11 - Understanding Research Results: Statistical Inference
Recommend Documents
early example of such a quantitative comparison is found in the work of Trabue who studied the development of language ability (measured by the âcompletion-.
See http:lljsi.cbs.n1isale-iase.htm for details. UNDERSTANDING PROBABILITY
AND STATISTICAL. INFERENCE THROUGH RESAMPLING. Clifford Koriold.
need to find connections that students can make to more familiar contexts, use ..... 3.4 THE USE OF THE SOLO TAXONOMY IN ASSESSING LEARNING. ...... dard deviation of the sample means (known, rather confusedly, as the standard .... ics, a process is r
This pdf file is from the IASE website at ht~:! ... for keeping probability in the data-
analysis (or statistics) curriculum. First, ... understand statistical inference.
conceptual understanding have the potential to transform the learning of ....
Statistical analyses using r and inZight software were conducted on the coded
data ...
Probabilistic statistical inference is a crucial part of the pro- cess of informing ...
Similarly, probability and statistical inference become crucial as we voyage out ...
In statistical inference, we go from specific to general via a mathematical model.
... (Duxbury). Hogg, R.V. and E.A. Tanis Probability and Statistical. Inference.
Sep 24, 2013 ... Goal : Identify a good estimator δ(x) of g(θ). ... MSE is the average squared
distance between the estimator and ..... Theory of point estimation.
Jul 26, 2003 - precise way the class of all possible instruments. Thus ..... recording the values q = f(r) and p = g(r) where r is the observed value of R. It follows that ..... The triad, or Mercedes-Benz logo, has an outcome space consisting.
ders, so far the more extensive application of hypothesis testing in geodesy. ... Statistical tests are a means for deciding between two competing hypothesis, the.
Oct 1, 2001 - Equation (3) is a solution of the celebrated Schrödinger equation i(d/dt)ψ = Hψ or ... Schrödinger Cat, see Section 8.4, is a consequence of this ...
data producers. These new approaches allow students to maintain better focus on the big ideas of statistics. These new approaches are a great step forward for ...
It is mainly through examples that I hope to leave you more interested in, and
more sanguine about, applications of. subjectiVe probability to statistical
inference.
Aug 24, 2009 - This volume collects twenty of David A. Freedman's most accessible and ... of Political Science at the University of California, Berkeley.
Jan 26, 2012 - Richard D. Gillâand MËadËalin I. GutËaâ . 15 January, 2011. Abstract. We study asymptotically optimal statistical inference concerning.
Nov 9, 1997 - Cars with cell phones have a 50% higher rate of acci- ... should ban car phones. 2. People ... bers have been drawn, but the ticket holder is ignorant of the ... This is a simple application of conditional probability as summarized by t
Jan 26, 2012 - by Hayashi and Matsumoto (2004) to the quantum i.i.d. model, can ...... In general, the pure states of dimension d can be identified with the Rie-.
1996,24 (1),82-91. Intuitive statistical inference: Categorization of binomial samples depends on sampling context. CHARLES P. SHIMp, KARREN A. LONG, and ...
Jul 9, 2010 - The idea is to draw them using Feynman rules derived ..... formulas directly in LATEX, in addition to performing the convolution or ...
Apr 15, 2015 - Compute a two-tailed Z test to find out whether the difference between .... And I'm happy to go along wit
We consider a statistical model M ' ipEx(θ G θ 5 Xj, i.e. a paramer ... adopting the Einstein convention of summing over any index that appears both as subscript ...
Apr 15, 2015 - The clinical observation scale goes from 0 to 10, with any score below 3 considered evidence for appropri
in Moscow for the period of 1962â2005 and in Denmark for. 1983â2005 are .... Vestine (1934) collected the NLC reports from 1885â1933 and first noted that the ...
11 - Understanding Research Results: Statistical Inference
UNDERSTANDING RESEARCH. RESULTS: ... in populations of scores based on
a sample of data from that population ... due to the IV. ✓ Statistical Significance:
Unlikely to be due to chance alone ... Calculating Effect Size (r, Cohen's d, , etc.).
UNDERSTANDING RESEARCH RESULTS: STATISTICAL INFERENCE
A FEW TERMS
A FEW TERMS
SAMPLES AND POPULATIONS 9 Inferential statistics are necessary because 9The results of a given study are based on data obtained from a single sample of researcher participants and 9Data are not based on an entire population of scores 9 Allows conclusions on the basis of sample data
INFERENTIAL STATISTICS 9 Allow researchers to make inferences about the true differences in populations of scores based on a sample of data from that population 9 Allows that the difference between sample means reflects random error rather than a real difference
NULL AND RESEARCH HYPOTHESES 9 Null Hypothesis 9H0: Population Means are Equal 9Any differences between groups are due to chance alone 9 Research Hypothesis 9H1: Population Means are Not Equal 9Any differences between groups are due to the IV 9 Statistical Significance: Unlikely to be due to chance alone
PROBABILITY AND SAMPLING DISTRIBUTIONS 9 Probability: The Case of ESP 9Are correct answers due to chance or due to something more? 9 Sampling Distributions 9Assumes Null is True 9Binomial Distributions 9 Sample Size
THE T TEST 9 t value is a ratio of two aspects of the data 9The difference between the group means and 9The The variability within groups t=
EXAMPLE: THE T AND F TESTS 9 Degrees of Freedom 9The number of scores that are free to vary when making an estimate. 9 One-Tailed vs. Two-Tailed Tests 9Directional vs. vs Nondirectional Hypotheses? 9 The F Test (analysis of variance) 9Systematic Systematic variance / Between Between-Groups Groups Variance 9Error variance / Within-Groups Variance
ONE-TAILED VS. TWO-TAILED TESTS What is a directional hypothesis?
Is a one-tailed test valid?
EXAMPLE: THE T AND F TESTS 9 Calculating Effect Size (r, Cohen’s d, η p , etc.) 2
9 Confidence Intervals and Statistical Significance 9 Statistical Significance
TYPE I AND TYPE II ERRORS 9 Type I Errors 9Made when the null hypothesis is rejected but the null hypothesis yp is actuallyy true 9Obtained when a large value of t or F is obtained by chance alone 9 Type yp II Errors 9Made when the null hypothesis is accepted although in the population the research hypothesis is true 9Factors related to making a Type II error 9Significance (alpha) level 9Sample size 9Effect size
TYPE I AND TYPE II ERRORS
THE EVERYDAY CONTEXT OF TYPE I AND TYPE II ERRORS
SIGNIFICANCE LEVEL & STATISTICAL ERRORS 9 Researchers traditionally have used either a .05 or a .01 significance level in the decision to reject the null hypothesis 9 A Agreementt that th t the th consequences off making ki a Type T I error are more serious than those associated with a Type II error 9Arlo’s Two Cents: It depends on context. 9 9e.g., A new drug d which hi h may cure AIDS 9 Interpreting p g nonsignificant g results 9Absence of evidence is not evidence of absence. 9Nothing is ever proven or disproven!
CHOOSING A SAMPLE SIZE: POWER ANALYSIS Power is a statistical test that determines optimal sample size based on probability of correctly rejecting the null hypothesis yp Power = 1 – p(Type II error) Eff Effect sizes i range and dd desired i d power
Smaller effect sizes require larger samples to be significant Higher desired power demands a greater sample size Researchers usually use a power between .70 70 and .90 90
IMPORTANCE OF REPLICATIONS Scientists attach little importance to results of a single study Detailed understanding requires numerous studies examining same variables i bl Researchers look at the results of studies that replicate previous investigations
SIGNIFICANE OF PEARSON’S R CORRELATION COEFFICIENT Is the correlation statistically significant? Ho: r = 0 H1: r ≠ 0 It is proper to conduct a t-test to compare the r-value with the null correlation of 0.00 ?
COMPUTER ANALYSIS OF DATA 9 Software Programs include 9SPSS 9SAS 9Minitab 9Microsoft Excel
9 Steps in analysis 9Input data
9Rows represent cases or each participant’s scores 9Columns represent p ap participant’s p score for a specific p variable
9Conduct analysis 9Interpret output
SELECTING THE APPROPRIATE SIGNIFICANCE TEST IV
DV
Statistical Test
Nominal Male-Female
Nominal Vegetarian – Yes / No
Chi Square
Nominal (2 Groups) Interval / Ratio Male-Female Grade Point Average
t test
Nominal (3 groups) Study time (Low, Medium, High)
Interval / Ratio Test Score
One-way ANOVA
Interval / Ratio Optimism Score
Interval / Ratio Sick Days Last Year
Pearson’s correlation
SELECTING THE APPROPRIATE SIGNIFICANCE TEST 9 Multiple Independent Variables 9Nominal Scale Data – ANOVA Factorial Design 9Ordinal Scale Data – no appropriate test is available 9Interval or Ratio Scale Data – Multiple Regression
