:values that are computed from a complete census which are considered to be precise and valid measures of the population • Parameters represent “what we wish to know” about a population. Statistics are used to estimate population parameters.

23. The Concepts of Inference and Statistical Inference • Inference:drawing a conclusion based on some evidence • Statistical inference:a set of procedures in which the sample size and sample statistics are used to make estimates of population parameters

25. Parameter Estimation • Parameter estimation:the process of using sample information to compute an interval that describes the range of values of a parameter such as the population mean or population percentage is likely to take on

26. Parameter Estimation • Parameter estimation involves three values: • Sample statistic (mean or percentage generated from sample data) • Standard error (variance divided by sample size; formula for standard error of the mean and another formula for standard error of the percentage) • Confidence interval (gives us a range within which a sample statistic will fall if we were to repeat the study many times over

27. Parameter Estimation • Standard error: while there are two formulas, one for a percentage and the other for a mean, both formulas have a measure of variability divided by sample size. Given the sample size, the more variability, the greater the standard error.

28. Standard Error of the Mean

29. Standard Error of the Percentage

30. Parameter Estimation • Confidence intervals:the degree of accuracy desired by the researcher and stipulated as a level of confidence in the form of a percentage • Most commonly used level of confidence:95%; corresponding to 1.96 standard errors

31. Parameter Estimation • What does this mean? It means that we can say that if we did our study over 100 times, we can determine a range within which the sample statistic will fall 95 times out of 100 (95% level of confidence). This gives us confidence that the real population value falls within this range.

32. Hypothesis Testing • Hypothesis: an expectation of what the population parameter value is • Hypothesis testing:a statistical procedure used to “accept” or “reject” the hypothesis based on sample information • Intuitive hypothesis testing:when someone uses something he or she has observed to see if it agrees with or refutes his or her belief about that topic

33. Hypothesis Testing • Statistical hypothesis testing: • Begin with a statement about what you believe exists in the population • Draw a random sample and determine the sample statistic • Compare the statistic to the hypothesized parameter

34. Hypothesis Testing • Statistical hypothesis testing: • Decide whether the sample supports the original hypothesis • If the sample does not support the hypothesis, revise the hypothesis to be consistent with the sample’s statistic

35. What is a Statistical Hypothesis? • A hypothesis is what someone expects (or hypothesizes) the population percent or the average to be. • If your hypothesis is correct, it will fall in the confidence interval (known as supported). • If your hypothesis is incorrect, it will fall outside the confidence interval (known as not supported)

36. How to Test Statistical Hypothesis 2.5% 2.5% 95% +1.96 -1.96

37. Types of Statistical Analyses Used in Marketing Research • Test af sammenhænge mellem • undersøgelsesspørgsmål og kriterier • undersøgelsesspørgsmål indbyrdes

38. Sammenligning af to populationer i Studievalgsundersøgelsen • Sammenligninger ved hjælp af tabelanalyse

40. Sammenligning af to populationer i Studievalgsundersøgelsen

43. Sammenligning af to populationer i Studievalgsundersøgelsen

45. Sammenligning af gennemsnittet for to spørgsmål i Studievalgsundersøgelsen

47. Sammenligning af gennemsnittet for flere end to populationer i Studievalgsundersøgelsen