10 统计概念.pdf
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1、?10.Statistical Concepts?2000?71By J.Dusek Statistical Concepts Throughout the text reference is made to experiments of the sorts described in the previous section.All observations,whether made in the laboratory or in a naturalistic setting,must be organized,categorized,and summarized before any mea
2、ning can be attributed to them.This process of data compression produces numerical measures:for example,scores on a performance measure or a listing of heights and weights for the sample studied.These numerical measures describe the data collected;therefore they belong in the realm of descriptive st
3、atistics.Testing of hypotheses is done through the use of inferential statistics.In this section we shall discuss some concepts related to both descriptive and inferential statistics.Descriptive Statistics Descriptive statistics techniques are used to summarize the data that are collected in an expe
4、riment and to communicate the findings of the experiment to the scientific community.A listing of various techniques employed in both descriptive statistics and inferential statistics is given in Table A-2.Since many of these terms are probably familiar to you,we shall review them only briefly in or
5、der to refresh your memory.?10.Statistical Concepts?2000?72TABLE A-2 Statistical Concepts Descriptive Statistics summarize and describe data.Measures of central tendency:mean-average of the scores median-the middle score(50%of the scores are higher and 50%are lower)mode-the most frequently occurring
6、 score Measures of variability:range-the difference between the lowest and the highest score standard deviation-square root of the variance variance-the sum of the squared deviations of the scores from the mean divided by the number of scores Measures of association:correlation coefficient-a measure
7、 of association between two variables a factor-a cluster of test scores or items that are highly related to each other and not related to scores or items in other factors Inferential Statistics are used to test hypotheses.Random sample:a sample drawn from a population in such a way that every member
8、 of the population has an equal chance of being picked Experimental group:the subjects receiving the experimental treatment?10.Statistical Concepts?2000?73Control group:the subjects receiving no experimental treatment Significance level:the probability that differences between the experimental and c
9、ontrol groups at the end of the experiment are due to chance t-test:technique used to assess differences between experimental and control groups in a two-group experiment F-test:technique used to assess differences when more than two groups are tested or more than one variable is manipulated Indepen
10、dent variable(s):the variable(s)manipulated in the experiment Dependent variable(s):the variable(s)measured in the experiment Measures of Central Tendency.One way to summarize data is through various measures of central tendency,each of which reflects to some degree the typical score.There are sever
11、al such measures,including the mean,the median,and the mode.The mean is commonly employed to communicate differences between groups of subjects who vary according to age,sex,or experimental treatment.However,the mean may also be employed in a naturalistic experiment.Hence,by looking at the mean one
12、is able to speak of scores increasing or decreasing as a function of age level,sex,or some other variable of interest.The median and the mode are less frequently employed.The median,which is used for dividing a distribution of scores into two equal groups?10.Statistical Concepts?2000?74of scores,is
13、most frequently used to separate subjects into two groups for experimental purposes.For example,in a number of experiments children and adolescents have been divided into low-anxious and high-anxious groups by taking a median split on anxiety level(for example,Dusek&Hill,1970).The investigators cond
14、ucting these experiments wish to find out if the problem-solving strategies of low-and high-anxious subjects differ,and if these differences exist at various age levels.The mode is used primarily to describe a distribution of scores in order to highlight scores that are obtained relatively frequentl
15、y.Measures of Variability.Just as there are measures of central tendencies,or similarities,in the scores obtained in an experiment,so too are there measures of variability.One measure of variability is simply the range of the scores,the highest to the lowest score.Obviously,this statistic provides s
16、ome information about the scores but it doesnt tell us very much.In order to describe more completely the nature of the distribution of scores,psychologists use two measures:the standard deviation and the variance,the latter being the square of the former.The standard deviation and the variance are
17、direct measures of the variability of all the scores within the distribution from the mean score.The smaller the standard deviation or variance,the more compact(closer to the mean)the distribution of scores,and the larger the standard deviation or variance,?10.Statistical Concepts?2000?75the more di
18、sparate the scores.In a bell-shaped distribution,68 percent of the scores fall within plus or minus one standard deviation from the mean.For example,IQ tests are designed to have a mean score of 100,and a standard deviation of either 15 or 16.By knowing this information we know that a score of 116 i
19、s one standard deviation above,and a score of 84 one standard deviation below,the mean IQ.By knowing the mean of the distribution and the standard deviation of the scores,then,we are able to discern the relative position of any given score within the distribution.The final descriptive statistic we s
20、hall discuss is the correlation coefficient,denoted by r,which is a measure of the relationship between two scores derived from each subject.For example,we might wish to know the relationship between intelligence and school performance.In order to calculate this relationship we would need to have an
21、 IQ score on each subject as well as some measure of school performance.The correlation coefficient,then,allows us to determine how closely the two sets of scores,the IQ score and the school performance measure,are related.The correlation coefficient may take on any value from?1 to+1.The larger the
22、absolute value of the number,that is,the number irrespective of the sign attached to it,the stronger the relationship.The smaller the absolute value of the number,the weaker the relationship.A correlation of 0 demonstrates that there is no relationship between the two?10.Statistical Concepts?2000?76
23、sets of scores.A correlation of+1 indicates that there is a perfect positive relationship between the scores.In our example of IQ scores,this means that the highest score on IQ is matched with the highest score on the school measure,and the lowest score on IQ is matched with the lowest score on the
24、school measure,with all the intermediate scores falling in a perfect rank ordering.A correlation of 1 indicates that the highest IQ score goes with the lowest school performance score and the lowest IQ score with the highest school performance score,with all of the other intervening scores having th
25、e same perfect inverse relationship.In psychology,it is extremely rare to find correlations that are+l.0 or?1.0.We are much more used to dealing with correlations on the order of.5 or.6.These correlations indicate that there is some degree of relationship between the two scores but also that the two
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