Sampling Distributions and Statistical Inference

1982 ◽  
pp. 101-128
Author(s):  
G. Barrie Wetherill
Keyword(s):  
Statistical Inference ◽  
Sampling Distributions

scholarly journals Introducing Statistical Inference: Design of a Theoretically and Empirically Based Learning Trajectory

2021 ◽  
Author(s):  
Marianne van Dijke-Droogers ◽  
Paul Drijvers ◽  
Arthur Bakker
Keyword(s):  
Statistical Inference ◽  
Statistics Education ◽  
Real Life ◽  
Numerical Data ◽  
Black Box ◽  
Simulation Software ◽  
Learning Trajectory ◽  
9Th Grade ◽  
Sampling Distributions ◽  
Repeated Sampling

AbstractThis paper comprises the results of a design study that aims at developing a theoretically and empirically based learning trajectory on statistical inference for 9th-grade students. Based on theories of informal statistical inference, an 8-step learning trajectory was designed. The trajectory consisted of two similar four step sequences: (1) experimenting with a physical black box, (2) visualizing distributions, (3) examining sampling distributions using simulation software, and (4) interpreting sampling distributions to make inferences in real -life contexts. Sequence I included only categorical data and Sequence II regarded numerical data. The learning trajectory was implemented in an intervention among 267 students. To examine the effects of the trajectory on students’ understanding of statistical inference, we analyzed their posttest results after the intervention. To investigate how the stepwise trajectory fostered the learning process, students’ worksheets during each learning step were analyzed. The posttest results showed that students who followed the learning trajectory scored significantly higher on statistical inference and on concepts related to each step than students of a comparison group (n = 217) who followed the regular curriculum. Worksheet analysis demonstrated that the 8-step trajectory was beneficial to students’ learning processes. We conclude that ideas of repeated sampling with a black box and statistical modeling seem fruitful for introducing statistical inference. Both ideas invite more advanced follow-up activities, such as hypothesis testing and comparing groups. This suggests that statistics curricula with a descriptive focus can be transformed to a more inferential focus, to anticipate on subsequent steps in students’ statistics education.

Statistical Inference in Life-Table Experiments: The Finite Rate of Increase

1984 ◽  
Vol 41 (9) ◽  
pp. 1361-1374 ◽  
Author(s):  
Paul J. Rago ◽  
Robert M. Dorazio
Keyword(s):  
Monte Carlo ◽  
Statistical Inference ◽  
Life Table ◽  
Variance Estimator ◽  
Cohort Size ◽  
Finite Rate ◽  
Lower Mode ◽  
Sampling Distributions ◽  
Rate Of Increase ◽  
Initial Cohort

Life-table experiments are frequently used to examine the effects of food level, toxicants, and other experimental treatments on a population's finite rate of increase λ. Although methods for computing the variance of λ have been suggested, the sampling distribution of λ, which is needed for statistical inference, has not been described. We used Monte Carlo procedures to simulate sampling distributions of λ for a variety of assumptions regarding survivorship and fecundity schedules and initial cohort sizes. The distribution of λ can be bimodal when cohort size is small and when juvenile mortality is large. Under these circumstances the probability that none of the initial cohort members reproduces is high enough to produce a significant frequency of zero values for λ. Zero therefore becomes the lower mode of the distribution. Many commonly observed mortality schedules and commonly used cohort sizes yield distributions of λ that are skewed toward low values. Although the skewness and variance of distributions of λ decrease as cohort size increases, these distributions are asymptotically non-normal. Normal-based statistical procedures for comparing experimental estimates of λ may therefore be misleading. To compare estimates of λ obtained from life-table experiments, we recommend using a Monte Carlo approach to generate sampling distributions of λ and then comparing these distributions directly. We illustrate this procedure with life-table data from Daphnia pulex cohorts raised at different levels of pH. We also show that a Taylor series variance estimator yields confidence intervals for λ that approximate those obtained from simulations. This variance estimator is less conservative, and therefore more useful, than a previous estimator derived by Lenski and Service (1982. Ecology 63: 655–662).

Essentials of Statistical Inference

2005 ◽  
Author(s):  
G. A. Young ◽  
R. L. Smith
Keyword(s):  
Statistical Inference

Randomization and Statistical Inference

1975 ◽  
Vol 4 (8) ◽  
pp. 723-735
Author(s):  
Robert Easterling
Keyword(s):  
Statistical Inference

Statistical Inference for Measurement Models

1970 ◽  
Vol 15 (6) ◽  
pp. 402, 404-405
Author(s):  
ROBERT E. DEAR
Keyword(s):  
Statistical Inference ◽  
Measurement Models
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