Sampling Methods PDF

Sampling Jaycee N. Toledo, CBO, SO II, DTA, RMT, MSMT (c) 12/5/2024 5: Intro to estimation 1 Sampling A population is that totality of all values (or measurements) of particular characteristics for a specified group of objects that are of interest to the...

Sampling Jaycee N. Toledo, CBO, SO II, DTA, RMT, MSMT (c) 12/5/2024 5: Intro to estimation 1 Sampling A population is that totality of all values (or measurements) of particular characteristics for a specified group of objects that are of interest to the researcher. A sample is a finite portion of a population that will be used or investigated in the study Sampling is the process of choosing a representative portion of a population. 12/5/2024 5: Intro to estimation 2 Sampling Sampling is done for any or all of the following reasons: 1. Due to limitations of time, money, personnel, it is impossible to study every item in the populations. 2. Examining an item may require that the item be destroyed; 3. Samples due to its small size can be thoroughly studies; 4. Fewer errors ar encountered om the collection and handling of data; and 5. The study of a larger or more varied populations can be carried out at a lesser cost. 12/5/2024 5: Intro to estimation 3 Sampling Types of sample ◼ Probability sample – when the selection of items is done according to some chance mechanism where elements have an equal chance of being selected. ◼ Non-probability sample – items selected by judgement where elements do not have an equal chance of being taken. 12/5/2024 5: Intro to estimation 4 Sampling metods Simple Random Sampling ◼ is a process of selecting a sample from a set of all sampling units or a population such that each sampling unit is given a chance of being included in the sample. ◼ Ex. Lottery sampling 12/5/2024 5: Intro to estimation 5 Sampling metods Stratified Random Sampling ◼ is a method of sampling in which a population is divided into distinct subgroups, known as strata, based on shared characteristics, and then a random sample is drawn from each stratum. 12/5/2024 5: Intro to estimation 6 Sampling metods Cluster Sampling ◼ Is one of the most economical ways of obtaining a sample for a survey. It consists of selecting clusters of units in a population and then obtaining a simple random sample of these clusters. 12/5/2024 5: Intro to estimation 7 Sampling metods Convenience sampling ◼ is a non-probability sampling method where participants are selected based on their easy accessibility and availability to the researcher. In this method, researchers choose individuals who are most convenient to sample, rather than using random selection. This often means selecting people who are readily available, such as those in the researcher’s immediate surroundings, such as colleagues, classmates, or people nearby. 12/5/2024 5: Intro to estimation 8 Sampling metods Multistage sampling ◼ is a complex form of sampling that involves selecting a sample in multiple stages, often by combining several sampling methods. This approach is typically used when a population is large, geographically dispersed, or difficult to sample directly. ◼ Multistage sampling can involve selecting clusters at one or more stages, and then applying another sampling method, such as random sampling or stratified sampling, within those clusters. 12/5/2024 5: Intro to estimation 9 Statistics It deals with experimental designs and procedures which include data collection, classification, organization and interpretation, and decision-making regarding these data. 12/5/2024 5: Intro to estimation 10 Statistics ◼ Descriptive statistics – refers to the methods of data collection, organization, classification and summarizationand presentation. It includes procedures for constructing graphs, tables and charts. It also refers to the calculation of statistical description such as the measures of central tendency and the measures of variability. 12/5/2024 5: Intro to estimation 11 Statistics ◼ Inferential statistics – it refers to the process of arriving at a conclusion about a population based on the information obtained from a sample.  Parameters – a number that describes the characteristics of a population.  Statistic – a number that describes the characteristics of the sample. 12/5/2024 5: Intro to estimation 12 Hypothesis ◼ Is a prediction based on a body of knowledge, scientific theory, or observations.  Null hypothesis (Ho) – indicates the value of the population parameter to be tested.  Alternative hypothesis (Ha) – is the operational statement of the experimenter’s research hypothesis. 12/5/2024 5: Intro to estimation 13 Hypothesis ◼ Is a prediction based on a body of knowledge, scientific theory, or observations.  Null hypothesis (Ho) – indicates the value of the population parameter to be tested.  Alternative hypothesis (Ha) – is the operational statement of the experimenter’s research hypothesis. 12/5/2024 5: Intro to estimation 14 Level of significance and the sample size ◼ In stating the level of significance (α), the researcher set up the rejection region and acceptance region for the null hypothesis. ◼ The rejection region is called the critical region and the remaining region called the acceptance region. 12/5/2024 5: Intro to estimation 15 Level of significance and the sample size 12/5/2024 5: Intro to estimation 16 One sample hypothesis test of Means ◼ Use the Z-test when N > 30 to compare the mean of particular sample to the mean of the population. 12/5/2024 5: Intro to estimation 17 One sample hypothesis test of Means Liwanag Bulb Company claims that it sells light bulb with an average life of 1000 hours A sample of 64 new bulb were allowed to burn out to test this claim. The average lifetime of the sample was found to be 975 hours with a standard deviation of 75 hours. Does this indicate that the average life of the bulb is not 1000 hours? Use 5% level of significance. 12/5/2024 5: Intro to estimation 18 One sample hypothesis test of Means Given Data: Claimed population mean (μ): 1000 hours Sample mean (xˉ): 975 hours Sample standard deviation (s): 75 hours Sample size (N): 64 Significance level (α): 0.05 (5%) 12/5/2024 5: Intro to estimation 19 One sample hypothesis test of Means Given Data: Claimed population mean (μ): 1000 hours Sample mean (xˉ): 975 hours Sample standard deviation (s): 75 hours Sample size (N): 64 Significance level (α): 0.05 (5%) 12/5/2024 5: Intro to estimation 20 One sample hypothesis test of Means 12/5/2024 5: Intro to estimation 21 One sample hypothesis test of Means 12/5/2024 5: Intro to estimation 22 One sample hypothesis test of Means 12/5/2024 5: Intro to estimation 23 One sample hypothesis test of Means ◼ Use the T-test when the sample size is small or N < 30. 12/5/2024 24 One sample hypothesis test of Means Cash Uy Company claims that each can of mixed nuts they manufacture contains an average of 10 cashew nuts. A sample of 25 cans were obtained and it was found out that the average number of cashew nuts is 8 and the standard deviation is 3. Can we accept the claim of the mixed nuts company? Use the 5% level of signifance. 12/5/2024 5: Intro to estimation 25 One sample hypothesis test of Means Given Data: Claimed population mean (μ): 10 cashew nuts Sample mean (xˉ): 8 cashew nuts Sample standard deviation (s): 3 cashew nuts Sample size (N): 25 cans Significance level (α): 0.05 (5%) 12/5/2024 5: Intro to estimation 26 One sample hypothesis test of Means 12/5/2024 5: Intro to estimation 27 One sample hypothesis test of Means 12/5/2024 5: Intro to estimation 28 One sample hypothesis test of Means 12/5/2024 5: Intro to estimation 29 Two sample hypothesis test of Means 12/5/2024 5: Intro to estimation 30 One sample hypothesis test of Means The Bureau of Environmental Protection made a study of a river community with regard to the amount of semi-treated sewage released into the river. Five randomly selected specimens of river water were drawn at a location above the town, and another five below. The dissolved oxygen (DO) readings in parts per million (ppm) are as follows: Above town: 4.9, 5.2, 5.1, 4.8, 56 Below town: 5.0, 4.9, 4.8, 4.7, 4.9 12/5/2024 5: Intro to estimation 31 Two sample hypothesis test of Means 12/5/2024 32 Two sample hypothesis test of Means 12/5/2024 33 Two sample hypothesis test of Means 12/5/2024 34 Two sample hypothesis test of Means 12/5/2024 35 Two sample hypothesis test of Means 12/5/2024 36 Two sample hypothesis test of Means 12/5/2024 37 Three or more sample hypothesis test of Means ◼ Use the Analysis of Variance (ANOVA) to compare three or more (more than two) sample means. ◼ F-statistic: The test statistic in ANOVA is the F-statistic, which is the ratio of the variance between groups to the variance within groups. A higher F-value suggests that the group means are significantly different. 12/5/2024 38 Three or more sample hypothesis test of Means ◼ Use the Analysis of Variance (ANOVA) to compare three or more (more than two) sample means. ◼ F-statistic: The test statistic in ANOVA is the F-statistic, which is the ratio of the variance between groups to the variance within groups. A higher F-value suggests that the group means are significantly different. 12/5/2024 39 Three or more sample hypothesis test of Means 12/5/2024 40 Three or more sample hypothesis test of Means Groups of students were randomly assigned to be taught using four different teaching techniques. They were tested at the end of a specified period of time. Because of dropouts in the experimental groups, the number of students varied from group to group. Do the following data present sufficient evidence to indicate a difference in the mean achievement for students taught using the for teaching techniques. 12/5/2024 41 Three or more sample hypothesis test of Means A B C D 65 75 59 94 87 69 78 89 73 83 67 80 79 81 62 88 81 72 83 69 79 76 90 12/5/2024 42 Three or more sample hypothesis test of Means 12/5/2024 43 Three or more sample hypothesis test of Means 12/5/2024 44 Three or more sample hypothesis test of Means Since the p-value (0.028) is less than 0.05, we reject the null hypothesis, indicating that there is a statistically significant difference in the mean achievement scores among the four teaching techniques. ​ 12/5/2024 45  THANK YOU 12/5/2024 46