Inferential Statistics.pptx
- 2. Definitions • Inferential statistics permits generalization from samples to populations. • Sampling error is main problems that faces the challenge of generalizing from samples to populations. Sampling error involves the role of chance in deciding on the findings or results. • Inferential statistics deals with the sampling error. They are used to estimate the role of chance in the findings, such as differences between groups, relation between two groups and deciding whether the difference or the relationship is a significant finding or a result of chance only. • The other way to check that chance had nothing to do with the findings is to repeat the study several times, which can become awkward, time-consuming and impractical.
- 3. Definition • Population or universe : the entire group of items under examination (everyone in your statistics class, all students at JU, all teachers in Jiren High School ( JHS) etc.). • Sample : a group taken from the population (a sample of 10 students in your statistics class, 1000 randomly selected students at JU, 5 female teachers selected by purposive sampling at JHS). • Parameter: an objective measure that describes some characteristic of the population (average score on the attitude of students towards PE in JU , average age of students at JU, average endurance score of of female students at JU) • Statistic : an objective measure that describes some characteristic of the sample (average PE attitude score of 350 randomly selected students, average age of 1000 randomly selected students from JU, average income of 5 female teachers selected by purposive sampling at JHS). • Statistical inference : the process of using data obtained from a sample to make estimate and test hypotheses about the characteristics of a population
- 4. Purpose of Inferential statistics • Although there are various uses of statistical techniques, some very common situations psychological research are: 1. Infer (or estimate) parameters, such as the mean and the variance, of the populations based on their samples. 2. Compare the inferred parameters of the populations: are they significantly different
- 5. The concept and procedures of hypothesis testing •Hypothesis testing involves making inferences about the nature of a population on the basis of observations of a sample drawn from a population • The logic of hypothesis testing follows the chain of reasoning in inferential statics as shown below .
- 6. Cont’d • Chain of reasoning in HT
- 7. Cont’d • The process of HT involves determining the difference between the hypothesized value of the population (parameter) and the value of the sample selected from the population (statistic ) . • If the difference b/n the parameter and the statistic is very large we reject the hypothesis or we retain the hypothesis if the difference b/n the parameter and the statistic very small. • In other words HT involves determining the magnitude of the difference b/n the observed value of the statistic ( for example mean) and the hypothesized value of the parameter ( for example µ ) .
- 8. • Cont’d Population value ( parameter ) Magnitude of the difference b/n the observed statistic and the hypothesized parameter? Small difference Large difference Don’t Reject p >.05 Reject p<.05
- 9. TYPE OF TEST • One sample t test • Independent sample t or z test • ANOVA • Linear and Multiple Regression analysis • Non parametric statistics
- 10. One sample t or z test • One sample t test helps us to conduct hypothesis test whether a sample mean is significantly differ from a known population mean. • T test : is used to test hypothesis about known population mean (µ) when the value of σ is unknown. Z = (Mean-µ)/σmean , where σmean = S2/√n
- 11. Example • The endurance score of a general population (µ) of football players as measured by a Coopper test is normally distributed with a mean 3000 meter. The researcher suspects that the endurance level of football players in country x is less than the general population. The researcher administered a Coopper test for 45 participants. The data are indicated as follows. • 3000,2000,2500,3000,3500,2000,1500,4000,3000,3500, 3000,2000,3000,4500,2000,1000,2500,2800,2000,3000, 3200,3000,2800,4000,3000,1500,2000,2400,2000,3000, 4000,2000,2500,3000,3000,3100,3200,3000,3200,2500, 4000,3200,1500,2000,3200
- 12. Question • Test the hypothesis that the observed mean is significantly less than from the hypothesized value. • Ho: µ= 3000 • H1: µ < 3000
- 13. Cont’d One-Sample Statistics N Mean Std. Deviation Std. Error Mean copte 45 2757.78 761.425 113.507
- 14. Cont’d One-Sample Test Test Value = 3000 t df Sig. (2- tailed) Mean Difference 95% Confidence Interval of the Difference Lower Upper copte -2.134 44 .038 -242.222 -470.98 -13.46
- 15. Conclusion • Reject Ho as p<.05
- 16. Reporting the results • The mean score the endurance level of football players in country x was found to be 2757.78 with a standard deviation of 761.425 as indicated in table ….below. The one sample t test indicates that the the endurance level of football players in country x was significantly less than the endurance score of a general population of football players as measured by a Copper test , t(44)= -2.134, p<.05.
- 17. Cont’d One-Sample Statistics N Mean Std. Deviation Std. Error Mean copte 45 2757.78 761.425 113.507
- 18. SPSS • Data entry 1. Enter all the scores from the sample in one column of the data editor, var0001 Data analysis 1. Click analyse, select compare means, and click on one sample t test 2. Highlight the column label for the set of scores (var0001) in the left box and click the arrow to move it into the test variable box 3. In the Test value at the bottom of one sample t Test window , enter the hypothesized value for the population mean from the null hypothesis. 4. Click OK
- 19. SPSS output • The program will produce a table of one sample statistics showing the number of scores , the sample mean and the standard deviation , the estimated standard error and the mean. • A second table produce the results of One Sample Test, including the value of t, the degree of freedom , the level of significance (the p-value or alpha level for the test ) and the size of the mean difference b/n the sample mean , the hypothesized population mean and the confidence interval.
- 20. Activity • The mean attitude score towards PE for the general population of students in JHS is normally distributed with a mean of 3.5. The researcher believes that the mean attitude score towards PE for students who actively participate in PE class is grater than the mean attitude score of the general population of students. The researcher selects 30 students and administered an attitude scale. The data are indicated as follow. Note: the higher the score the higher the attitude
- 21. Cont’d • 3,3,4,2,3,4,5,2,4,4,4,2,1,3,4,5,5,2,4,2,5,4,4,5,4, 2,1,1,2,3,4,5,4,3,4 Question • Test the hypothesis that the observed mean is significantly different from the hypothesized value.
- 22. Independent sample t test • The independent sample t test helps us to check whether two groups of means differ significantly. • t= (Mean1-Mean2 )/ Smean1-Smean2 , • where Smean1 and Smean2 is the estimated standard error for the two means.
- 23. Activity 1. A researcher wants to determine whether players perform better a football skill with lecture methods or with both lecture and demonstration. Ten players are randomly assigned to two experimental condition; their scores on skill performance are given below. ____________________________________________________________________ Lecture Lecture +Demonstration Lecture Lecture + Demonestration (Group 1) (Group 2) (Group 1) (Group 2) ___________________________________________________________________ 8 4 9 6 10 8 10 15 7 7 11 11 12 10 6 9 6 12 13 8 ____________________________________________________________________
- 24. Question • Test whether the two means are statistically significantly different • Ho: µlecture =: µlecture+ demon • H1: µlecture ≠ : µlecture+ demon
- 25. Cont’d Group Statistics VAR0 0002 N Mean Std. Deviatio n Std. Error Mean skillper 1 10 9.2000 2.44040 .77172 2 10 9.0000 3.16228 1.00000
- 26. Cont’d Independent Samples Test Levene's Test for Equality of Variances t-test for Equality of Means F Sig. t df Sig. (2- tailed) Mean Difference Std. Error Difference 95% Confidence Interval of the Difference Lower Upper skillper Equal variances assumed .313 .583 .158 18 .876 .20000 1.26315 -2.45379 2.85379 Equal variances not assumed .158 16.913 .876 .20000 1.26315 -2.46606 2.86606
- 27. Conclusion • Fail to reject Ho as p>.05
- 28. Reporting the result • As indicated in the table ……., the groups that has been taught with lecture methods perform better (M=9.2 , S=2.44) than the group that has been taught with lecture and demonstration (M= 9.0, S=3.16). This differences was not statistically significant, t(18)=.158, P>.05.
- 29. SPSS • Data entry 1. The scores are entered in what is called stacked format , which means that all the scores from both samples/groups are entered in one column of the data editor (var00001). Enter the scores for the sample/group 2 directly beneath the scores from sample/group 1 with no gaps. 2. Values are then entered into a second column (var00002) to identify the sample or treatment condition corresponding to each of the scores. For example enter a 1 beside each score from sample/group 1 and enter a 2 besides each score from sample/group 2.
- 30. Data Analysis 1. Click analyze, select compare means, and click in independent sample t test. 2. Highlight the column label for the set of scores (var00001) in the left box and click the arrow to move it into the test variables box 3. Highlight the column label for the set of scores (var00002) in the left box and click the arrow to move it into the group variable box 4. Click on define groups 5. Assuming that you used the numbers 1 and 2 to identify the two set of scores , enter the values 1 and 2 into appropriate group box. 6. Click continue 7. Click OK
- 31. SPSS output • SPSS produce summery table showing the number of scores , the mean , the standard deviation , and the standard error of the two samples. • T values , degrees of freedom , p, size of the mean difference and CI are displayed on the second table
- 32. Activity • A researcher wants to conduct study entitled “Sex difference as a function of Anxiety before a major competition” • Anxiety scores (Y) Sex (X ; Male coded 1, Femle code 0) • 15.00 male • 25.00 male • 12.00 male • 20.00 male • 20.00 female • 16.00 female • 18.00 female • 22.00 female • 20.00 female • 12.00 female
- 33. Question • Test whether the two means are statistically significantly different