On the basis of the analysis of the information, the hypothesis:

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2 GEOGRAPHY PRODUCING A GEOGRAPHY REPORT Generally a study begins with an observation. If a difference or trend appears possible a hypothesis (idea) may be formed. A hypothesis is an idea or tentative theory not supported by hard evidence usually stating that some relationship between variables exists. The null hypothesis is the opposite statement, i.e. that no relationship exists between variables, and it is this statement which is to be tested. Therefore, rather than prove the hypothesis we disprove the null hypothesis. The hypothesis may then be tested using an appropriate method to collect sufficient primary, of first hand, information. On the basis of the analysis of the information, the hypothesis: 1. May be accepted 2. May be rejected 3. May be inconclusive and more information required If the original hypothesis is rejected, then a new one may be inserted, more information collected and the process repeated. The null hypothesis is often printed as H0. The alternative hypothesis is referred to as H1. DEVISING A NULL HYPOTHESIS 1. Look at the pictures below. Come up with suitable null hypotheses that you could test out in the field. H0: Ho:

3 Ho: WHAT DATA WILL YOU NEED? Once you have decided the aim and hypothesis of your investigation, you need to decide on the data required and what method of collection will be necessary. Sampling is used when it is impossible, or not necessary, to collect large amounts of data. Collecting small amounts of carefully selected data enables you to obtain a representative view of the feature as a whole. Random sampling is one that shows no bias and in which every member of the population has an equal chance of being d selected. Systematic sampling is collected in a consistent manner by the selection, for example, of every tenth house or person. Stratified sampling is based on knowing something in advance about the population of area in question. For example, if you are surveying a population and you know its age distribution, your sample must reflect that age distribution. Other collection methods include: Questionnaires Interviews Attitude tests, e.g. bi-polar tests or rating scales Surveys, e.g. land use

4 Transects Environmental Impact Assessments Traffic/pedestrian flows You may also need to collect secondary data which involves gathering data which has already been put into written, statistical or mapped form. This information may come in the form of: National government material, e.g. population trends National media (newspapers, magazines) Local data (estate agents) Geographical material (Geographical magazine, Geofile etc.) Maps and charts Internet 2. For one of the hypotheses you identified produce a plan of what data you need to test your Null Hypothesis and how you will gather it. PRESENTING YOUR RESULTS When you are ready to present your results, it is important that you use appropriate techniques. There is a wide range of techniques available to you graphical, cartographic and tabular but what you eventually select must be appropriate to the purpose of the investigation. Most investigations will include a choice of techniques along the following lines: Identification or description of differences Description of spatial patterns Identification of relationships Classification of data according to characteristics

5 Identifying differences Use Graphical Cartographic Describing spatial patterns Identification of relationships Classification of data Line graphs Cumulative frequency curves Pie/bar graphs Proportional circles Histograms Long/cross sections Kite diagrams Radial diagrams Scattergraphs Triangular graphs Pie graphs, bar graphs and proportional symbols can be placed on a base map to show spatial variations Isopleths Choropleths Flow diagrams and desire lines 3. Look at the data below. It shows the measurement of the lengths of ten flowering stalks of the soft rush (Juncus effuses) in centimetres. Produce an appropriate method of presenting this data ANALYSIS AND INTERPRETATION OF DATA The use of statistical analysis is a common feature of geographical investigations. Objective analysis of data can be used to support the conclusions suggested by a subjective view of the results of the investigation. Statistical analysis should assist in the evaluation of the significance of the results and form an integral part of the write-up of the investigation. There should be careful consideration of the most effective form of statistical analysis, and why that technique is appropriate.

6 Reason for using statistics The summarising and comparison of data The dispersion and variability of data The correlation of two sets of data The degree of concentration of geographical phenomena The measurement of patterns in a distribution The degree to which there are differences between observed data and expected data, and the statistical difference of them Statistical techniques Measures of central tendency: mean, mode, median Range Inter-quartile range (dispersion graphs) Standard deviation Spearman Rank Correlation co-efficient and tests of significance Location quotients Nearest neighbor statistic Chi-squared test Mann-Whitney U test SIMPLE STATISTIC ANALYSIS Looking back at the data on the lengths of rush, not all lengths are identical, but a useful piece of information would be their average or mean length. This is calculated by summing all the individual lengths and dividing by the number in the sample, using the equation: x = x Another useful statistic concerning the data is the median. This is that value for which half of the values lie above and half lie below. n The larger the difference between the mean and the median, the more a set of data is said to be skewed. 4. Calculate the mean and the mean values of the soft rush lengths. Does the data appear symmetrical or skewed?

7 If a set of continuous variables is plotted the result is likely to be a bell-shaped curve (a normal distribution). The curve implies that most individuals are aggregated around the average or mean length but increasingly fewer are very long or very short. In a normal curve 68.2% of all individuals will lie within one standard deviation (σ) either side of the mean. The standard deviation is a measure of the dispersal of observations around the highest point (which is the mean in a normal curve). The equation is shown as: σ = (x y)2 n Where x refers to each observation, y to the mean, n to the number of points and (x y) 2 tells us to take the mean from each observation, and then to square the results. Objective: To calculate the mean and standard deviation of a set of results which determine the oxygen content of a sample of pond water. Using a chemical technique to determine oxygen content (mg/l) pf pond water a group of students obtained the following results: Using the equation for standard deviation: n = and 3.08 x = = 3.43 x 2 = Using σ = (x y)2 n σ = σ = 0.35 The analysis of the data shows that the mean value for oxygen concentration is 3.43 and that the standard deviation is 0.35.

8 From this we can say that there is: a 68% probability of the mean lying in the range 3.43 ± 0.35, i.e. between 3.78 and 3.08 a 95% probability of the mean lying in the range 3.43 ± 0.7 (2σ), i.e. between 2.73 and 4.13 a 99.5% probability of the mean lying in the range 3.43 ± 1.05 (3σ), i.e. between 2.38 and 4.48 We now have a clearer idea of the true oxygen concentration of the pond water.

9 5. Calculate the standard deviation of the data set (x) of another type of grass found in the same area as the Soft Rush. Complete the table to help you = 5674 x y (x-y) (x-y) 2 WHAT DOES IT ALL MEAN? WRITING A CONCLUSION Once you have drawn up your results and performed your statistical analysis, you need to be able to describe and explain what it means and whether you can disprove your null hypothesis. You should be able to interpret each section of your results and formulate conclusions for each one. Your conclusion should summarise all your major findings and draw up a picture of your data analysis in relation to your null hypothesis.

10 6. For the data in task 5: a. draw up the information as a continuous line graph; b. work out the mean and median; c. write a brief summary interpreting the results of your data

Business Statistics. Successful completion of Introductory and/or Intermediate Algebra courses is recommended before taking Business Statistics.

Business Statistics. Successful completion of Introductory and/or Intermediate Algebra courses is recommended before taking Business Statistics. Business Course Text Bowerman, Bruce L., Richard T. O'Connell, J. B. Orris, and Dawn C. Porter. Essentials of Business, 2nd edition, McGraw-Hill/Irwin, 2008, ISBN: 978-0-07-331988-9. Required Computing