Several newq-supercongruences are obtained using transformation formulas for basic hypergeometric series, together with various techniques such as suitably combining terms, and creative microscoping, a method recently developed by the first author in collaboration with Zudilin. More concretely, the results in this paper includeq-analogues of supercongruences (referring top-adic identities remaining valid for some higher power ofp) established by Long, by Long and Ramakrishna, and several otherq-supercongruences. The six basic hypergeometric transformation formulas which are made use of are Watson’s transformation, a quadratic transformation of Rahman, a cubic transformation of Gasper and Rahman, a quartic transformation of Gasper and Rahman, a double series transformation of Ismail, Rahman and Suslov, and a new transformation formula for a nonterminating very-well-poised $${}_{12}\phi _{11}$$12ϕ11 series. Also, the nonterminatingq-Dixon summation formula is used. A special case of the new $${}_{12}\phi _{11}$$12ϕ11 transformation formula is further utilized to obtain a generalization of Rogers’ linearization formula for the continuousq-ultraspherical polynomials.

We give q-analogues of the following two Ramanujan-type formulas for $1/\pi$: $\sum _{k=0}^{\mathrm{\infty }}(6k+1)\frac{(\frac{1}{2}{)}_k^3}{k{!}^3{4}^k}=\frac{4}{\pi }\mathrm{and}\sum _{k=0}^{\mathrm{\infty }}(-1{)}^k(6k+1)\frac{(\frac{1}{2}{)}_k^3}{k{!}^3{8}^k}=\frac{2\sqrt{2}}{\pi }.$ Our proof is based on two q-WZ pairs found by the first author in his earlier work.

We prove some congruences on sums involving fourth powers of central q-binomial coefficients. As a conclusion, we confirm the following supercongruence observed by Long [Pacific J. Math. 249 (2011), 405–418]: $$\sum\limits_{k = 0}^{((p^r-1)/(2))} {\displaystyle{{4k + 1} \over {{256}^k}}} \left( \matrix{2k \cr k} \right)^4\equiv p^r\quad \left( {\bmod p^{r + 3}} \right),$$ where p⩾5 is a prime and r is a positive integer. Our method is similar to but a little different from the WZ method used by Zudilin to prove Ramanujan-type supercongruences.