# Independent-Samples t Test with SPSS

## IAbstract

The number of hours worked by male and female respondents does exhibit apparent differences. The study then performed independent-samples t-test to determine if the apparent differences are statistically significant. Evidently, independent samples t-test indicate that the mean number of hours worked by male respondents is statistically significantly higher (32.61± 24.113) than the mean number of hours worked by male respondents (21.90±21.891), t(1488) = 8.988, p = 0.000.

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### Statistical Assumptions

1. The dependent variable, which is the number of hours worked, should exist as a continuous variable (Macdonald, 2015).
2. The independent variable, which is the gender, should comprise two categories, namely male and female (­Green & Salkind, 2014).
3. The observations made in each category should be independent to prevent researcher’s bias.
4. The dependent variable should not have significant outliers that magnify the variation in data points (Field, 2013).
5. The dependent variable should follow the normal distribution.
6. Variance should be homogenous for data to provide robust interpretation (Goodwin, 2010).

### Variables

• The dependent variable is the number of hours worked in the past week.
• The independent variable is the gender of respondents.

### Hypotheses

• H0: There is no statistically significant difference in the mean number of hours worked in the past week by male and female respondents.
• H1: There is statistically significant difference in the mean number of hours worked in the past week by male and female respondents.

### P-Value and Confidence Interval

The p-value for the independent-samples t-test under the assumption of equal variances is 0.000. At 95% confidence interval, 13.050 is the upper limit and 8.374 is the lower limit. The confidence interval implies that the difference between means falls between 13.050 and 8.374 at the probability of 0.95. Essentially, the confidence interval of the difference between means in independent-samples t-test shows the probable difference of the means at a given significance level (Hatcher, 2013).

### Hypothesis Testing

The p-value is a significant value that determines whether to reject or retain the null hypothesis. According to Wilcox (2012), the p-value is greater than the significant level fails to reject the null hypothesis while p-value that is less than significant level rejects the null hypothesis. In this case, since p-value (p = 0.000) is less than 0.05, it rejects the null hypothesis, which states that there is no statistically significant difference in the mean number of hours worked in the past week by male and female respondents. Hence, the hypothesis testing holds that there is statistically significant difference in the mean number of hours worked in the past week by male and female respondents.

### Report of the Results

The descriptive statistics shown in Table 1 indicates that there is an apparent difference in the mean number of hours worked in the past week by male and female respondents. Descriptive statistics summarize data and highlight pattern and trends, which are central to making inferences (Hill & Lewicki, 2007; Weinberg & Abramowitz, 2008). Apparently, the mean number of hours worked by male respondents (M = 32.61, SD = 24.113) than the mean number of hours worked by female respondents (M = 21.90, SD = 21.891). In this view, hypothesis testing using independent-samples t-test was used to establish if the apparent difference is statistically significant.

The independent-samples t-test shows that there is statistically significant difference in the mean number of hours worked in the past week by male and female respondents. Frankfort-­Nachmias and Nachmias (2008) state that independent-samples t-test relates two means and establish if their difference is statistically significant. Fundamentally, the findings indicate that the mean number of hours worked by male respondents is statistically significantly higher (32.61± 24.113) than the mean number of hours worked by male respondents (21.90±21.891), t(1488) = 8.988, p = 0.000. Therefore, the findings indicate that the difference between the mean number of hours worked in the past week by male and female respondents is statistically significant.

## References

Field, A. (2013). Discovering statistics using IBM SPSS statistics. London: SAGE Publication.

Frankfort-­Nachmias, C., & Nachmias, D. (2008). Research methods in the social sciences (7th ed.). New York: Worth.

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­Green, S. B., & Salkind, N. J. (2014). Using SPSS for Windows and Macintosh: Analyzing and understanding data (7th ed.). Upper Saddle River, NJ: Pearson.

Goodwin, C. J. (2010). Research in psychology: Methods and design. Hoboken: John Wiley.

Hatcher, L. (2013). Step-by-step basic statistics using SAS: Student guide. Cary: SAS Institute.

Hill, T., & Lewicki, P. (2007). Statistics: Methods and applications. Tulsa: StatSoft.

Macdonald, S. (2015). Essentials of Statistics with SPSS. Raleigh: Lulu Publisher.

Weinberg, S. L., & Abramowitz, S. K. (2008). Statistics using SPSS: An integrative approach. Cambridge: Cambridge University Press.

Wilcox, R. (2012). Introduction to robust estimation and hypothesis testing. London: Academic.

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## Appendices

Table 1 below shows descriptive statistics of the number of hours worked in the past week by male and female respondents.

Table 1

 Group Statistics RESPONDENTS SEX N Mean Std. Deviation Std. Error Mean NUMBER OF HOURS WORKED LAST WEEK MALE 701 32.61 24.113 .911 FEMALE 789 21.90 21.891 .779

The following table (Table 2) indicates the results of independent-samples t-test.

Table 2

 Independent Samples Test NUMBER OF HOURS WORKED LAST WEEK Equal variances assumed Equal variances not assumed Levene’s Test for Equality of Variances F 1.175 Sig. .279 t-test for Equality of Means t 8.988 8.937 df 1488 1422.796 Sig. (2-tailed) .000 .000 Mean Difference 10.712 10.712 Std. Error Difference 1.192 1.199 95% Confidence Interval of the Difference Lower 8.374 8.361 Upper 13.050 13.064

## Syntax

Table 3 below shows the syntax that the SPSS used in generating results of independent-samples t-test.

Table 3

 Notes Output Created 23-JAN-2016 22:18:09 Comments Input Data C:Documents and SettingsDesktopgss04student_corrrected 30FINAL.sav Active Dataset DataSet1 Filter Weight Split File N of Rows in Working Data File 1500 Missing Value Handling Definition of Missing User defined missing values are treated as missing. Cases Used Statistics for each analysis are based on the cases with no missing or out-of-range data for any variable in the analysis. Syntax T-TEST GROUPS=SEX(1 2) /MISSING=ANALYSIS /VARIABLES=HRS1 /CRITERIA=CI(.95). Resources Processor Time 00:00:00.00 Elapsed Time 00:00:00.02

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