QUANTITATIVE TECHNIQUES

T-TEST Statistics

The t test is used to compare to groups to answer the differential research questions. Its values determines the difference by comparing means

Hypothesis for T-testHO: there is no DifferenceH1: There is difference

Types of T-testThere are three types of T-test

One sample t-test Independent sample t-test Paired sample t-test

T-TEST Statistics

One sample t-test

One sample t-test is used to determine if there is difference between population mean (Test value) and the sample mean (X)

Assumptions and conditions of 1 sample t-test The dependent variable should be normally distributed

within the population The data are independent.(scores of one participant are not

depend on scores of the other :participant are independent of one another )

Example: is the mean SAT-Math score in the modified HSB data set significantly different from the presumed population mean of 500?

T-TEST Statistics

One-Sample Statistics

N Mean Std. Deviation Std. Error Meanscholastic aptitude test - math 75 490.53 94.553 10.918

One-Sample Test

Test Value = 500

t DfSig. (2-tailed)

Mean Difference

95% Confidence Interval of the Difference

Lower Upperscholastic aptitude test - math -.867 74 .389 -9.467 -31.22 12.29

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Interpretation:

To investigate the difference between population and the sample, one-sample t-test is conducted. The One-Sample Statistics table provides basic descriptive statistics for the variable under consideration. The Mean AT-Math for the students in the sample will be compared to the hypothesize population mean, displayed as the Test Value in the One-Sample Test table. On the bottom line of this table are the t value, df, and the two-tailed sig. (p) value, which are circled. Note that p=.389 so we can say that the sample mean (490.53) is not significantly different from the population mean of 500. The table also provides the difference (-9.47) between the sample and population mean and the 95% Confidence Interval. The difference between the sample and the population mean is likely to be between +12.29 and -31.22 points. Notice that this range includes the value of zero, so it is possible that there is no difference. Thus, the difference is not statistically significant.

T-TEST Statistics

Independent sample t-testIndependent sample T-test is used to compare two independent groups (Male and Female)with respect to there effect on same dependent variable.

Assumptions and conditions of Independent T-testVariance of the dependent variable for two categories of the

independent variable should be equal to each other Dependent variable should be scale Data on dependent variable should be independent.

Example: Do male and female students differ significantly in regard to their average math achievement scores

T-TEST Statistics

The first table, Group Statistics, shows descriptive statistics for the two groups (males and females) separately. Note that the means within each of the three pairs look somewhat different. This might be due to chance, so we will check the t test in the next table.The second table, Independent Sample Test, provides two statistical tests. The left two columns of numbers are the Levene’s test for the assumption that the variances of the two groups are equal. This is not the t test; it only assesses an assumption! If this F test is not significant (as in the case of math achievement and grades in high school), the assumption is not violated, and one uses the Equal variances assumed line for the t test and related statistics. However, if Levene’s F is statistically significant (Sig. <.05), as is true for visualization, then variances are significantly different and the assumption of equal variances is violated. In that case, the Equal variances not assumed line used; and SSPS adjusts t, df, and Sig. The appropriate lines are circled.

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Thus, for visualization, the appropriate t=2.39, degree of freedom (df) = 57.15, p=.020. This t is statistically significant so, based on examining the means, we can say that boys have higher visualization scores than girls. We used visualization to provide an example where the assumption of equal variances was violated (Levene’s test was significant). Note that for grades in high school, the t is not statistically significant (p=.369) so we conclude that there is no evidence of a systematic difference between boys and girls on grades. On the other hand, math achievement is statistically significant because p<.05; males have higher means. The 95% Confidence Interval of the Difference is shown in the two right-hand column of the output. The confidence interval tells us if we repeated the study 100 times, 95 of the times the true (population) difference would fall within the confidence interval, which for math achievement is between 1.05 points and 6.97 points. Note that if the Upper and Lower bounds have the same sign (either + and + or – and -), we know that the difference is statistically significant because this means that the null finding of zero difference lies outside of the confident interval. On the other hand, if zero lies between the upper or lower limits, there could be no difference, as is the case of grades in h.s. The lower limit of the confidence interval on math achievement tells us that the difference between males and females could be as small as 1.05 points out 25, which are the maximum possible scores. Effects size measures for t tests are not provided in the printout but can be estimated relatively easily. For math achievement, the difference between the means (4.01) would be divided by about 6.4, an estimate of the pooled (weighted average) standard deviation. Thus, d would be approximately .60, which is, according to Cohen (1988), a medium to large sized “effect.” Because you need means and standard deviations to compute the effect size, you should include a table with means and standard deviations in your results section for a full interpretation of t tests.

T-TEST Statistics

Paired sample t-testPaired sample T-test is used to compare two paired groups (e.g. Mothers and fathers) with respect to there effect on same dependent variable.

Assumptions and conditions of Paired sample T-testThe independent variable is dichotomous and its levels (or

groups) are paired, or matched, in some way (husband-wife, pre-post etc)

The dependent variable is normally distributed in the two conditions

Example: Do students’ fathers or mothers have more education?

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Paired Samples Statistics

Mean N Std. Deviation Std. Error Mean

Pair 1 father's education4.73 73 2.830 .331

mother's education4.14 73 2.263 .265

Paired Samples Correlations

N Correlation Sig.

Pair 1 father's education & mother's education73 .681 .000

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The first table shows the descriptive statistics used to compare mother’s and father’s education levels. The second table Paired Samples Correlations, provides correlations between the two paired scores. The correlation (r=.68) between mother’s and father’s education indicates that highly educate men tend to marry highly educated women and vice versa. It doesn’t tell you whether men or women have more education. That is what t in the third table tells you.The last table shows the Paired Samples t Test. The Sig. for the comparison of the average education level of the students’ mothers and fathers was p=.019. Thus, the difference in educational level is statistically significant, and we can tell from the means in the first table that fathers have more education; however, the effect size is small (d=.28), which is computed by dividing the mean of the paired differences (.59) by the standard deviation (2.1) of the paired differences. Also, we can tell from the confidence interval that the difference in the means could be as small as .10 of a point or as large as 1.08 points on the 2 to 10 scale.

Thank you!