A statistical test with SPSS steps paired sample t test.pptx

statistical presentation, the test used for research data analysis

1. Paired sample t test By Mrs. Aneeqa Waheed

2. Paired Samples  t  test The Paired Samples  t  Test compares two means that are from the same individual, object, or related units. The two means can represent things like: A measurement taken at two different times (e.g., pre-test and post-test with an intervention administered between the two time points) A measurement taken under two different conditions (e.g., completing a test under a "control" condition and an "experimental" condition) Measurements taken from two halves or sides of a subject or experimental unit (e.g., measuring hearing loss in a subject's left and right ears).

3. Purpose The purpose of the test is to determine whether there is statistical evidence that the mean difference between paired observations on a particular outcome is significantly different from zero. The Paired Samples  t  Test is a parametric test.

4. This test is also known as: Dependent  t  Test Paired  t  Test Repeated Measures  t  Test The variable used in this test is known as: Dependent variable, or test variable (continuous), measured at two different times or for two related conditions or units

5. Uses of paired sample t test The Paired Samples  t  Test is commonly used to test the following: Statistical difference between two time points Statistical difference between two conditions Statistical difference between two measurements Statistical difference between a matched pair

6. Note:  The Paired Samples  t  Test can only compare the means for two (and only two) related (paired) units on a continuous outcome that is normally distributed. The Paired Samples  t  Test is not appropriate for analyses involving the following: 1) unpaired data; 2) comparisons between more than two units/groups; 3) a continuous outcome that is not normally distributed; and 4) an ordinal/ranked outcome. To compare unpaired means between two groups on a continuous outcome that is normally distributed, choose the Independent Samples  t  Test. To compare unpaired means between more than two groups on a continuous outcome that is normally distributed, choose ANOVA. To compare paired means for continuous data that are not normally distributed, choose the nonparametric Wilcoxon Signed-Ranks Test. To compare paired means for ranked data, choose the nonparametric Wilcoxon Signed-Ranks Test.

7. Data Requirements /Assumptions Your data must meet the following requirements: Dependent variable that is continuous (i.e., interval or ratio level) Note:  The paired measurements must be recorded in two separate variables. Related samples/groups (i.e., dependent observations) The subjects in each sample, or group, are the same. This means that the subjects in the first group are also in the second group. Random sample of data from the population Normal distribution (approximately) of the difference between the paired values No outliers in the difference between the two related groups Note:  When testing assumptions related to normality and outliers, you must use a variable that represents the difference between the paired values - not the original variables themselves. Note:  When one or more of the assumptions for the Paired Samples  t  Test are not met, you may want to run the nonparametric Wilcoxon Signed-Ranks Test instead.

8. Hypotheses The hypotheses can be expressed in two different ways that express the same idea and are mathematically equivalent: H : µ 1  = µ 2  ("the paired population means are equal") H 1 : µ 1  ≠ µ 2  ("the paired population means are not equal")

9. Data

10. How to check assumption of normal distribution and outliers for paired sample t test To check this assumption, firstly compute difference between pre score and post score. Procedure Go to transform Compute variable Give name of target variable as “difference” Click type and label, give label name as “ difference”, continue Under numeric expression, move first variable and then add sign of subtract ‘-’ move 2 nd variable Click ok In data view new variable is added with name “difference” Make decimals to zero in variable view

11. Procedure of checking normal distribution and outliers for paired sample t test Go to analyze Descriptive statistics Explore Move difference variable to dependent variable Click statistics, check outliers, continue Click on plots, uncheck stem and leaf, check histogram, check normality plots with tests, continue Click ok

12. Interpretation of output of normality In order for your data to be approximately normally distributed, the value of skewness should be between -1.00 to +1.00 and the value of kurtosis should be between -2.00 to +2.00 As a general rule of thumb: If  skewness  is less than -1 or greater than 1, the distribution is highly  skewed . If  skewness  is between -1 and -0.5 or between 0.5 and 1, the distribution is moderately  skewed . If  skewness  is between -0.5 and 0.5, the distribution is approximately symmetric. Another method is, see the skewness and divide the value of statistic by standard error. You will get z value. This value should be between -1.96 - +1.96 Another method is to see Shapiro- wilk test. In order for our data to be normal, The sig. value/p value in Shapiro wilk test should be greater than .05. the value less than .05 means that the distribution of our variable is significantly different from normal distribution. Another approach is to look for histogram… it should be shown as bell shaped curve.. it should not be positively or negatively skewed. Another approach is to see normal Q-Q plot also known as quantile quantile plot.. all the points should follow the line. If  the data is  normally  distributed, the points in the  QQ - normal plot  lie on a straight diagonal line. You can add this line to you  QQ plot  with the command qqline (x) , where x is the vector of values. The deviations from the straight line are minimal. This indicates  normal  distribution.

13. Interpretation of outliers An  outlier  is an observation that lies an abnormal distance from other values in a random sample from a population.  In Output window: Go to Boxplot > Look at circles and *. These are potential outliers. If there's none, then there's no potential outliers in your dataset. If there are circles or *, then there are potential outliers in your dataset. 

14. Procedure of Paired sample t test Go to Analyze Compare means Click on Paired sample t test Move 1st variable in variable 1 of pair 1 Move 2 nd variable in variable 2 of pair 1 Click ok

15. Effect size calculator

16. According to Cohen (1988) 0.1 small 0.3 medium 0.6 large Criteria of effect size

17. Table and interpretation according to APA 7