• Join over 1.2 million students every month
  • Accelerate your learning by 29%
  • Unlimited access from just £6.99 per month

Hypothesis method

Extracts from this document...

Introduction

Table of content

TABLE OF CONTENT

INTRODUCTION

Statistical Hypotheses:

Null Hypothesis:

TYPES OF TESTS

ERROR

STEPS IN HYPOTHESIS TESTING

PRACTICAL EXAMPLES

LIMITATIONS FOR ENVIRONMENTAL SAMPLING

SUMMARIZE

FREQUENCIES

HISTOGRAM

DATA VIEW FROM SPSS

VARIABLE VIEW FROM SPSS


Introduction

There are two types of statistical inferences: estimation of population parameters and hypothesis testing. Hypothesis testing is one of the most important tools of application of statistics to real life problems. Most often, decisions are required to be made concerning populations on the basis of sample information. Statistical tests are used in arriving at these decisions.

Statistical Hypotheses:

They are defined as assertion or conjecture about the parameter or parameters of a population, for example the mean or the variance of a normal population. They may also concern the type, nature or probability distribution of the population.

Statistical hypotheses are based on the concept of proof by contradiction. For example, say, we test the mean (δ) of a population to see if an experiment has caused an increase or decrease in δ. We do this by proof of contradiction by formulating a null hypothesis.

Null Hypothesis:

It is a hypothesis which states that there is no difference between the procedures and is denoted by H0. For the above example the corresponding H0 would be that there has been no increase or decrease in the mean. Always the null hypothesis is tested, i.e., we want to either accept or reject the null hypothesis because we have information only for the null hypothesis.

Types of Tests

...read more.

Middle

A better method for comparing several population means is an analysis of variance, abbreviated as ANOVA.

ANOVA test is based on the variability between the sample means. This variability is measured in relation to the variability of the data values within the samples. These two variances are compared through means of the F ratio test.

If there is a large variability between the sample means, this suggests that not all the population means are equal. When the variability between the samples means is large compared to the variability within the samples, it can be concluded that not all the population means are equal.

The tests used in the testing of hypothesis, viz., t-tests and ANOVA have some fundamental assumptions that need to be met, for the test to work properly and yield good results. The main assumptions for the t-test and ANOVA are listed below.

The primary assumptions underlying the t-test are:

  • The samples are drawn randomly from a population in which the data are distributed normally distributed.
  • In the case of a two sample t-test, δ12 = δ22.Therefore it is assumed that s12 and s22 both estimate a common population variance, δ2. This assumption is called the homogeneity of variances
  • In the case of a two sample t-test, the measurements in sample 1 are independent of those in sample 2.

Like the t-test, analysis of variance is based on a model that requires certain assumptions.

Three primary assumptions of ANOVA are that:

  • Each group is obtained randomly, with each observation independent of all other observations and the groups independent of each other.
  • The samples represent populations in which the data are normally distributed.
  • δ12 = δ22 = δ32 = ... = δk2. The assumption of homogeneity of variances is similar to the discussion above under the t-test. The group variances are assumed to be an estimate of a common variance, δ2.
...read more.

Conclusion

le>

Frequencies

Figure 7

Statistics

Amount Spent

N

Valid

30

Missing

2

Mean

320.7333

Std. Error of Mean

41.45531

Median

261.5000a

Mode

150.00b

Std. Deviation

227.06006

Percentiles

10

77.5000c

20

133.3333

30

204.5000

40

247.5000

50

261.5000

60

346.6667

70

360.0000

80

417.5000

90

687.5000

a. Calculated from grouped data.

b. Multiple modes exist. The smallest value is shown

c. Percentiles are calculated from grouped data.

Figure 8

Amount Spent

Frequency

Percent

Valid Percent

Cumulative Percent

Valid

45.00

1

3.1

3.3

3.3

50.00

1

3.1

3.3

6.7

55.00

1

3.1

3.3

10.0

100.00

1

3.1

3.3

13.3

120.00

1

3.1

3.3

16.7

125.00

1

3.1

3.3

20.0

150.00

2

6.3

6.7

26.7

200.00

1

3.1

3.3

30.0

209.00

1

3.1

3.3

33.3

222.00

1

3.1

3.3

36.7

245.00

1

3.1

3.3

40.0

250.00

1

3.1

3.3

43.3

255.00

1

3.1

3.3

46.7

258.00

1

3.1

3.3

50.0

265.00

1

3.1

3.3

53.3

300.00

1

3.1

3.3

56.7

345.00

1

3.1

3.3

60.0

350.00

2

6.3

6.7

66.7

355.00

1

3.1

3.3

70.0

365.00

1

3.1

3.3

73.3

368.00

1

3.1

3.3

76.7

390.00

1

3.1

3.3

80.0

445.00

1

3.1

3.3

83.3

500.00

1

3.1

3.3

86.7

525.00

1

3.1

3.3

90.0

850.00

1

3.1

3.3

93.3

880.00

1

3.1

3.3

96.7

900.00

1

3.1

3.3

100.0

Total

30

93.8

100.0

Missing

System

2

6.3

Total

32

100.0

Histogram

Figure 9

image00.png

Data View From SPSS

image01.png

Variable View From SPSS

image02.png

...read more.

This student written piece of work is one of many that can be found in our University Degree Statistics section.

Found what you're looking for?

  • Start learning 29% faster today
  • 150,000+ documents available
  • Just £6.99 a month

Not the one? Search for your essay title...
  • Join over 1.2 million students every month
  • Accelerate your learning by 29%
  • Unlimited access from just £6.99 per month

See related essaysSee related essays

Related University Degree Statistics essays

  1. A Critical Appraisal of Three Research Studies Related To Peripheral Venous Cannulae and the ...

    However, there is no discussion as to the validity or reliability of the tool. It is also unclear as to whether Curran et al (2000) carried out a pilot study or not. There is a reference in the paper to collecting data on forty catheters, which is not the total number of the whole data collection.

  2. Dorfman, Robert (1943) essay 'The detection of defective members of large populations

    In this experiment, Dorfman undergoes a methodological and practical process to demonstrate his idea. He executes this by first pooling N blood samples into group pools with n members, rather than testing each blood sample from the individual men. With the assumption that the tests are conducted under "sufficiently sensitive

  1. Practical 3 on SPSS

    The clustered bar chart, the patients who have lost weight, have no anxiety levels are the ones who have no or mild depression levels However the patients who have gained weight and have mild, moderate and severe anxiety levels, show that they have mild and moderate depression levels.

  2. A practical using SPSS

    However it doesn't show the precise weights in detailed. The stem and leaf plot again shows both quantitative and qualitative data of weights and does show the exact weights in detailed information. It also showed the extreme value outside the range. The box plot shows the maximum, minimum, upper quartile, lower quartile and the median but does show the exact weights.

  1. How statistical interpretation can cause data to appear misleading

    their position in the league and their attitudes towards intimidatory behaviour and reasons why. Systematic sampling samples the population in a specific systematic method. For instance, instead of questioning every player in the league, the researcher can use systematic sampling to question every third and eighth name from the list,

  2. Dress code study. The method of random sampling in this investigation was cluster ...

    Furthermore, there would be a certain amount of chance variation even though all aspects of the sample were conducted properly. Thus, these were limitations that caused inaccuracy in our study. Investigation 1: Number of summons received by female student of Ausmat 17 The Centre of a Distribution Let X =

  1. Does the data indicate that the revised (one week) forecast is significantly more accurate ...

    1 0.536 0.401 -1500 (-1800)-(-1500) 1 1.480 0.155 -1200 (-1500)-(-1200) 1 3.425 1.717 -900 (-1200)-(-900) 9 5.405 2.391 -600 (-900)-(-600) 4 5.817 0.568 -300 (-600)-(-300) 5 4.270 0.125 >(-300) 3 3.067 0.001 Total 7 24 24.000 5.359 Table 1. Excel StatPro package- Chi-square test for errors of one month ahead

  2. HND business decision making

    to the participant, but most importantly to meet the aims of the methodology and provide the information needed. For this survey I have decided on twelve key questions. The reason for this is to keep the questionnaire short and simple for the participate.

  • Over 160,000 pieces
    of student written work
  • Annotated by
    experienced teachers
  • Ideas and feedback to
    improve your own work